brain.js

var fs = require("fs");
var brain = require("brain.js");

var net = new brain.NeuralNetwork({
	hiddenLayers: [27],
	learningRate: 1
});
var data = [
{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, 0, -1, 0, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, 1, -1, 0, 0, 0, 0], output: [1, 1, 0, 1, 0, 0.5, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 1, 0.5, 0.5, 0] },
{ input: [0, 0, 1, 1, -1, 1, 0, 0, -1], output: [0, 0.5, 1, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 0, 1, 1], output: [0.5, 1, 0.5, 0, 0, 0.5, 0, 1, 1] },
{ input: [0, 1, 1, -1, -1, 0, -1, 1, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 1], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 1] },
{ input: [1, 0, -1, -1, -1, 1, 0, 1, 1], output: [1, 0.5, 0, 0, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0, 1] },
{ input: [1, 0, 1, 0, -1, -1, 1, -1, 1], output: [1, 0, 1, 0.5, 0, 0, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 1, 0, 1, 0.5, 0, 1] },
{ input: [0, 1, -1, 1, -1, 1, 0, -1, 1], output: [0.5, 1, 0, 1, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, -1, 0, 1, -1, 1, 0, 1, 0], output: [0, 0, 0.5, 1, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, -1, 1, 0, 1, 1], output: [0, 0, 0, 1, 0, 1, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 0, 0, 0], output: [0, 1, 1, 1, 0, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 1, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 0, 1, -1], output: [0.5, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0] },
{ input: [0, -1, 0, 1, 1, 0, 0, 1, -1], output: [0.5, 0, 0.5, 1, 1, 0, 0.5, 1, 0] },
{ input: [0, -1, 0, 1, 1, -1, 1, 1, -1], output: [0.5, 0, 0, 1, 1, 0, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 1, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, 1, 0, 0, 1, 0], output: [0, 0, 0, 1, 1, 0.5, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 0], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 0, 0, 1, 0, 1, 0], output: [0, 1, 0, 0.5, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 0, -1, 1, 1, 1, 0], output: [0, 1, 0, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, -1, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 0.5, 1, 0.5, 1, 0.5, 0] },
{ input: [0, 0, -1, 1, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 1, 1, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 0, 0, 0, 1, 0, -1, 1, 1], output: [0, 0, 0.5, 0.5, 1, 0.5, 0, 1, 1] },
{ input: [-1, -1, 0, 0, 1, 1, -1, 1, 1], output: [0, 0, 0, 0.5, 1, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, -1, 1, 1, 0, 0, 0], output: [0, 0.5, 1, 0, 1, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, -1, 0, 1, 0, 1], output: [0, 0, 0, 1, 0, 0.5, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, -1, 0, 1, 0, 1], output: [0, 0, 0, 1, 0, 0.5, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 1, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 1, 0.5, 0.5, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 0, 0, 0, -1, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 1, -1, 0, -1, 1, 0], output: [0, 1, 1, 1, 0, 0.5, 0, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 1, 1, -1, 0, 1, -1, 1], output: [0, 0, 1, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 0, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 0.5, 1] },
{ input: [-1, 1, 0, 0, -1, 1, -1, 0, 1], output: [0, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 1, 1, -1, 0, 0, -1], output: [0.5, 1, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 0, 0, 1, 0, 1, 1, -1], output: [0, 0.5, 0, 0.5, 1, 0.5, 1, 1, 0] },
{ input: [-1, 0, -1, 0, 1, 1, 1, 1, -1], output: [0, 0, 0, 0.5, 1, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 0, 1], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, 0, 1, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 1, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, -1, 1, 1, 0, 1], output: [0, 0, 0, 1, 0, 1, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [1, 0, -1, 0, -1, 1, 0, -1, 1], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 1, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 1, 0] },
{ input: [0, 1, 1, -1, -1, 0, 1, 1, -1], output: [0, 1, 1, 0, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 1, 0], output: [1, 1, 0, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 1, 0, 0, -1], output: [0.5, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0] },
{ input: [0, 1, 0, -1, 1, 1, 0, 0, -1], output: [0.5, 1, 0.5, 0, 1, 1, 0.5, 0, 0] },
{ input: [0, 1, 1, -1, 1, 1, 0, -1, -1], output: [0.5, 1, 1, 0, 1, 1, 0, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 0, 1, 1, 1, 0], output: [0, 0, 0, 0.5, 0.5, 1, 1, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 1, 0.5, 0.5, 0] },
{ input: [0, 0, 1, 1, -1, 1, 0, 0, -1], output: [0, 0.5, 1, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, 0, -1, 1, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 0, 0, 1], output: [1, 1, 0, 0, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, -1, 1, -1, 1], output: [0.5, 0, 1, 0.5, 0, 0, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 1, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 1, 0.5, 0.5, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 0, 0, 0, -1, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 1, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 0, 1, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, -1, 1, 0], output: [0, 0.5, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, -1, 1, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 0, 1, -1], output: [0.5, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0] },
{ input: [0, -1, 0, 1, 1, 0, 0, 1, -1], output: [0.5, 0, 0.5, 1, 1, 0, 0.5, 1, 0] },
{ input: [1, -1, 0, 1, 1, -1, 0, 1, -1], output: [1, 0, 0, 1, 1, 0, 0.5, 1, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 1, -1, 0, 0], output: [1, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 0, 0, 1, 0, 1, 0], output: [0, 1, 0, 0.5, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 1, 0], output: [0, 1, 0, 1, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 1], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, -1, 1, 0, -1, -1, 1, 0, 1], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 1, -1, 0, -1, 1, 1, 0, 0], output: [0, 1, 0, 0.5, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 1, 0, 0, 0, 0, 1, 1, -1], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, -1, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 0, 0, -1, 1, 1, 1, -1], output: [0, 0.5, 0.5, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 1, 0, 1, -1, 0, -1, 0, 0], output: [1, 1, 0, 1, 0, 0.5, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, -1, -1, 1, 1, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 1, 0, 0.5] },
{ input: [1, 0, -1, -1, -1, 1, 1, -1, 1], output: [1, 0, 0, 0, 0, 1, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 1, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, -1, 1, 1, 1, 0], output: [0, 0.5, 0, 1, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 0, 1, 0, 0, 0, -1], output: [0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0, 0] },
{ input: [0, 1, 1, 0, 1, 0, 0, -1, -1], output: [0.5, 1, 1, 0.5, 1, 0.5, 0, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, -1, 0, 0, 1, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, 1, 0, 0, -1, -1, 0, 0, 1], output: [1, 1, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 1, 0, -1, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, -1, 1, -1, 1], output: [0.5, 0, 1, 0.5, 0, 0, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, -1, -1, 1, 0, 0, 1], output: [1, 0.5, 0, 0, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 1, 1, -1, 0, 1, -1, 1], output: [0, 0, 1, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 1, 1, 0], output: [1, 0, 1, 0, 0, 0, 1, 1, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 1, 0], output: [1, 1, 0, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 0, 1, 0, 0, 0, -1], output: [0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0, 0] },
{ input: [0, 1, 0, 1, 1, 0, 0, -1, -1], output: [0.5, 1, 0.5, 1, 1, 0.5, 0, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 1, 0, 1], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 1], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, -1, 1, 0], output: [0, 0.5, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 0, 1, 0, -1, 0, -1, 1, 1], output: [0, 0.5, 1, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 0], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [0, 0, -1, 1, -1, 1, 0, -1, 1], output: [0.5, 0, 0, 1, 0, 1, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0] },
{ input: [-1, 0, 1, 1, 0, 1, 0, 0, -1], output: [0, 0.5, 1, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 1], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 0, 1], output: [0, 1, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 1, 0, 0, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 1, 0, 1], output: [0.5, 1, 0.5, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 1], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 1, 0.5, 0.5, 0] },
{ input: [0, 0, 1, 1, -1, 1, 0, 0, -1], output: [0, 0.5, 1, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, -1, 1, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 1, 0, 0.5, 0, 0, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 1, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 1, 0] },
{ input: [0, 1, 1, -1, -1, 0, 1, 1, -1], output: [0, 1, 1, 0, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, -1, 1, 1, 1, 0, 0], output: [0, 0.5, 0, 0, 1, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, -1, 1, 1, 1, 1, 0], output: [0, 0, 0, 0, 1, 1, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 1], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 1], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, -1, 1, 0, -1, -1, 0, 1, 1], output: [1, 0, 1, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [0, 1, 0, 0, -1, -1, 1, 0, 1], output: [0.5, 1, 0.5, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 1], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [1, 0, 0, 1, 1, -1, 0, 0, -1], output: [1, 0.5, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 1, 0.5, 0.5, 0] },
{ input: [0, 1, 1, 0, -1, 1, 0, 0, -1], output: [0, 1, 1, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 1, 0], output: [1, 1, 0, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 0, 1], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 0, 0, 1, 0, 1, 1], output: [0, 0.5, 0, 0.5, 0.5, 1, 0, 1, 1] },
{ input: [-1, 0, -1, 0, 1, 1, -1, 1, 1], output: [0, 0, 0, 0.5, 1, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 1], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 1], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 0, 0, 0, 1], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 1], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 1, 0, 0, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 1], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, -1, 1, 0, -1, -1, 1, 0, 1], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, 0, 0, 0, 1], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, -1, 1, 0, -1, -1, 0, 1, 1], output: [1, 0, 1, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 0, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 0, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 1, -1, 0, -1, 1, 1, 0, 0], output: [0, 1, 0, 0.5, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 1, 1, 0], output: [1, 0, 1, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 1, 0, -1, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 1, 0], output: [1, 1, 0, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, -1, -1, 1, 0, 1, 0], output: [1, 0.5, 0, 0, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 1, 1, -1, 0, 0, -1], output: [0.5, 1, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, 0, 0, 0, 0], output: [0, 1, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 1, 0, 0, 0], output: [1, 1, 0, 0, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 0.5, 1, 0.5, 1, 0.5, 0] },
{ input: [0, 0, -1, 1, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 1, 1, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, 0, -1, 1, 1, 1, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [1, 0, -1, 0, -1, 1, 0, -1, 1], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 1, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 0, 1, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 1, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 0, 0, 1, 0, 0, -1, 1, 1], output: [0, 0.5, 0, 1, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 0, -1, 1, 1, 0, -1, 1, 1], output: [0, 0, 0, 1, 1, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 1, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 0, 0, 0], output: [0, 1, 1, 1, 0, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 1], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, -1, -1, -1, 0, 0, 1, 1], output: [1, 1, 0, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, 0, -1, 1, 1, 0, 1], output: [0, 0, 0, 0.5, 0, 1, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, -1, 0, 0, 1], output: [1, 0, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 1, 0, 0, 0, 1, 0], output: [0, 0, 0.5, 1, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, 0, 0, 1, 1, 0], output: [0, 0, 0, 1, 0.5, 0.5, 1, 1, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 0.5, 1, 0.5, 1, 0.5, 0] },
{ input: [0, 1, -1, 0, 1, 0, 1, 0, -1], output: [0.5, 1, 0, 0.5, 1, 0, 1, 0.5, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, -1, 0, 1, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 1, 0, 1, 0, 0.5, 0.5] },
{ input: [1, -1, 0, 1, -1, 1, -1, 0, 1], output: [1, 0, 0, 1, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 0, 0, 1, 1], output: [0, 1, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 0, 1, 0], output: [1, 0, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [0, 1, 0, -1, -1, 1, 0, 1, 0], output: [0, 1, 0.5, 0, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, -1, -1, 1, 0, 1, 1], output: [0, 1, 0.5, 0, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, 0, 1, 0, 0, 0], output: [0, 1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, -1, 0, 1, 0, 0, 0], output: [0, 1, 1, 0, 0.5, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, -1, 0, 1, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 1, 0, 1, 0, 0.5, 0.5] },
{ input: [1, -1, 0, 1, -1, 1, -1, 1, 0], output: [1, 0, 0, 1, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, -1, 1, 1, 0, 0, 0], output: [0, 1, 0.5, 0, 1, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [1, 0, 0, 1, 1, -1, 0, 0, -1], output: [1, 0.5, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 0, 1, 1, 0], output: [0, 0, 0, 0.5, 1, 0.5, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [0, 0, -1, 1, -1, 1, 0, -1, 1], output: [0.5, 0, 0, 1, 0, 1, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 0, -1, 1, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 1, 0, 1, 0, 0.5, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 1, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 0], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 0, 1, 1, 0], output: [0, 0, 0, 0.5, 1, 0.5, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, -1, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 1, 0, 0, -1, 0, 1, 1, -1], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, 0, -1, 0, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, 0, -1, 1, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 1, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, 0, 0, -1, 1, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, -1, 1, -1, 1, 1], output: [0, 1, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 0, 0, 1, 0, 1, 0], output: [0, 1, 0, 0.5, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 1, 0], output: [0, 1, 0, 1, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 0, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 0, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 0, 1, 1, 0], output: [0, 0, 0, 0.5, 1, 0.5, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 1, 0, 0, 0, 1, 0], output: [0, 0, 0.5, 1, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, 1, 0, 0, 1, 0], output: [0, 0, 0, 1, 1, 0.5, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [1, 0, -1, 0, -1, 1, 0, -1, 1], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, -1, 1, 0, 0, 1], output: [0, 0, 0, 1, 0, 1, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 1, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 1, 0.5, 0.5, 0.5, 0, 1, 0.5] },
{ input: [-1, 0, 1, 0, 1, 0, -1, 1, 0], output: [0, 0.5, 1, 0, 1, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 1, 0], output: [1, 1, 0, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 1], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, -1, 1, 1, 0, 0, 1], output: [0, 0.5, 0, 0, 1, 1, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, -1, 1, 1, 1, 0, 1], output: [0, 0, 0, 0, 1, 1, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0, 0.5] },
{ input: [-1, 0, 1, 1, -1, 1, 1, -1, 0], output: [0, 0.5, 1, 1, 0, 1, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0, 1] },
{ input: [1, 0, 0, -1, -1, 1, 1, -1, 1], output: [1, 0, 0.5, 0, 0, 1, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 1, -1], output: [0, 0.5, 1, 0.5, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 0, 0, 1, 0, 1, 0], output: [0, 1, 0, 0.5, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 1, 0], output: [0, 1, 0, 1, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 1, 0.5, 0.5, 0] },
{ input: [0, 0, 1, 0, -1, 1, 0, 1, -1], output: [0, 0.5, 1, 0.5, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 0, 0, 0, 1], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, 0, -1, 0, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, 0, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 1], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 0, -1, 1, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 1, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 1, 1, 0, 0], output: [1, 0, 1, 0, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, 0, 1, 0, 0, 0], output: [0, 1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, -1, 0, 1, 0, 0, 0], output: [0, 1, 1, 0, 0.5, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 0.5, 1, 0.5, 1, 0.5, 0] },
{ input: [0, 1, -1, 0, 1, 0, 1, 0, -1], output: [0.5, 1, 0, 0.5, 1, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 1, 0.5, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 1, -1, 0, 0], output: [1, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 1, 0, 0, 0], output: [1, 1, 0, 0, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 0, 0, 1, 0, 1, 1, -1], output: [0, 0.5, 0, 0.5, 1, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 1, -1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 1, 0, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0, 1] },
{ input: [1, 0, 1, -1, -1, 0, 1, -1, 1], output: [1, 0, 1, 0, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, 0, 0, 0, 0], output: [1, 0, 1, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, 1, -1, 0, 0], output: [1, 0, 1, 1, 0, 1, 0, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 1, 1, -1, 0, 0, -1], output: [0.5, 1, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 0, 1, 0, 0, 0, -1], output: [0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0, 0] },
{ input: [0, 1, 0, 0, 1, 1, 0, -1, -1], output: [0.5, 1, 0.5, 0.5, 1, 1, 0, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, -1, 1, 0], output: [0, 0.5, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 0, 1, 0, -1, 1, -1, 1, 0], output: [0, 0.5, 1, 0.5, 0, 1, 0, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 1], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 0], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 0, 1, -1, 0, 1, 1, -1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, 0, 1, 0, 0, 0], output: [0, 1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, -1, 0, 1, 0, 0, 1], output: [0, 1, 0.5, 0, 0.5, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 1, 0, 0], output: [0, 1, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 0, 1, 0, 0, 0, -1], output: [0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0, 0] },
{ input: [0, 1, 0, 1, 1, 0, 0, -1, -1], output: [0.5, 1, 0.5, 1, 1, 0.5, 0, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 1, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 1, 0, 0, 0], output: [1, 1, 0, 0, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 0, 0, 1], output: [1, 0, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 1, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 0, 0, 0, 1], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 0, 1, 0, 0, 1, 1, -1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [0, 1, 1, 0, -1, -1, 0, 0, 1], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 0, 1], output: [0, 1, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, 0, -1, 1, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 1, 0, -1, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 1, 0, 0, 0, 1, 0], output: [0, 0, 0.5, 1, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, 0, 1, 0, 1, 0], output: [0, 0, 0, 1, 0.5, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 0, 0, 0, 1, 1, 1, -1], output: [0, 0.5, 0.5, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, 0, 1, 0, 0, 0], output: [0, 1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, -1, 0, 1, 0, 0, 1], output: [0, 1, 0.5, 0, 0.5, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 0, 1], output: [0, 1, 0, 1, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, -1, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 0, 0, 0, 1, 1, 1, -1], output: [0, 0.5, 0.5, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 1, -1, -1, 0, 1, 0, 0], output: [0.5, 1, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 0, 1, 0], output: [1, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [0, 1, 0, -1, -1, 1, 0, 1, 0], output: [0, 1, 0.5, 0, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, -1, -1, 1, 0, 1, 1], output: [0, 1, 0.5, 0, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [0, 1, 1, 0, -1, -1, 0, 0, 1], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 0, 1], output: [0, 1, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, 0, 0, 0, 0], output: [0, 1, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, -1, 0, 1, 0], output: [1, 0, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 0, 0, 1], output: [1, 0, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 0, 1], output: [0, 1, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, 0, 0, -1, 1, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 1, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 1, 0, 1] },
{ input: [1, 0, -1, 0, -1, 1, 1, -1, 1], output: [1, 0, 0, 0.5, 0, 1, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 0, 1, 1, 0], output: [0, 0, 0, 0.5, 1, 0.5, 1, 1, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 0, 0, -1, 1, 1, 1, -1], output: [0, 0.5, 0.5, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, -1, 0, 0, 0], output: [1, 0, 1, 1, 0, 0, 0, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, -1, -1, 0, 1], output: [1, 0, 1, 1, 0, 0, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 1, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 1, 1, -1, 0, 0, -1], output: [0.5, 1, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 0, 1, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 0, 0, 0, 1, 0, -1, 1, 1], output: [0, 0, 0.5, 0.5, 1, 0.5, 0, 1, 1] },
{ input: [-1, -1, 0, 1, 1, 0, -1, 1, 1], output: [0, 0, 0, 1, 1, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, -1, 1, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 1, 0, 0.5, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 0, 1], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 0, 0, 1, 0, 0, 1], output: [0, 1, 0, 0.5, 0.5, 1, 0, 0.5, 1] },
{ input: [-1, 1, -1, 0, 0, 1, -1, 1, 1], output: [0, 1, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 0, 0, 1], output: [1, 1, 0, 0, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 1, 0.5, 0.5, 0] },
{ input: [0, -1, 1, 1, -1, 1, 1, 0, -1], output: [0, 0, 1, 1, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 0, 1, 0, 0, 0, -1], output: [0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0, 0] },
{ input: [1, 1, 0, 0, 1, 0, 0, -1, -1], output: [1, 1, 0, 0.5, 1, 0.5, 0.5, 0, 0] },
{ input: [1, 1, -1, 1, 1, 0, 0, -1, -1], output: [1, 1, 0, 1, 1, 0, 0.5, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0] },
{ input: [-1, 1, 1, 0, 0, 1, 0, 0, -1], output: [0, 1, 1, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 1, -1, 0, 0], output: [1, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 0, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 0, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, -1, 1, 1, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 1, 0.5, 0.5, 0] },
{ input: [0, 0, 1, 1, -1, 1, 0, 0, -1], output: [0, 0.5, 1, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 1, -1, 0, -1, 1, 1, 0, 0], output: [0, 1, 0, 0.5, 0, 1, 1, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [0, 1, 0, 0, -1, -1, 1, 0, 1], output: [0.5, 1, 0.5, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 0, 1, 0, 0, 1, 1, -1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, 0, 0, -1, 1, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, -1, 1, -1, 1, 1], output: [0, 1, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, -1, 0, 1, -1, 1, 0, 1, 0], output: [0, 0, 0.5, 1, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, -1, 1, 0, 1, 1], output: [0, 0, 0, 1, 0, 1, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 1, 0, 1, 0, 0, 1, 0], output: [0, 0, 1, 0.5, 1, 0.5, 0, 1, 0.5] },
{ input: [-1, -1, 1, 0, 1, 0, -1, 1, 1], output: [0, 0, 1, 0, 1, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 1, 0, 0, 0, 1, 0], output: [0, 0, 0.5, 1, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 1, 1, 0, 0, 0, 1, 0], output: [0, 0, 1, 1, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 1, 1, -1, 0, 0, 1, 1], output: [0, 0, 1, 1, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, -1, 1, 0], output: [0, 0.5, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 0, 1, 0, -1, 1, -1, 1, 0], output: [0, 0.5, 1, 0.5, 0, 1, 0, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, 0, 0, 0, 0], output: [0, 1, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, 0, 0, 0, 0], output: [1, 0, 1, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, 1, -1, 0, 0], output: [1, 0, 1, 1, 0, 1, 0, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, -1, 0, 0, 0], output: [1, 0, 1, 1, 0, 0, 0, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, -1, -1, 0, 1], output: [1, 0, 1, 1, 0, 0, 0, 0, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, -1, 0, 1, -1, 1, 1, 0, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, -1, 0, 1, -1, 1, 1, 0, 1], output: [0, 0, 0, 1, 0, 1, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, 0, 0, 0, 0], output: [0, 1, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 1, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, 0, 0, -1, 1, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, -1, 1, -1, 1, 1], output: [0, 1, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 0, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 0, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 0.5, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 0, 1, 1, 0], output: [0, 0, 0, 0.5, 1, 0.5, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, -1, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 1, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 0, 0, 1, 1], output: [0, 0, 0.5, 0.5, 1, 0.5, 0, 1, 1] },
{ input: [-1, -1, 1, 0, 1, 0, -1, 1, 1], output: [0, 0, 1, 0, 1, 0.5, 0, 1, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, 0, 0, 0, 0], output: [1, 0, 1, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, -1, 1, 1, -1, 1, -1, 0, 0], output: [1, 0, 1, 1, 0, 1, 0, 0, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 1, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 1, 0.5, 0.5, 0.5, 0, 1, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, -1, 1, 0], output: [0, 0.5, 1, 0, 0.5, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 0, 1], output: [0, 1, 0, 1, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 0, 0, -1, 1, 1, 1, -1], output: [0, 0.5, 0.5, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 1, 0, 0, 0], output: [1, 1, 0, 0, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 0, 1], output: [0, 1, 0, 1, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, -1, 0, 0, 1], output: [1, 0, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 0, 1], output: [0, 1, 0, 1, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 1, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, -1, 1, 1, 1, 0], output: [0, 0.5, 0, 1, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 1], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 1], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 1, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 1, 0] },
{ input: [0, 1, 1, -1, -1, 0, 1, 1, -1], output: [0, 1, 1, 0, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 1, 0, 0, 0], output: [1, 1, 0, 0, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [0, 1, 0, 1, 1, -1, 0, 0, -1], output: [0.5, 1, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 0, 1, 0], output: [0, 1, 1, 0.5, 0, 0, 0.5, 1, 0.5] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 1, 0], output: [0, 1, 1, 0.5, 0, 0, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 1, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 1, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 1, -1, -1, 0, 1, 0, 0], output: [0.5, 1, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 1], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [-1, 1, 1, 0, -1, -1, 0, 1, 1], output: [0, 1, 1, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 1, 1, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 0, 0, 0, 1, 0, -1, 1, 1], output: [0, 0, 0.5, 0.5, 1, 0.5, 0, 1, 1] },
{ input: [-1, -1, 1, 0, 1, 0, -1, 1, 1], output: [0, 0, 1, 0, 1, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 1, 1, 0, 0], output: [1, 0, 1, 0, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0, 0.5, 1, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 1, 0], output: [1, 1, 0, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 1, 0.5, 0.5, 0] },
{ input: [0, 0, 1, 0, -1, 1, 0, 1, -1], output: [0, 0.5, 1, 0.5, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 1], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 1, 0], output: [1, 1, 0, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 1, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, -1, 1, 0, 1, 1], output: [0, 0.5, 0, 1, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, -1, -1, 1, 0, 1, 0], output: [1, 0.5, 0, 0, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 1, 0, 0], output: [0, 1, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, 0, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 0, 0, 1, 0], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 1, 0] },
{ input: [0, -1, 1, 1, -1, 1, 0, 1, -1], output: [0, 0, 1, 1, 0, 1, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 1, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 1, 0.5, 0.5, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 0, 0, 0, -1, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 1, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 0, 0, 0], output: [0, 1, 1, 1, 0, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 1, 0, 1], output: [0.5, 1, 0.5, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 1, 0, 0, 0, 1, 0], output: [0, 0, 0.5, 1, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, 0, 0, 0, 1, 1], output: [0, 0, 0, 1, 0.5, 0.5, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [1, 0, 0, 0, 1, 0, 0, 0, -1], output: [1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [1, 0, -1, 0, 1, 0, 0, 1, -1], output: [1, 0.5, 0, 0.5, 1, 0, 0.5, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, -1, 1, 0], output: [0, 0.5, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, -1, 1, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 1, -1, 0, 0], output: [1, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, 0, -1, 1, 1, 0, 1], output: [0, 0, 0, 0.5, 0, 1, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, -1, 0, 0, 1, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, -1, 0, 1, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 1, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, 1, 0, 0, -1, -1, 0, 0, 1], output: [1, 1, 0.5, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 1, 1, 0, 0] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 0.5, 1, 0.5, 1, 0.5, 0] },
{ input: [0, 1, -1, 0, 1, 0, 1, 0, -1], output: [0.5, 1, 0, 0.5, 1, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, 1, -1, 1, 1, 0, 0], output: [0, 0, 0, 1, 0, 1, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 0, 1, 0], output: [1, 1, 0, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, -1, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 1, 0, 0], output: [0, 0, 0, 0.5, 1, 1, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 0, 1, 0, 1, 1], output: [0, 0.5, 0, 0.5, 0.5, 1, 0, 1, 1] },
{ input: [-1, 0, -1, 0, 1, 1, -1, 1, 1], output: [0, 0, 0, 0.5, 1, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, -1, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, 0, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 1, 0, 1], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 0, 0, 0], output: [0, 1, 1, 1, 0, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 1, 0, 0, 0, 1, 0], output: [0, 0, 0.5, 1, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 1, 1, 0, 0, 0, 1, 0], output: [0, 0, 1, 1, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 1, 1, -1, 0, 0, 1, 1], output: [0, 0, 1, 1, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0] },
{ input: [-1, 0, 1, 0, 1, 1, 0, 0, -1], output: [0, 0.5, 1, 0.5, 1, 1, 0, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, -1, 1, 1, 0, 0, 0], output: [0, 0.5, 1, 0, 1, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 0, 0, 1, 0, 0, -1, 1, 1], output: [0, 0.5, 0, 1, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 0, -1, 1, 0, 1, -1, 1, 1], output: [0, 0.5, 0, 1, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 1, 0, 0], output: [0, 1, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, -1, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0, 0.5, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 1, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0] },
{ input: [-1, 1, 1, 0, 0, 1, 0, 0, -1], output: [0, 1, 1, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 0, 1, -1, 0, 1, 1, -1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, -1, -1, 1, 0, 0, 1], output: [1, 0.5, 0, 0, 0, 1, 0, 0.5, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 1, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 1, 0.5] },
{ input: [1, 1, -1, -1, -1, 1, 0, 1, 0], output: [1, 1, 0, 0, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, 0, 1, 0, 0, 0], output: [0, 1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, -1, 0, 1, 0, 0, 1], output: [0, 1, 0.5, 0, 0.5, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, -1, 0, 1, -1, 1, 1, 0, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, -1, 0, 1, -1, 1, 1, 1, 0], output: [0, 0, 0.5, 1, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, -1, 0, 0, 1], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0, 1] },
{ input: [-1, 0, 1, 1, -1, -1, 1, -1, 1], output: [0, 0, 1, 1, 0, 0, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 1, 0, 1] },
{ input: [1, 0, -1, 0, -1, 1, 1, -1, 1], output: [1, 0, 0, 0.5, 0, 1, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 1, -1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [1, 0, -1, 0, -1, 1, 0, -1, 1], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [1, 0, 0, 1, 1, -1, 0, 0, -1], output: [1, 0.5, 0, 1, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0, 1] },
{ input: [1, 0, 1, 0, -1, -1, 1, -1, 1], output: [1, 0, 1, 0.5, 0, 0, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0] },
{ input: [-1, 0, 1, 0, 0, 1, 1, 0, -1], output: [0, 0.5, 1, 0.5, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 0], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, 0, -1, -1, 0, 1, 0], output: [1, 0, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, 0, 1, 0, -1, -1, 0, 0, 1], output: [1, 0, 1, 0.5, 0, 0, 0.5, 0.5, 1] },
{ input: [1, -1, 1, 0, -1, -1, 1, 0, 1], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 0, 1, 0, 0], output: [1, 1, 0, 0, 0, 0, 1, 0.5, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 1], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 1, -1, -1, -1, 0, 0, 1, 1], output: [1, 1, 0, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 0, 1, 0, 1, 1, 0], output: [0, 0, 0, 0.5, 1, 0.5, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 1, 0, 0, 1, 0], output: [0, 0, 0.5, 0.5, 1, 0.5, 0.5, 1, 0.5] },
{ input: [-1, -1, 0, 1, 1, 0, 0, 1, 0], output: [0, 0, 0, 1, 1, 0.5, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, 0, 0, 0, -1], output: [0.5, 0.5, 0.5, 1, 1, 0, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 1, 1, -1, 0, 1, -1], output: [0.5, 0.5, 0, 1, 1, 0, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, -1, 1, 1, 1, 0, 0], output: [0, 0.5, 0, 0, 1, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, -1, 1, 1, 1, 0, 1], output: [0, 0, 0, 0, 1, 1, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, 0, 1, 0, 0, 0], output: [0, 1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, -1, 0, 1, 0, 1, 0], output: [0, 1, 0.5, 0, 0.5, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 0], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 1], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 1, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 1, 0] },
{ input: [-1, 0, 1, 0, 0, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 1, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 1, 0] },
{ input: [0, 1, 0, -1, -1, 1, 1, 1, -1], output: [0, 1, 0.5, 0, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 0.5, 1, 0.5, 1, 0.5, 0] },
{ input: [0, 0, -1, 1, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 1, 1, 0, 1, 0.5, 0] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 0, 1], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 0, 1], output: [0, 0, 0, 0.5, 1, 1, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 1, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, -1, 1, 0, 1, 1], output: [0, 0.5, 0, 1, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [0, 0, -1, 0, -1, 1, 1, -1, 1], output: [0.5, 0, 0, 0.5, 0, 1, 1, 0, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, 0, -1, 0, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, 0, -1, 0, 0, 1, 0], output: [1, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, -1, -1, 1, 0, 1, 0], output: [1, 0.5, 0, 0, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 1, -1, 1, -1, 0, 0, 1, 1], output: [0, 1, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [1, 0, 0, 0, 1, 0, 0, 0, -1], output: [1, 0.5, 0, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [1, 1, -1, 0, 1, 0, 0, 0, -1], output: [1, 1, 0, 0.5, 1, 0, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, 0, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [-1, 1, 1, 0, -1, 0, -1, 1, 1], output: [0, 1, 1, 0, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 1, -1, 0, 0], output: [1, 0.5, 0, 1, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, -1, 1, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 1, 0, 0.5, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 1, -1, -1, 0, 1, 0, 0], output: [0.5, 1, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 1, 1, 0], output: [0.5, 0.5, 1, 0, 0, 0, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, -1, 0], output: [0.5, 0, 1, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 1, -1, 0, -1, 1, 0, 0, 0], output: [0.5, 1, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, -1, 1, 0], output: [0.5, 0.5, 0, 1, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 0, 1, -1, 1, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 1, 1, 0, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 0.5, 1, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 0, 1, 1], output: [0.5, 1, 0.5, 0, 0, 0.5, 0, 1, 1] },
{ input: [0, 1, 0, -1, -1, 1, -1, 1, 1], output: [0.5, 1, 0, 0, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 1, 0, 0], output: [1, 0, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 1, 0, 1, 0.5, 0, 1] },
{ input: [1, 0, -1, 1, -1, 1, 0, -1, 1], output: [1, 0.5, 0, 1, 0, 1, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0, 0.5, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 0, 0, 1], output: [0, 0.5, 0, 1, 0, 0.5, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 1, -1, 1, 0, 0, 1], output: [0, 0, 0, 1, 0, 1, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 1, 0, -1, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 1], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 1] },{ input: [0, 0, 0, 0, 1, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 0] },
{ input: [0, 0, 0, 0, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 0.5, 1, 0.5, 1, 0.5, 0] },
{ input: [0, 0, -1, 1, 1, 0, 1, 0, -1], output: [0.5, 0.5, 0, 1, 1, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 1, 0, 0, -1, 0, 0, -1, 1], output: [0.5, 1, 0, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 1, -1, 0, -1, 0, 0, -1, 1], output: [1, 1, 0, 0.5, 0, 0.5, 0, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 0] },
{ input: [-1, 0, 1, 0, 0, 1, 1, 0, -1], output: [0, 0.5, 1, 0.5, 0, 1, 1, 0.5, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, -1, 0, 1, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 1, 0, 1, 0, 0.5, 0.5] },
{ input: [1, -1, 0, 1, -1, 1, -1, 1, 0], output: [1, 0, 0, 1, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 1, 0, -1, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 1, -1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 1, -1, -1, 1, 0, 0], output: [0, 0.5, 1, 1, 0, 0, 1, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, -1, 1, 0, 0], output: [0, 1, 1, 1, 0, 0, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 0, 1], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 0, 1], output: [0, 0, 0, 0.5, 1, 1, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 0, 1, -1, 0, 1, 1, -1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 1, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 1, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 1, -1, 1, 0, 1, 0], output: [0, 1, 0, 1, 0, 1, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 1, -1, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 1, 1, -1, 0, 1, -1, 1], output: [0, 0, 1, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 0, 1, 0], output: [0, 0, 0, 0.5, 1, 1, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, -1, 1, 0], output: [1, 0.5, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, -1, 0, 0, -1, 1, 0, 0, 1], output: [1, 0, 0.5, 0.5, 0, 1, 0.5, 0, 1] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 1, 0, 0.5, 0, 0.5, 0.5] },
{ input: [1, 0, 0, 1, -1, 0, -1, 0, 1], output: [1, 0.5, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 1, 0] },
{ input: [0, 0, 1, 0, -1, 0, 1, 1, -1], output: [0, 0.5, 1, 0.5, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, -1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0, 1] },
{ input: [0, 0, -1, 1, -1, 1, 0, -1, 1], output: [0.5, 0, 0, 1, 0, 1, 0.5, 0, 1] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, -1, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, -1, 0, 1, 0], output: [0, 1, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 0, -1, 0, -1, 1, 0, 1, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 0, -1, -1, 0, 1, 1, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 1, 0] },
{ input: [0, 1, 1, -1, -1, 0, 1, 1, -1], output: [0, 1, 1, 0, 0, 0.5, 1, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 1, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 1, -1, 0, 0, 0, 0], output: [0, 1, 1, 1, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 1, 0, 0, 0], output: [1, 0, 1, 0, 0, 1, 0.5, 0.5, 0] },
{ input: [1, -1, 1, -1, -1, 1, 1, 0, -1], output: [1, 0, 1, 0, 0, 1, 1, 0, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 1, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, -1, 1, 0], output: [0.5, 1, 0, 0.5, 0, 0.5, 0, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 0.5, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 1, 0.5, 0.5] },
{ input: [1, 0, 1, 0, -1, -1, 1, 0, 0], output: [1, 0.5, 1, 0, 0, 0, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 1], output: [1, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, -1, -1, 0, 0, 0, 0], output: [1, 1, 0, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, -1, -1, 1, 0, 0, 0], output: [1, 1, 0, 0, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 1, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 0.5, 1, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, -1, 1, 1, -1, 1, 0, 0, 0], output: [0.5, 0, 1, 1, 0, 1, 0.5, 0.5, 0] },
{ input: [0, -1, 1, 1, -1, 1, 1, 0, -1], output: [0, 0, 1, 1, 0, 1, 1, 0.5, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, -1, 0, 0, -1, 1, 0, 1, 0], output: [1, 0, 0.5, 0.5, 0, 1, 0, 1, 0.5] },
{ input: [1, -1, 0, 0, -1, 1, -1, 1, 1], output: [1, 0, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, -1, 0, 0, -1, 1, 0, 0, 1], output: [1, 0, 0.5, 0.5, 0, 1, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 0, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 0.5, 1] },
{ input: [-1, 1, 0, 1, -1, 0, -1, 0, 1], output: [0, 1, 0, 1, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 0], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, -1, 1], output: [0.5, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 0, 0, 0, 0, 0, 1, 1], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 0, 0, 0, -1, 1, 1], output: [0, 1, 0.5, 0.5, 0, 0.5, 0, 1, 1] },
{ input: [-1, 1, 0, 1, -1, 0, -1, 1, 1], output: [0, 1, 0, 1, 0, 0.5, 0, 1, 1] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, 0, 0, -1, 0, 0, 0, 0], output: [1, 1, 0, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 1, -1, 0, -1, 0, 0, 0, 1], output: [1, 1, 0, 0.5, 0, 0.5, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, 0, -1, 0, -1, 1, 0, 0, 0], output: [1, 0.5, 0, 0.5, 0, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 0, 0, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 1, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 1, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 1], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 1] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 1], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 1, -1, 0], output: [0.5, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 1] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 1, 0, 1] },
{ input: [1, 0, -1, 0, -1, 1, 1, -1, 1], output: [1, 0, 0, 0.5, 0, 1, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, 0, -1, 1, 1, 1, 0], output: [0, 0.5, 0, 0.5, 0, 1, 1, 1, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, -1, 1, 1, 0, 0, 1], output: [0, 0.5, 0, 0, 1, 1, 0.5, 0.5, 1] },
{ input: [-1, 0, -1, -1, 1, 1, 1, 0, 1], output: [0, 0, 0, 0, 1, 1, 1, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, -1, -1, 0, 0, 1, 0], output: [1, 0.5, 0.5, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 1, -1, -1, 0, 0, 0, 0], output: [1, 0, 1, 0, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, -1, 1, -1, -1, 0, 0, 1, 0], output: [1, 0, 1, 0, 0, 0, 0.5, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 1, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, -1, 1, 1, 1, 0, 0], output: [0, 0.5, 0, 0, 1, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, -1, 1, 1, 1, 1, 0], output: [0, 0, 0, 0, 1, 1, 1, 1, 0.5] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0, 1, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 1, -1, 1, 1, 0, 0, 0], output: [0, 0.5, 1, 0, 1, 1, 0, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, 0, 0, 0, 0], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0.5, 0.5] },
{ input: [0, 0, 1, 0, -1, -1, 0, 0, 1], output: [0.5, 0.5, 1, 0, 0, 0, 0.5, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [1, 0, 0, 0, -1, 0, 0, -1, 1], output: [1, 0, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 0.5] },
{ input: [-1, 0, 1, 0, 0, 0, 0, 1, 0], output: [0, 0.5, 1, 0.5, 0.5, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 0, 0, 0, -1, 1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 0, 1, 0.5] },
{ input: [-1, 1, 1, 0, -1, 1, -1, 1, 0], output: [0, 1, 1, 0.5, 0, 1, 0, 1, 0] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 1, 0, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 1, 0.5, 0.5] },
{ input: [-1, 0, -1, 0, 1, 1, 1, 0, 0], output: [0, 0, 0, 0.5, 1, 1, 1, 0.5, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, 0, 0, -1, 1], output: [0.5, 0.5, 1, 0.5, 0, 0, 0.5, 0, 1] },
{ input: [0, 0, 1, 0, -1, -1, 1, -1, 1], output: [0.5, 0, 1, 0.5, 0, 0, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 1, 0, 0, 0], output: [0, 0.5, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 0, 0, 1, 0, 1, 0], output: [0, 0.5, 0, 0.5, 0.5, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 0, 0, 1, 0, 1, 0], output: [0, 1, 0, 0.5, 0, 1, 0.5, 1, 0.5] },
{ input: [-1, 1, -1, 0, -1, 1, 0, 1, 1], output: [0, 1, 0, 0.5, 0, 1, 0, 1, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, -1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 1, 0, 0.5] },
{ input: [-1, 1, 1, 0, -1, 0, 1, -1, 0], output: [0, 1, 1, 0.5, 0, 0.5, 1, 0, 0] },{ input: [0, 0, 0, 1, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 0, 1], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0, 1] },
{ input: [-1, 0, 1, 1, -1, 0, 1, -1, 1], output: [0, 0, 1, 1, 0, 0.5, 1, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 0, -1, 1, 0, 0, 0], output: [0.5, 0.5, 0, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [0, 0, -1, 0, -1, 1, 0, 0, 1], output: [0.5, 0.5, 0, 0.5, 0, 1, 0, 0.5, 1] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 1, 0, 0, 0], output: [0, 0.5, 0.5, 1, 0, 1, 0.5, 0.5, 0] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 1] },
{ input: [0, 0, 0, 1, -1, 0, 0, 0, 1], output: [0.5, 0.5, 0.5, 1, 0, 0.5, 0.5, 0, 1] },
{ input: [0, 0, 1, 1, -1, 0, 0, -1, 1], output: [0.5, 0, 1, 1, 0, 0.5, 0.5, 0, 1] },{ input: [0, 0, 0, 0, 0, 0, 1, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 0, 0, 1, -1, 0, 1, 0, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 0.5, 0.5] },
{ input: [-1, 0, 0, 1, -1, 0, 1, 1, 0], output: [0, 0.5, 0.5, 1, 0, 0.5, 1, 1, 0] },{ input: [1, 0, 0, 0, 0, 0, 0, 0, 0], output: [1, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [1, 0, 0, 0, -1, 1, 0, 0, 0], output: [1, 0, 0.5, 0.5, 0, 1, 0.5, 0.5, 0.5] },
{ input: [1, -1, 0, 0, -1, 1, 1, 0, 0], output: [1, 0, 0.5, 0.5, 0, 1, 1, 0, 0.5] },{ input: [0, 0, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 0.5, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 0, 0, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [-1, 1, 0, 0, -1, 0, 0, 1, 0], output: [0, 1, 0.5, 0.5, 0, 0.5, 0.5, 1, 0] },{ input: [0, 1, 0, 0, 0, 0, 0, 0, 0], output: [0.5, 1, 0.5, 0.5, 0, 0.5, 0.5, 0.5, 0.5] },
{ input: [0, 1, 0, 0, -1, 0, 1, 0, 0], output: [0.5, 1, 0.5, 0, 0, 0.5, 1, 0.5, 0.5] },
{ input: [0, 1, 1, -1, -1, 0, 1, 0, 0], output: [0.5, 1, 1, 0, 0, 0, 1, 0.5, 0.5] }
];


net.train(data, {
	errorThresh: 0.005,
	iterations: 20000,
	log: true,
	logPeriod: 10,
	learningRate: 0.6
});

var output = net.run([-1, 1, 0, 0, 0, 0, 1, 1, -1]);  //
console.log(output);