E.cpp

#include <bits/stdc++.h>
using namespace std;

//----------------------------------- DEBUG -----------------------------------
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
// debug & operator << (debug & dd, P p) { dd << "(" << p.x << ", " << p.y << ")"; return dd; }

//----------------------------------- END DEBUG --------------------------------

// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
template<class Fun> class y_combinator_result {
    Fun fun_;
public:
    template<class T> explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
    template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(std::ref(*this), std::forward<Args>(args)...); }
};
template<class Fun> decltype(auto) y_combinator(Fun &&fun) { return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun)); }
 

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

#define trav(a,x) for (auto& a : x)
#define uid(a, b) uniform_int_distribution<int>(a, b)(rng)

//----------------------------------- DEFINES ----------------------------------- 

#define sz(x) (int)(x).size()
#define mp make_pair
#define eb emplace_back
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define ins insert
#define nl '\n'
#define Stringize( L )     #L 
#define MakeString( M, L ) M(L)
#define $Line MakeString( Stringize, __LINE__ )
#define Reminder __FILE__ "("  ") : Warning: "

//----------------------------------- END DEFINES -------------------------------- 

//-------------------------- CUSTOM UNORDERED MAP HASH ---------------------------

struct custom_hash{
    static uint64_t splitmix64(uint64_t x){
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }
    size_t operator()(uint64_t a) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(a + FIXED_RANDOM);
    }
    template<class T> size_t operator()(T a) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        hash<T> x;
        return splitmix64(x(a) + FIXED_RANDOM);
    }
    template<class T, class H> size_t operator()(pair<T, H> a) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        hash<T> x;
        hash<H> y;
        return splitmix64(x(a.first) * 37 + y(a.second) + FIXED_RANDOM);
    }
};
template<class T, class H>using umap=unordered_map<T,H,custom_hash>;

//----------------------- CUSTOM UNORDERED MAP HASH END--------------------------

template<typename T>
struct fenwick_tree {
    int tree_n = 0;
    T tree_sum = 0;
    vector<T> tree;
 
    fenwick_tree(int n = -1) {
        if (n >= 0)
            init(n);
    }
 
    static int highest_bit(int x) {
        return x == 0 ? -1 : 31 - __builtin_clz(x);
    }
 
    void init(int n) {
        tree_n = n;
        tree_sum = 0;
        tree.assign(tree_n + 1, 0);
    }
 
    // O(n) initialization of the Fenwick tree.
    template<typename T_array>
    void build(const T_array &initial) {
        assert(int(initial.size()) == tree_n);
        tree_sum = 0;
 
        for (int i = 1; i <= tree_n; i++) {
            tree[i] = initial[i - 1];
            tree_sum += initial[i - 1];
 
            for (int k = (i & -i) >> 1; k > 0; k >>= 1)
                tree[i] += tree[i - k];
        }
    }
 
    // index is in [0, tree_n).
    void update(int index, const T &change) {
        assert(0 <= index && index < tree_n);
        tree_sum += change;
 
        for (int i = index + 1; i <= tree_n; i += i & -i)
            tree[i] += change;
    }
 
    // Returns the sum of the range [0, count).
    T query(int count) const {
        count = min(count, tree_n);
        T sum = 0;
 
        for (int i = count; i > 0; i -= i & -i)
            sum += tree[i];
 
        return sum;
    }
 
    // Returns the sum of the range [start, tree_n).
    T query_suffix(int start) const {
        return tree_sum - query(start);
    }
 
    // Returns the sum of the range [a, b).
    T query(int a, int b) const {
        return query(b) - query(a);
    }
 
    // Returns the element at index a in O(1) amortized across every index. Equivalent to query(a, a + 1).
    T get(int a) const {
        assert(0 <= a && a < tree_n);
        int above = a + 1;
        T sum = tree[above];
        above -= above & -above;
 
        while (a != above) {
            sum -= tree[a];
            a -= a & -a;
        }
 
        return sum;
    }
 
    bool set(int index, T value) {
        assert(0 <= index && index < tree_n);
        T current = get(index);
 
        if (current == value)
            return false;
 
        update(index, value - current);
        return true;
    }
 
    // Returns the largest p in `[0, tree_n]` such that `query(p) <= sum`. Returns -1 if no such p exists (`sum < 0`).
    // Can be used as an ordered set/multiset on indices in `[0, tree_n)` by using the tree as a 0/1 or frequency array:
    // `set(index, 1)` is equivalent to insert(index). `update(index, +1)` is equivalent to multiset.insert(index).
    // `set(index, 0)` or `update(index, -1)` are equivalent to erase(index).
    // `get(index)` provides whether index is present or not, or the count of index (if multiset).
    // `query(index)` provides the count of elements < index.
    // `find_last_prefix(k)` finds the k-th smallest element (0-indexed). Returns `tree_n` for `sum >= set.size()`.
    int find_last_prefix(T sum) const {
        if (sum < 0)
            return -1;
 
        int prefix = 0;
 
        for (int k = highest_bit(tree_n); k >= 0; k--)
            if (prefix + (1 << k) <= tree_n && tree[prefix + (1 << k)] <= sum) {
                prefix += 1 << k;
                sum -= tree[prefix];
            }
 
        return prefix;
    }
};

void run_cases() {
    int n;
    cin >> n;
    fenwick_tree<int64_t> left, right;
    left.init(n + 10); right.init(n + 10);
    map<int,int> compress;
    vector<int> a(n);
    trav(u, a) cin >> u;
    vector<int> tmp = a;
    sort(all(tmp));

    int id = 1;
    for(auto u: tmp) {
        compress[u] = id++;
    }

    for(int i=n-1;i>=1;i--) {
        int mapped = compress[a[i]];
        right.set(mapped, 1);
    }

    int64_t ans = 0;
    left.set(compress[a[0]], 1);
    right.set(compress[a[0]], 0);
    for(int i=1;i<n-1;i++) {
        int mapped = compress[a[i]];
        left.set(mapped, 1);
        right.set(mapped, 0);
        ans += left.query_suffix(mapped + 1) * right.query(0, mapped);

    }
    cout << ans;
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(nullptr);

    int tests = 1;
    // cin >> tests;

    for(int test = 1;test <= tests;test++) {
        run_cases();
    }
}