Problem:
Score : 300 points

Problem Statement

You are given N real values A_1, A_2, \ldots, A_N.
Compute the number of pairs of indices (i, j)
such that i < j and the product A_i \cdot A_j is integer.

Constraints

2 \leq N \leq 200\,000

0 < A_i < 10^4

A_i is given with at most 9 digits after the decimal.

Input

Input is given from Standard Input in the following format.

N
A_1
A_2
\vdots
A_N

Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Sample Input 1

5
7.5
2.4
17.000000001
17
16.000000000

Sample Output 1

3

There are 3 pairs with integer product:

7.5 \cdot 2.4 = 18

7.5 \cdot 16 = 120

17 \cdot 16 = 272

Sample Input 2

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001

Sample Output 2

8

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_set>
#include <vector>
using namespace std;
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ull;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpii;
typedef vector<pair<ll, ll>> vpll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vc> vvc;
typedef vector<vs> vvs;
typedef vector<vll> vvll;
typedef map<int, int> mii;
typedef set<int> si;
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i <= (n); ++i)
#define arep(i, v) for (auto i : v)
#define irep(it, stl) for (auto it = stl.begin(); it != stl.end(); it++)
#define drep(i, n) for (int i = (n)-1; i >= 0; --i)
#define fin(ans) cout << (ans) << '\n'
#define STLL(s) strtoll(s.c_str(), NULL, 10)
#define mp(p, q) make_pair(p, q)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
#define MATHPI acos(-1)
#define fi first
#define se second
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
template <class T>
inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
inline void dump(T& v) {
    irep(i, v) { cout << (*i) << ((i == --v.end()) ? '\n' : ' '); }
}
inline string getline() {
    string s;
    getline(cin, s);
    return s;
}
inline void yn(const bool b) { b ? fin("yes") : fin("no"); }
inline void Yn(const bool b) { b ? fin("Yes") : fin("No"); }
inline void YN(const bool b) { b ? fin("YES") : fin("NO"); }
struct io {
    io() {
        ios::sync_with_stdio(false);
        cin.tie(0);
    }
};
const int INF = INT_MAX;
constexpr ll LLINF = 1LL << 60;
constexpr ll MOD = 1000000007;
constexpr ld EPS = 1e-11;

template <typename T>
class Sum {
   public:
    // 単位元
    T unit;

    Sum(void) {
        // 単位元
        unit = 0;
    }

    // 演算関数
    T calc(T a, T b) { return a + b; }
};

template <typename T, class MONOID>
class SegmentTree {
   public:
    // セグメント木の葉の要素数
    int n;

    // セグメント木
    vector<T> tree;

    // モノイド
    MONOID mono;

    SegmentTree() : n(1 << (int)ceil(log2(64))), tree(vector<T>(n << 1)) {
        for (int i = 0; i < 64; ++i) {
            update(i, mono.unit);
        }
    }

    // k番目の値(0-indexed)をxに変更
    void update(int k, T x) {
        k += n;
        tree[k] += x;
        for (k = k >> 1; k > 0; k >>= 1) {
            tree[k] = mono.calc(tree[k << 1 | 0], tree[k << 1 | 1]);
        }
    }

    // [l, r)の最小値(0-indexed)を求める．
    T query(int l, int r) {
        T res = mono.unit;
        l += n;
        r += n;
        while (l < r) {
            if (l & 1) {
                res = mono.calc(res, tree[l++]);
            }
            if (r & 1) {
                res = mono.calc(res, tree[--r]);
            }
            l >>= 1;
            r >>= 1;
        }
        return res;
    }

    T operator[](int k) {
        // st[i]で添字iの要素の値を返す
        if (k - n >= 0 || k < 0) {
            return -INF;
        }
        return tree[tree.size() - n + k];
    }

    void show(void) {
        int ret = 2;
        for (int i = 1; i < 2 * n; ++i) {
            if (tree[i] == mono.unit)
                cout << "UNIT ";
            else
                cout << tree[i] << " ";
            if (i == ret - 1) {
                cout << endl;
                ret <<= 1;
            }
        }
        cout << endl;
    }
};

int main() {
    int n;
    cin >> n;
    ll ans = 0;
    vector<SegmentTree<ll, Sum<ll>>> st(64);
    rep(_, n) {
        // string T;
        // cin >> T;
        // int dot = 0;
        // for (int j = 0; j < T.size(); j++) {
        //     if (T[j] == '.') break;
        //     dot++;
        //     if (j == T.size() - 1) {
        //         T += ".";
        //         break;
        //     }
        // }
        // T += "0000000000";
        // ll t = STLL(T.substr(0, dot));
        // t *= 1e9;
        // t += STLL(T.substr(dot + 1, 9));
        // // fin(t);
        // if (STLL(T.substr(dot + 9)) > 0) continue;
        ld t;
        cin>>t;
        t*=1e9;

        ll two = 0, five = 0;
        ll it = t;
        while (it % 2 == 0) {
            it /= 2;
            two++;
        }
        while (it % 5 == 0) {
            it /= 5;
            five++;
        }
        // cout << two << " " << five << endl;
        for (ll i = max(18 - two, 0LL); i < 64; i++) {
            ans += st[i].query(max(18 - five, 0LL), 64);
        }
        st[two].update(five, 1);
    }
    fin(ans);
}