#include <bits/stdc++.h>
#define MAX (ll)(2e1)
#define INF (ll)(1e18)
#define MOD (ll)(1e9)

using namespace std;
using ll = long long;
using cd = complex<double>;

ll cc[20][20];
ll gcd (ll a, ll b) {
 if (!a || !b) {
  return max (a, b);
 }
 ll r = a % b;
 while (r) {
  a = b;
  b = r;
  r = a % b;
 }
 return b;
}

map<ll, ll> ma;

int main () {
 ll n;
 cin >> n;
 ll ar[n];
 vector<pair<ll, ll>> vp;
 for (ll i = 0; i < n; i++) {
  double v;
  cin >> v;
  ll xx = gcd (llround(v * MOD), INF);
  ll pt = 0, pf = 0;
  while (xx % 2 == 0) {
   xx /= 2;
   pt++;
  }
  while (xx % 5 == 0) {
   xx /= 5;
   pf++;
  }
  cc[pt][pf]++;
  vp.push_back (make_pair (pt, pf));
 }
 ll ans = 0;
 for (auto v : vp) {
  ll x = 18 - v.first, y = 18 - v.second;
  for (ll i = x; i <= 18; i++)  {
   for (ll j = y; j <= 18; j++) {
    ans += cc[i][j];
   }
  }
  if (v.first * 2  >= 18 && 2 * v.second >= 18) {
   ans--;
  }
 }
 cout << ans / 2 << "\n";
}


### Prompt

Your task is to create a CPP solution to the following problem:

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).

Examples

Input

5
7.5
2.4
17.000000001
17
16.000000000


Output

3


Input

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


Output

8

### Response

```cpp
#include <bits/stdc++.h>
#define MAX (ll)(2e1)
#define INF (ll)(1e18)
#define MOD (ll)(1e9)

using namespace std;
using ll = long long;
using cd = complex<double>;

ll cc[20][20];
ll gcd (ll a, ll b) {
 if (!a || !b) {
  return max (a, b);
 }
 ll r = a % b;
 while (r) {
  a = b;
  b = r;
  r = a % b;
 }
 return b;
}

map<ll, ll> ma;

int main () {
 ll n;
 cin >> n;
 ll ar[n];
 vector<pair<ll, ll>> vp;
 for (ll i = 0; i < n; i++) {
  double v;
  cin >> v;
  ll xx = gcd (llround(v * MOD), INF);
  ll pt = 0, pf = 0;
  while (xx % 2 == 0) {
   xx /= 2;
   pt++;
  }
  while (xx % 5 == 0) {
   xx /= 5;
   pf++;
  }
  cc[pt][pf]++;
  vp.push_back (make_pair (pt, pf));
 }
 ll ans = 0;
 for (auto v : vp) {
  ll x = 18 - v.first, y = 18 - v.second;
  for (ll i = x; i <= 18; i++)  {
   for (ll j = y; j <= 18; j++) {
    ans += cc[i][j];
   }
  }
  if (v.first * 2  >= 18 && 2 * v.second >= 18) {
   ans--;
  }
 }
 cout << ans / 2 << "\n";
}


```