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

#define pb push_back
#define mp make_pair
#define f1 first
#define s2 second

#define fastio ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define debug(x...) cerr << "[" << #x << "]: " << x << "\n";

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<ll, ll> pl;

ld const PI = 4*atan((ld)1);

int main()
{
	fastio;

	int n;
	cin >> n;

	map<ii, int> ctr;
	for (int i = 0; i < n; ++i)
	{
		double x;
		cin >> x;

		ll y = llround(x * 1e9);
		int two = 0, five = 0;
		while (y % 2 == 0)
			y /= 2, two++;
		while (y % 5 == 0)
			y /= 5, five++;
		ctr[mp(two, five)]++;
	}

	ll res = 0;
	for (auto x : ctr)
		for (auto y : ctr)
		{
			if (x.f1.f1 + y.f1.f1 >= 18 && x.f1.s2 + y.f1.s2 >= 18)
			{
				if (x.f1 < y.f1) res += (ll) x.s2 * y.s2;
				else if (x.f1 == y.f1) res += (ll) x.s2 * (y.s2 - 1) / 2;
			}
		}

	cout << res << '\n';
	return 0;
}

### Prompt

In Cpp, your task is to solve 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>
using namespace std;

#define pb push_back
#define mp make_pair
#define f1 first
#define s2 second

#define fastio ios :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define debug(x...) cerr << "[" << #x << "]: " << x << "\n";

typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<ll, ll> pl;

ld const PI = 4*atan((ld)1);

int main()
{
	fastio;

	int n;
	cin >> n;

	map<ii, int> ctr;
	for (int i = 0; i < n; ++i)
	{
		double x;
		cin >> x;

		ll y = llround(x * 1e9);
		int two = 0, five = 0;
		while (y % 2 == 0)
			y /= 2, two++;
		while (y % 5 == 0)
			y /= 5, five++;
		ctr[mp(two, five)]++;
	}

	ll res = 0;
	for (auto x : ctr)
		for (auto y : ctr)
		{
			if (x.f1.f1 + y.f1.f1 >= 18 && x.f1.s2 + y.f1.s2 >= 18)
			{
				if (x.f1 < y.f1) res += (ll) x.s2 * y.s2;
				else if (x.f1 == y.f1) res += (ll) x.s2 * (y.s2 - 1) / 2;
			}
		}

	cout << res << '\n';
	return 0;
}

```