#include <bits/stdc++.h>

typedef long long LL;

int n;
std::map <std::pair <int, int>, int> mp;

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		double x; scanf("%lf", &x);
		LL QAQ = llround(x * 1e9);
		int _2 = 0, _5 = 0;
		while (QAQ % 2 == 0) QAQ /= 2, ++_2;
		while (QAQ % 5 == 0) QAQ /= 5, ++_5;
		++mp[std::make_pair(_2, _5)];
	}
	LL ans = 0;
	for (auto x: mp) for (auto y: mp) if (x.first.first + y.first.first >= 18 && x.first.second + y.first.second >= 18)
		if (x.first == y.first) ans += 1LL * x.second * (x.second - 1) / 2;
		else if (x.first < y.first) ans += 1LL * x.second * y.second;
	printf("%lld\n", ans);
	return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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>

typedef long long LL;

int n;
std::map <std::pair <int, int>, int> mp;

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; ++i) {
		double x; scanf("%lf", &x);
		LL QAQ = llround(x * 1e9);
		int _2 = 0, _5 = 0;
		while (QAQ % 2 == 0) QAQ /= 2, ++_2;
		while (QAQ % 5 == 0) QAQ /= 5, ++_5;
		++mp[std::make_pair(_2, _5)];
	}
	LL ans = 0;
	for (auto x: mp) for (auto y: mp) if (x.first.first + y.first.first >= 18 && x.first.second + y.first.second >= 18)
		if (x.first == y.first) ans += 1LL * x.second * (x.second - 1) / 2;
		else if (x.first < y.first) ans += 1LL * x.second * y.second;
	printf("%lld\n", ans);
	return 0;
}
```