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: Runtime Error)

#include<bits/stdc++.h>
#define cs const
using namespace std;
typedef long long ll;
cs int N = 2e5 + 50, M = 70;
int n, c[2][M][M];
int main(){
	#ifdef FSYolanda
	freopen("1.in","r",stdin);
	#endif
	scanf("%d", &n); ll ans = 0;
	for(int i = 1; i <= n; i++){
		double y; scanf("%lf", &y);
		int a = 0, b = 0, typ = -1;
		for(int j = 0; j <= 12; j++) y *= 10, --a;
		ll x = y;
		while(x && (x % 10 == 0)) ++a, x /= 10;
		if(x & 1) typ = 1; else typ = 0;
		while(x && (x & 1 ^ 1)) x >>= 1, ++b;
		while(x && (x % 5 == 0)) x /= 5, ++b;
		assert(b <= 50);
		for(int j = -12; j <= 12; j++)
		for(int k = 0; k <= 50; k++)
		if(j + a + min(k, b) >= 0)
		ans += (ll)c[typ ^ 1][j + 12][k];
		for(int j = -12; j <= 12; j++)
		for(int k = 0; k <= 50; k++)
		if(j + a >= 0)
		ans += c[typ][j + 12][k];
		++c[typ][a + 12][b];
//		cout << ans << " " << a << " " << b << " " << typ << endl;
	} cout << ans; return 0;
}