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)

#pragma GCC optimize(2)
#include <bits/stdc++.h>

namespace __temp_inbuilt{
	int read(void){
		int res = 0, sign = 1;
		char ch = std::getchar();
		while(!std::isdigit(ch)){
			if(ch == '-')
				sign = -1;
			ch = std::getchar();
		}
		while(std::isdigit(ch))
			res = res * 10 + ch - 48, ch = std::getchar();
		return sign * res;
	}
	
	template<class Tp>
		void write(const Tp &x){
			if(x > 9)
				write(x / 10);
			std::putchar(x % 10 + 48);
	}
}

using __temp_inbuilt::read;

template<class Tp>
	void writeln(const Tp &x){
		if(x < 0)
			std::putchar('-');
		__temp_inbuilt::write(x > 0 ? x : -x);
		std::putchar('\n');
	}

template<class Tp>
	void writesp(const Tp &x){
		if(x < 0)
			std::putchar('-');
		__temp_inbuilt::write(x > 0 ? x : -x);
		std::putchar(' ');
	}

template<class Tp>
	void write(const Tp &x){
		if(x < 0)
			std::putchar('-');
		__temp_inbuilt::write(x > 0 ? x : -x);
	}

typedef long long ll;
typedef unsigned long long ull;
typedef double rl;
typedef long double RL;

const rl PI = 3.1415926535898, E = 2.71828182845904;

namespace contest{
	int n;
	int cnt[200][200], l5 = 40, l2 = 60;
	ll ans;
	int main(){
    	std::ios::sync_with_stdio(false);
    	std::cin.tie(0);
    	std::cin >> n;
		for(int i = 1; i <= n; ++i){
			long double a; std::cin >> a;
			ll b = a * 1e10;
			int c5 = 0, c2 = 0;
			while(b > 0 && b % 5 == 0)
				b /= 5, ++c5;
			while(b > 0 && b % 2 == 0)
				b /= 2, ++c2;
			for(int j = std::max(20 - c5, 0); j <= l5; ++j)
				for(int k = std::max(20 - c2, 0); k <= l2; ++k)
					ans += cnt[j][k];
			++cnt[c5][c2];
			l5 = std::max(l5, c5),
			l2 = std::max(l2, c2);
		}
		std::cout << ans;
		return 0;
	}
}

int main(){
	contest::main();
	return 0;
}