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 Python (3.8.2) (judge verdict: Wrong Answer)

#!/usr/bin/env python
# coding: utf-8

from collections import Counter

def ri():
    return int(input())

def rl():
    return list(input().split())

def rli():
    return list(map(int, input().split()))

def calc(b, d25):
    d2, d5 = -d25[0], -d25[1]
    while b%2 == 0:
        d2 += 1
        b //= 2
    while b%5 == 0:
        d5 += 1
        b //= 5
    return (d2, d5)

def main():
    n = ri()
    ndic = Counter()
    ans = 0
    for i in range(n):
        a = input()
        d = a.split(".")
        if len(d) == 1:
            m = 0
        else:
            m = len(d[1])
        d25 = [m, m]
        b = int(a.replace(".", ""))
        c25 = calc(b, d25)
        if c25[0] == -9 and c25[1] == -9:
            continue
        for e in ndic:
            if c25[0] + e[0] >= 0 and c25[1] + e[0] >= 0:
                ans += ndic[e]
        ndic[c25] += 1
    print(ans)

if __name__ == '__main__':
    main()