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: Time Limit Exceeded)

def main():
    n = int(input())
    ans = 0
    cnt = [[[0]*80 for j in range(80)] for i in range(20)]
    for _ in range(n):
        a = list(map(str, input().split(".")))
        x = 0
        if len(a) == 1:
            x = int(a[0]) * 10**9
        else:
            x = int(a[0]) * 10**9 + int(a[1]) * pow(10, 9-len(a[1]))
        cnt_10, cnt_2, cnt_5 = 0, 0, 0
        while x % 10 == 0:
            cnt_10 += 1
            x //= 10
        while x % 2 == 0:
            cnt_2 += 1
            x //= 2
        while x % 5 == 0:
            cnt_5 += 1
            x //= 5
        for i in range(15):
            if i + cnt_10 >= 18:
                for j in range(50):
                    ans += sum(cnt[i][j])
            else:
                p = 18 - cnt_10 - i
                if cnt_2 >= p:
                    for j in range(p, 50):
                        ans += cnt[i][0][j]
                if cnt_5 >= p:
                    for j in range(p, 50):
                        ans += cnt[i][j][0]
        cnt[cnt_10][cnt_2][cnt_5] += 1
    print(ans)

if __name__ == "__main__":
    main()