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)

from decimal import Decimal
from numba import njit, i4, i8


def main():
    @njit(i8(i8, i4), cache=True)
    def div(n, d):
        cnt = 0
        while n % d == 0:
            n //= d
            cnt += 1
        return cnt

    @njit(cache=True)
    def solve(arr):
        ans = 0
        for i in range(len(arr)):
            for j in range(i + 1, len(arr)):
                (a, b), (c, d) = arr[i], arr[j]
                if a + c >= 18 and b + d >= 18:
                    ans += 1
        return ans

    n = int(input())
    arr = [int(Decimal(input()) * 10**9) for _ in range(n)]
    arr = [(div(x, 2), div(x, 5)) for x in arr]

    print(solve(arr))


if __name__ == '__main__':
    main()