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: Accepted)

import sys

sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
f_inf = float('inf')
mod = 10 ** 9 + 7
MAX = 50


def resolve():
    n = int(input())

    D = [[0] * MAX for _ in range(MAX)]
    for _ in range(n):
        a = int(round(float(input()) * 10 ** 9))
        t = a
        x = 0
        while t % 2 == 0:
            t //= 2
            x += 1
        t = a
        y = 0
        while t % 5 == 0:
            t //= 5
            y += 1
        D[x][y] += 1

    res = 0
    for x1 in range(MAX):
        for y1 in range(MAX):
            for x2 in range(max(0, 18 - x1), MAX):
                for y2 in range(max(0, 18 - y1), MAX):
                    if x1 == x2 and y1 == y2:
                        res += D[x1][y1] * (D[x1][y1] - 1)
                    else:
                        res += D[x1][y1] * D[x2][y2]
    print(res // 2)


if __name__ == '__main__':
    resolve()