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 numpy as np

N = int(input())

A = []
for i in range(N):
    num = float(input()) * 10 ** 9 + 0.5
    A.append(int(num))


def count2(n):
    ret = 0
    while(n % 2 == 0):
        ret += 1
        n /= 2
    return ret


def count5(n):
    ret = 0
    while(n % 5 == 0):
        ret += 1
        n /= 5
    return ret


table = {}
for i in range(19):
    for j in range(19):
        table[i, j] = 0

for a in A:
    c2 = count2(a)
    c5 = count5(a)
    if(c2 > 18):
        c2 = 18
    if(c5 > 18):
        c5 = 18
    table[c2, c5] += 1

res = 0
for i in range(19):
    for j in range(19):
        for k in range(19):
            for l in range(19):
                if i + k >= 18 and j + l >= 18:
                    if i == k and j == l:
                        res += table[i, j] * (table[i, j] - 1)
                    else:
                        res += table[i, j] * table[k, l]

print(res // 2)