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: Runtime Error)

import numpy as np


def div(n, d):
    cnt = 0
    while n % d == 0 and cnt < 18:
        n //= d
        cnt += 1
    return cnt


n = int(input())

arr2 = []
arr5 = []
for _ in range(n):
    x = round(float(input()) * 10**9)
    arr2.append(div(x, 2))
    arr5.append(div(x, 5))

arr2 = np.array(arr2)
arr5 = np.array(arr5)
shape = arr2.shape[0]

arr2 = (arr2 + np.zeros([shape, shape], np.int64)).astype(np.int32)
arr5 = (arr5 + np.zeros([shape, shape], np.int64)).astype(np.int32)

arr2 = np.tril(arr2 + arr2.T)
arr2 -= arr2.T
arr5 = np.tril(arr5 + arr5.T)
arr5 -= arr5.T

result = (arr2 >= 18).astype(np.int32) + (arr5 >= 18).astype(np.int32)

print(np.sum(result >= 2))