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 numba import njit


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


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

print(ans)