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: Wrong Answer)

def divide(n, p):
    c = 0
    while n%p == 0 and c < 18:
        c += 1
        n //= p
    return c
    

n = int(input())
dp = [[0]*19 for _ in range(19)]
    
for i in range(n):
    s = float(input())
    s = int(1000000000*s)
    c1, c2 = divide(s, 2), divide(s, 5)
    dp[c1][c2] += 1
    
ans = 0
for i1 in range(19):
    for j1 in range(19):
        for i2 in range(19):
            for j2 in range(19):
                if i1+i2 >= 18 and j1+j2 >= 18:
                    if i1 == i2 and j1 == j2:
                        ans += dp[i1][j1]*(dp[i1][j1]-1)//2
                    elif i1 < i2:
                        ans += dp[i1][j1]*dp[i2][j2]
            
        
print(ans)