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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

N = int(input())
A = [float(input()) for _ in range(N)]
for i in range(N):  A[i] *= 10 ** 9
  
c = [[0 for _ in range(19)] for _ in range(19)]

for i in range(N):
    p = A[i]
    cnt2 = 0
    while(not p % 2):
        p /= 2
        cnt2 += 1

    p = A[i]
    cnt5 = 0
    while(not p % 5):
        p /= 5
        cnt5 += 1
        
    c[min(cnt2, 18)][min(cnt5, 18)] += 1
    
ans = 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 and c[i][j]:  ans += (c[i][j] * (c[i][j] - 1))
                    else:  ans += c[i][j] * c[k][l]
print(ans // 2)