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)

# A

n = int(input())
a_l = [int(float(input()) * 10**9) for x in range(n)]

list = [[0] * 19 for _ in range(19)]
cs_list = [[0] * 19 for _ in range(19)]
b_l = [0, 0] * n

for i in range(n):
    _t2 = 0
    _t5 = 0
    _a = a_l[i]
    while _a % 2 == 0 and _t2 < 18:
        _t2 += 1
        _a /= 2

    _a = a_l[i]
    while _a % 5 == 0 and _t5 < 18:
        _t5 += 1
        _a /= 5
    
    list[_t2][_t5] += 1
    b_l[i] = [_t2, _t5]

for i in range(19):
    for j in range(19):
        for k in range(i+1):
            for l in range(j+1):
                cs_list[k][l] += list[i][j]

ans = 0
for i in range(n):
    _t,_f = b_l[i]
    if _t >= 9 and _f >= 9:
        ans -= 1
    ans += cs_list[18-_t][18-_f]
        
print(ans // 2)