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: Accepted)

n = int(input())
d = [[0] * 21 for _ in range(21)]
ans = 0
for _ in range(n):
    a = input()
    if '.' not in a:
        c2 = c5 = 0
    else:
        c2 = c5 = -(len(a) - (a.index('.') + 1))
    a = int(a.replace('.',''))
    while a % 2 == 0:
        a //= 2
        c2 += 1
    while a % 5 == 0:
        a //= 5
        c5 += 1
    c2 = min(10, c2)
    c5 = min(10, c5)
    for i in range(-c2, 11):
        for j in range(-c5, 11):
            ans += d[i+10][j+10]
    d[c2+10][c5+10] += 1
print(ans)