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)

import decimal

N = int(input())
A = [int(decimal.Decimal(input()) * 10 ** 9) for _ in range(N)]
B = [[0] * 19 for _ in range(19)]
for a in A:
    cnt2 = 0
    while a % 2 == 0:
        cnt2 += 1
        a //= 2
    cnt5 = 0
    while a % 5 == 0:
        cnt5 += 1
        a //= 5
    B[min(cnt2, 18)][min(cnt5, 18)] += 1
ans = 0
for i in range(361):
    a, r = divmod(i, 19)
    if a >= 9 and r >= 9:
        ans -= B[a][r]
    for j in range(361):
        b, s = divmod(j, 19)
        if a + b >= 18 and r + s >= 18:
            ans += B[a][r] * B[b][s]

ans //= 2
print(ans)