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)

from bisect import bisect_left
from decimal import Decimal

N, *A = map(Decimal, open(0).read().split())
N = int(N)
A.sort()

ints = [d for d in A if int(d) == d]
decs = [d for d in A if int(d) != d]

result = len(ints) * (len(ints) - 1) // 2
for i in range(len(decs)):
    a = decs[i]
    if a < 1:
        t = bisect_left(decs, 1 // a)
    else:
        t = i + 1
    for j in range(t, len(decs)):
        t = a * decs[j]
        if t == int(t):
            result += 1

    t = bisect_left(ints, 1 // a)
    for j in range(t, len(ints)):
        t = a * decs[j]
        if t == int(t):
            result += 1

print(result)