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)

import sys
import itertools
# import numpy as np
import time
import math
import heapq
from collections import defaultdict
from collections import Counter
sys.setrecursionlimit(10 ** 7)
 
INF = 10 ** 18
MOD = 10 ** 9 + 7
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

# map(int, input().split())
N = int(input())
MAX = 10 ** 9
A = [float(input()) * MAX for _ in range(N)]

d = defaultdict(int)
for a in A:
    two = 0
    while a % 2 == 0:
        two += 1
        a //= 2
    five = 0
    while a % 5 == 0:
        five += 1
        a //= 5
    d[(two, five)] += 1

ans = 0
for p1 in d.keys():
    for p2 in d.keys():
        if (p1[0] + p2[0] >= 18 and p1[1] + p2[1] >= 18):
            if p1 < p2:
                ans += d[p1] * d[p2]
            elif p1 == p2:
                ans += d[p1] * (d[p1] - 1) // 2
print(ans)