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 collections import defaultdict
con = 10 ** 9 + 7; INF = float("inf")

def getlist():
	return list(map(int, input().split()))

#処理内容
def main():
	N = int(input())
	D = defaultdict(int)
	table = [[0] * 100 for i in range(100)]
	tablesum = [[0] * 100 for i in range(100)]
	for i in range(N):
		A = input()
		num = ""
		mod5 = 0
		mod2 = 0
		for j in range(len(A)):
			if A[-1 - j] == ".":
				mod5 -= j
				mod2 -= j
			else:
				num += A[-1 - j]

		num = int(num[::-1])
		while True:
			if num % 2 == 0:
				mod2 += 1
				num = int(num // 2)
			else:
				break
		while True:
			if num % 5 == 0:
				mod5 += 1
				num = int(num // 5)
			else:
				break

		table[50 + mod2][50 + mod5] += 1
		tablesum[50 + mod2][50 + mod5] += 1
		# print(mod2, mod5)

	ans = 0
	# 累積
	for i in range(98, -1, -1):
		for j in range(98, -1, -1):
			tablesum[i][j] += tablesum[i + 1][j]

	for i in range(98, -1, -1):
		for j in range(98, -1, -1):
			tablesum[i][j] += tablesum[i][j + 1]

	ans += (tablesum[50][50]) * (tablesum[50][50] - 1) // 2

	for i in range(1, 50):
		for j in range(1, 100):
			ans += table[i][j] * tablesum[100 - i][100 - j]
			# if table[i][j] * tablesum[100 - i][100 - j] > 0:
				# print(i, j)
				# print(table[i][j], tablesum[100 - i][100 - j])

	for j in range(1, 50):
		ans += table[50][j] * tablesum[50][100 - j]

	print(ans)


if __name__ == '__main__':
	main()