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 sys
input = sys.stdin.readline
def waru(N,num):
  cnt = 0
  while N%num==0:
    N //= num
    cnt += 1
  return cnt
def solve():
  N = int(input())
  num = [[0]*101 for _ in range(101)]
  lis = [0]*N
  for i in range(N):
    a = int(round(float(input())*10**9))
    p,q = waru(a,2)-9-50,waru(a,5)-9-50
    num[p][q] += 1
    lis[i] = [p,q]
  cum2 = [[0]*101 for _ in range(101)]
  for i in range(99,-1,-1):
    for j in range(99,-1,-1):
      cum2[i][j] = cum2[i+1][j]+cum2[i][j+1]-cum2[i+1][j+1]+num[i][j]
  ans = 0
  for i in range(N):
    p,q = lis[i]
    x,y = p+50,q+50
    p = -x-50
    q = -y-50
    ans += cum2[p][q]
    if x>=0 and y>=0:
      ans -= 1
  return ans//2
print(solve())