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: Time Limit Exceeded)

from collections import defaultdict
def decomp(m):
    pf=defaultdict(int)
    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]+=1
            m//=i
    if m>1:pf[m]=1
    return (pf[2], pf[5])

n=int(input())
table=[[0]*50 for _ in range(50)]
ans=0
for i in range(n):
    a=input()
    ax=round(float(a)*(10**9))
    p2,p5=decomp(ax)
    if i!=0:
        for j in range(18-p2,19):
            ans+=sum(table[j][18-p5:])
    table[p2][p5]+=1

print(ans)