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 Ruby (2.7.1) (judge verdict: Wrong Answer)

*A = $<.read.split
N = A.shift.to_i
C = (0...19).map { [0]*19 }
s = 0
A.each {|a|
  a = (a.to_f * 4_000_000_000 + 2).to_i >> 2
  i = 0
  i += 1  while a[i] == 0
  a >>= i
  i = [i,18].min
  j,r = -1,0
  (j += 1; a,r = a.divmod 5)  while r == 0
  j = [j,18].min
  s += C[18-i,18].sum {|c| c[18-j,18].sum }
  C[i][j] += 1
}
p s