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 Fortran (GNU Fortran 9.2.1) (judge verdict: Time Limit Exceeded)

program integer_product
  implicit none
  integer :: n, p2(200000) = 0, p5(200000) = 0, i, j, m
  integer(8) :: a
  character(16) :: s
  read(*,*) n
  do i = 1, n
    read(*,*) s
    m = len_trim(s)
    do j = 1, m
      if (s(j:j) == '.') then
        p2(i) = j - m
        p5(i) = j - m
        s(j:m - 1) = s(j + 1:m)
        s(m:) = ''
        exit
      end if
    end do
    read(s,*) a
    do while (mod(a, 2_8) == 0)
      a = a / 2
      p2(i) = p2(i) + 1
    end do
    do while (mod(a, 5_8) == 0)
      a = a / 5
      p5(i) = p5(i) + 1
    end do
  end do
  a = 0
  do i = 1, n - 1
    do j = i + 1, n
      if (p2(i) + p2(j) >= 0 .and. p5(i) + p5(j) >= 0) a = a + 1
    end do
  end do
  write(*,'(i0)') a
end program integer_product