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: Wrong Answer)

program abc34
 implicit none
 integer::N,ia,ib,ic,c=0
 integer,parameter::srk=selected_real_kind(16)
 real(srk),allocatable::a(:)
 read(*,*)N
 allocate(a(N))
 do ia=1,N
  read(*,*)a(ia)
 end do
 do ib=1,N-1
  do ic=ib+1,N
   if(a(ib)*a(ic)==floor(a(ib)*a(ic)))then
    c=c+1
   end if
  end do
 end do
 print'(i0)',c
 deallocate(a)
end program abc34