Problem:
Score : 600 points

Problem Statement

Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i.
He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Note that a ball cannot belong to multiple pairs.
Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

1 \leq N \leq 2\times 10^5

1 \leq A_i \leq 10^9

A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
   implicit none
   integer(8) n,beki(31)
   integer(8),allocatable,dimension(:)::a
   integer(8) ::i,j,k,counter=0
   read(*,*)n
   allocate(a(n))
   read(*,*)a
   call heapsort(n,a)
   do i=1,31
      beki(i)=2**i
   enddo
 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
   do i=n,2,-1
      do j=i-1,1,-1
         do k=1,31
            if(beki(k)==a(i)+a(j) .and. a(i)/=0 .and. a(j)/=0)then
               counter=counter+1
               a(j)=0
            endif
         enddo
      enddo
   enddo
   write(*,*)counter
contains
subroutine heapsort(n,array)
  implicit none
  integer(8),intent(in) :: n
  integer(8),intent(inout) :: array(1:n)
  
  integer(8) ::i,k,j,l
  integer(8) :: t
  
  if(n.le.0)then
     write(6,*)"Error, at heapsort"; stop
  endif
  if(n.eq.1)return

  l=n/2+1
  k=n
  do while(k.ne.1)
     if(l.gt.1)then
        l=l-1
        t=array(L)
     else
        t=array(k)
        array(k)=array(1)
        k=k-1
        if(k.eq.1) then
           array(1)=t
           exit
        endif
     endif
     i=l
     j=l+l
     do while(j.le.k)
        if(j.lt.k)then
           if(array(j).lt.array(j+1))j=j+1
        endif
        if (t.lt.array(j))then
           array(i)=array(j)
           i=j
           j=j+j
        else
           j=k+1
        endif
     enddo
     array(i)=t
  enddo

  return
end subroutine heapsort
end program main