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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

main()
{
    long long N, i, j, A[200000], P=0, ans=0;
    scanf("%lld", &N);
    for(i=0;i<N;i++)scanf("%lld",&A[i]);
    for(i=0;i<N-1;i++)
    {
        if(A[i]==0)continue;
        for(j=i+1;j<N;j++)
        {
            if(A[j]==0)continue;
            P=A[i]+A[j];
            printf("P(%d,%d)=%d\n",i,j,P);
            if((P&(P-1))==0)
            {
                ans++;
                A[j]=0;
            }
        }
    }
    printf("%lld",ans);
}