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)

#include<stdio.h>
#include<stdlib.h>

long long beki[64];

int compare(const void *a, const void *b){
	long long int *A = (long long int *)a;
	long long int *B = (long long int *)b;
	if (*A < *B) return 1;
	if (*A > *B) return -1;
	return 0;
}

int main(){
	long long N,i,ans=0;
	scanf("%lld",&N);
	long long A[N];
	int used[N];
	for(i=0;i<N;i++)used[i]=0;
	for(i=0;i<N;i++)scanf("%lld",&A[i]);
	
	qsort(A,N,sizeof(long long),compare);
	
	beki[0]=1;
	for(int i=1;i<64;i++)beki[i]=beki[i-1]*2;
	
	int b=63;
	for(i=0;i<N;i++){
		if(used[i]==1)continue;
		while(beki[b]>A[i]*2)b--;
		for(int j=i+1;j<N && A[j]>=beki[b]-A[i];j++){
			if(A[j]=beki[b]-A[i] && used[j]==0){
				ans++;
				used[i]=used[j]=1;
				break;
			}
		}	
	}
	printf("%lld\n",ans);
	return 0;
}