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: Time Limit Exceeded)

#include <stdio.h>
#include <math.h>

long compare_long(const void *a, const void *b){
    return *(long*)a-*(long*)b;
}

int main(){
    int n,i,j,k,index,sum=0;
    long s,max,value,temp;

    scanf("%d",&n);

    long a[n];
    for(i=0;i<n;i++){
        scanf("%ld",&a[i]);
    }

    qsort(a,n,sizeof(long),compare_long);

    s=(int)floor(log2(a[n-1]+a[n-2]));
    temp=a[n-1];
    for(j=s;j>0;j--){
        max=(long int)fmin(temp,(long int)pow(2,j));
        for(i=0;a[i]<=max&&i<n;i++){
            if(a[i]!=0) index=i;
        }
        for(k=index;k>=0;k--){
            if(a[k]==0) continue;
        	value=(long int)pow(2,j)-a[k];
        	for(i=0;i<k&&a[i]<=value;i++){
            	if(a[i]==value && a[i]!=0 && i!=k){
                	sum++;
                	a[i]=0;
                	a[k]=0;
                	break;
            	}
        	}
        }
    }
    printf("%d",sum);
    return 0;
}