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>
long buffer[10000000];
int judge(long x){
    while(x>1){
        if (x%2 != 0)return 0;
        x/=2;
    }
    return 1;
}
void merge(long a[],long left,long right){
    if(left<right){
        long axis=(left+right)/2,i=left,p=0,q=left,r=0;
        merge(a,left,axis);
        merge(a,axis+1,right);
        while(i<=axis)buffer[p++]=a[i++];
        while(i<=right && r<p)a[q++]=(a[i]>=buffer[r])?a[i++]:buffer[r++];
        while(r<p)a[q++]=buffer[r++];
    }
}

int main(void){
    long c=0;
    int N;
    scanf("%d",&N);
    long a[N];
    for(int i=0;i<N;i++)scanf("%ld",&a[i]);
    merge(a,0,N-1);
    for(int i=0;i<N-1;i++){
        for(int j=i+1;j<N;j++){
            if(a[i]!=-1 && a[j]!=-1){
                if(judge(a[i]+a[j])==1){
                    a[i]=-1;
                    a[j]=-1;
                    c++;
                    break;
                }
            }
        }
    }
    printf("%ld\n",c);
    return 0;
}