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: Accepted)

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

typedef long long int int64;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))

int cmp(const void *a,const void *b){
  return *(int *)a-*(int *)b;
}

void run(void){
  int n;
  scanf("%d",&n);
  int *a=(int *)calloc(n,sizeof(int));
  int i;
  for(i=0;i<n;i++) scanf("%d",a+i);
  int *tmp=(int *)calloc(n,sizeof(int));
  int ans=0;
  for(i=30;i>=1;i--){
    qsort(a,n,sizeof(int),cmp);
    int len=0;
    int p=0;
    int q=n-1;
    while(p<q){
      if(a[p]+a[q]==(1<<i)){
	ans++;
	p++;
	q--;
      } else if(a[p]+a[q]<(1<<i)){
	tmp[len++]=a[p++];
      } else {
	tmp[len++]=a[q--];
      }
    }
    if(p==q){
      tmp[len++]=a[p];
    }
    memcpy(a,tmp,sizeof(int)*len);
    n=len;
  }
  printf("%d\n",ans);
}

int main(void){
  run();
  return 0;
}