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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define mp make_pair
#define pb push_back
#define rep(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)


int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  int a[n];
  rep(i,n) cin >> a[i];
  sort(a,a+n);
  bool used[n];
  rep(i,n) used[i]=false;
  int ind=n-1;
  int pw=30;
  int ans=0;
  while(ind>=0){
    if(used[ind]){
      ind--;
      continue;
    }
    while(a[ind]/((int)pow(2,pw))==0){
      pw--;
    }
    int k=a[ind]-pow(2,pw);
    int e=upper_bound(a,a+n,pow(2,pw)-k) - a;
    int s=lower_bound(a,a+n,pow(2,pw)-k) - a;
    for(int j=s;j<e;j++){
      if(!used[j]){
	if(j!=ind){
	  ans++;
	  used[ind]=true;
	  used[j]=true;
	  if(ind>=1){
	    if(a[ind-1]==a[ind] && a[j]==a[j+1]){
	      ind--;
	      continue;
	    }
	  }
	  break;
	}
      }
    }
    ind--;
  }
  cout << ans << endl;
  return 0;
    

}