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>

#define REP(i ,n) for(int i=0 ;i < n; i++)
#define REPB(i ,n) for(int i=n; i >= 0; i--)
#define FOR(i ,m ,n) for(int i=m; i < n; i++)
#define FORB(i, m, n) for(int i=m; i>= n; i--)
#define ll long long
#define pb push_back
#define popb pop_back
#define debug(i) cout << i << endl
using namespace std;
int main(){
  int n, at;
  int ans = 0;
  vector<int> a;

  cin >> n;

  REP(i,n){
      cin >> at;
      a.pb(at);
    }
    sort(a.begin(), a.end());

    REPB(i, (n-1)){
      if(a[i] < 0) continue;
      int max = log2(a[i] * 4);
        REP(j,i){
          REP(k, max){
            int sum = a[i] + a[j];
            int ch = pow(2, k);
            if(sum == ch){
                ans++;
                a[j] = -2000;
              }
          }
      }
    }
    cout << ans << endl;
    return 0;
}