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 pb push_back
#define S second
#define F first

using namespace std;
typedef long long ll;

typedef pair<int,int> pii;
const int maxn = 2e5 + 100;
#define int ll
int ind = 1;
int vis[maxn];
int bs[maxn];
int32_t main(){
    int n;
    cin >>n;
    multiset<int> v;
    for (int i =1;i <= n;i++){
        int a;
        cin >> a;
        bs[i] = a;
        v.insert(a);
    }
   // sort(v.begin(),v.end());
    int ans = 0;
    for (int i = 1;i <= n;i++){
        if (v.find(bs[i]) == v.end())continue;
        for (int j = 0;j < 32;j++){
            int b = (1 << j) - bs[i];
            if (b > bs[i] && v.count(b) != 0){
                auto it = v.find(b);
                ans++;
                v.erase(it);
            }
        }
    }
    cout << ans << endl;


}