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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rept(k,i,n) for(int i = (k); i < (int)(n); i++)
typedef long long ll;


int main() {
    int n;cin>>n;
    vector<ll> by(0);
    vector<ll> a(n);
    vector<bool> ch(n,true);
    for(ll i=1;i<=20000000000;i*=2) by.push_back(i);
    rep(i,n)cin>>a[i];
    sort(a.begin(),a.end());
    int ans=0;
    
    for(int i=n-1;i>=0;i--){
        if(!ch[i]) continue;
        ll k=a[i];
        ll l=*upper_bound(by.begin(),by.end(),k); 
        ch[i]=false;   
        auto its=lower_bound(a.begin(),a.end(),l-k);
        if(*its==l-k&&ch[its-a.begin()]){
            ans++;
            ch[its-a.begin()]=false;
            (*its)--;
        }
    }
    cout<<ans<<endl;
    return 0;
}