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 <iostream>
#include <algorithm>
#include <map>

using namespace std;
 
typedef long long ll;
typedef unsigned long long ull;
#define REP(i, n) for(int i=0; i<n; i++)
 

ll A[300100];

int main(){
    int N;
    cin >> N;
    map<ll, ll> mp;
    REP(i,N){
        ll a;
        cin >> a;
        A[i] = a;
        mp[a]++;
    }
    sort(A,A+N, greater<ll>());
    ll ans = 0;
    REP(i,N){
        for(ll n = (1LL << 31); n >= 1; n /= 2){
            if(mp[A[i]] == 0) continue;
            ll diff = n - A[i];
            if(!mp.count(diff)) continue;
            int add = 0;
            if(A[i] == diff){
                add = mp[diff]/2;
            }
            else{
                add = min(mp[diff], mp[A[i]]);
            }
            ans += add;
            mp[diff] -= add;
            mp[A[i]] -= add;
        }
    }
    cout << ans << endl;
}