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;
typedef long long ll;

void solve(long long N, vector<long long> A){
	map<long long, ll> mp;

	for(int i = 0; i < N; ++i) {
		mp[A[i]]++;
	}
	sort(A.begin(), A.end());
	A.erase(unique(A.begin(), A.end()), A.end());
	long long res = 0;
	for(int k = 30; k > 0; --k) {
		long long t = 1LL << k;
		for(int i = 0; i < A.size() && A[i] <= t / 2; ++i){
			ll a = A[i];
			ll b = t - a;
			if (a != b) {
				ll m = min(mp[a], mp[b]);
				mp[a] -= m;
				mp[b] -= m;
				res += m;
			} else {
				res += mp[a] / 2;
				mp[a] %= 2;
			}
		}
	}
	cout << res << endl;
}

int main(){	
	long long N;
	scanf("%lld",&N);
	vector<long long> A(N-1+1);
	for(int i = 0 ; i <= N-1 ; i++){
		scanf("%lld",&A[i]);
	}
	solve(N, A);
	return 0;
}