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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include <vector>
#include <iostream>
#include<algorithm>
#include<string>
#include <map>
#include <queue>
#include <stack>
#include<set>
#include<tuple>

#define DIV 1000000007
#define TE 2e5
using namespace std;
using ll = long long;
using ldb = long double;

int main() {
	int N; cin >> N ;
	vector<ll> a(N);
	map<ll, int> cnt;
	for (int i = 0; i < N; i++) {
		cin >> a[i];
		cnt[a[i]]++;
	}

	vector<ll> twos(35);
	twos[0] = 1;
	for (int i = 1; i < 35; i++) {
		twos[i] = twos[i - 1] * 2;
	}

	ll ans = 0;
	for (int i = 0; i < N; i++) {
		for (int j = 34; j >= 0; j--) {
			if (cnt[a[i]] != 0 && cnt[twos[j] - a[i]] != 0) {
				if (a[i] == twos[j] - a[i] && cnt[a[i]] < 2)continue;
				cnt[a[i]]--, cnt[twos[j] - a[i]]--;
				ans++;
				//cout << a[i] << " " << twos[j] - a[i] << endl;
				break;
			}
		}
	}

	cout << ans << endl;
}