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 <iostream>
#include<algorithm>
#include <cstdio>

using namespace std;

int main()
{

	unsigned long long i, j, n, ans;
	unsigned long long *A = new unsigned long long[200002]();
	char *have = new char[1000000002]();
	unsigned long long twoTable[29] = { 4 };

	cin >> n;
	for (i = 1; i <= n; i++) {
		cin >> A[i];
		have[A[i]]++;
	}
	
	for (i = 1; i < 29; i++) {
		twoTable[i] = twoTable[i - 1] * 2;
	}

	sort( &A[0] , &A[n + 1]);

	ans = 0;
	for (i = n; i > 0; i--) {
		if(have[A[i]]==true){
				for (j = 0; j < 29; j++) {
				if ((twoTable[j] > A[i]) && (twoTable[j]-A[i]<1000000001)) {
					int limit = 0;
					if (twoTable[j] == A[i] * 2) { limit = 1; }
					if (have[twoTable[j] - A[i]] > limit ) {
//						cout << twoTable[j] << " / " << A[i] << endl;
						have[twoTable[j] - A[i]]--;
						have[A[i]]--;
						ans++;
						j = 29;
					}
				}
			}
		}
	}


	delete have;

	cout << ans << endl;
	return 0;
}