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.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)

int N,ans = 0;
multiset<int> A;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);

	cin >> N;

	REP(i,N){
      	int x;
		cin >> x;
      	A.insert(x);
	}

	while(A.size() > 1){
		int x = *prev(A.end());
		A.erase(prev(A.end()));
		int d = 1;
		while(d <= x){
			d = d << 1;
		}
		if(A.find(d - x) != A.end()){
			ans++;
			A.erase(A.find(d - x));
		}
	}

	cout << ans << endl;

}
