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;

multiset < int > arr; int N , cnt;

int main(){
	cin >> N;
	for(int i = 1 , x ; i <= N ; ++i){cin >> x; arr.insert(x);}
	while(!arr.empty()){
		int t = *--arr.end(); arr.erase(arr.find(t)); int x = 1 << (int)(log2(t + 0.1) + 1);
		if(arr.find(x - t) != arr.end()){arr.erase(arr.find(x - t)); ++cnt;}
	}
	cout << cnt; return 0;
}