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 <stdio.h>
#include <iostream>
#include <algorithm>
#include <map>
using namespace std;
map<int,int> mp;
int a[200010];
int main(){
	int i,k,n,ans=0;
	scanf("%d",&n);
	for(i=1;i<=n;i++) scanf("%d",&a[i]),mp[a[i]]++;
	sort(a+1,a+n+1);
	for(i=n;i>=1;i--)
		if(mp[a[i]]){
			mp[a[i]]--;
			for(k=30;k>=0;k--)
				if(mp[(1<<k)-a[i]]) ans++,mp[(1<<k)-a[i]]--;
		}
	printf("%d",ans);
	return 0;
}
