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 <algorithm>
#define MN 200000
int n,a[MN+5],ans;
bool vis[MN+5];
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]);
	std::sort(a+1,a+1+n);
	for(int k=(1<<30);k>=2;k>>=1){
		int l=1;
		for(;a[n]>=(k>>1);n--){
			if(vis[n]) continue;
			while(l<n&&(vis[l]||a[l]+a[n]<k)) l++;
			if(l>=n) continue;
			if(a[l]+a[n]==k){
				vis[l]=vis[n]=true;
				ans++;
			}
		}
	}
	printf("%d\n",ans);
}