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;
int n,i,j,ans,now,a[200001];
map<int,int>g;
int main(){
	scanf("%d",&n);
	for(i=1;i<=n;i++)scanf("%d",&a[i]),g[a[i]]++;
	sort(a+1,a+n+1);
	for(i=n;i;i--)if(g[a[i]]){
		for(j=31;j>=0;j--){
			//printf("%d %d\n",i,j);
			now=1<<j;
			if(now<a[i])continue;
			now-=a[i];
			if(now!=a[i]&&g[now]||now==a[i]&&g[a[i]]>1){
				g[a[i]]--;g[now]--;ans++;break;
			}
		}
	}
	printf("%d",ans);
}