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;
const int inf=0x3f3f3f3f, maxn=200007, mod=1e9+7;

int a[maxn];
long long h[maxn];
int n,ans;
int main(){
	h[0]=1;
	for(int i=1;i<=31;i++)h[i]=h[i-1]<<1;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	for(int k=30;k>=1;k--){
		for(int i=1,j=n;i<j;i++){
			if(a[i]!=inf){
				while(j>i&&(a[j]==inf||a[i]+a[j]>h[k]))j--;
//				cout<<a[i]<<' '<<a[j]<<' '<<h[k]<<endl;
				if(j>i&&a[j]!=inf&&a[i]+a[j]==h[k])ans++,a[i]=a[j]=inf;
			}
		}
	}
	printf("%d\n",ans);
    return 0;
}
