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<iostream>
#include<stdio.h>
#include<string.h>
#include<set>
#include<map>
#include<algorithm>
using namespace std;
map<long long,int>p;
int n;
long long a[220000];
int main(){
	int ans;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%lld",&a[i]),p[a[i]]++;
	sort(a+1,a+1+n);
	for(int i=n;i>=1;i--){
		if(p[a[i]]==0)continue;
		p[a[i]]--;
		for(int j=1;j<=a[i]*2;j<<=1){
			if(j>a[i]){
				if(p[j-a[i]]){
					p[j-a[i]]--;
					ans++;
				}
				break;
			}
		}
	}
	printf("%d\n",ans);
}