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<cstdio>
#include<cstring>
#include<map> 
#include<algorithm>
#define maxn 200020
#define ll long long
using namespace std;
int n,a[maxn];
map<int,int>mp;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",&a[i]),++mp[a[i]];
	sort(a+1,a+n+1);
	int ans=0;
	for(int i=n;i;--i)
	if(mp[a[i]]>0){
		int x=1;
		while(x<=a[i])x<<=1;
		int bi=x-a[i];
		if(mp.count(bi)&&(mp[bi]>(a[i]==bi)))--mp[bi],--mp[a[i]],++ans;
	}
	printf("%d\n",ans);
	return 0;
}