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>
#define MAXN 250000
using namespace std;

int a[MAXN+10];
multiset<int> s;
map <int,int> b;

inline bool cmp(int x,int y){
	return y<x;
}
inline int get(int now){
	int x=pow(2,(int)(log2(now)));
	x*=2;	return x-now;
}

int ans;

int main(){

	int n;
	cin>>n;
	for(int i=1;i<=n;i++)
		scanf("%d",&a[i]),b[a[i]]++;
	sort(a+1,a+1+n,cmp);
	
	for(int i=1;i<=n;i++){
		int qwq=get(a[i]);
		
		if(a[i]==qwq&&b[qwq]<2)	continue;
		if(b[a[i]]&&b[qwq])	ans++,b[a[i]]--,b[qwq]--;
	}
	cout<<ans<<endl;
	return 0;
}