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<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>

#define fo(i,j,l) for(int i=j;i<=l;++i)
#define fd(i,j,l) for(int i=j;i>=l;--i)

using namespace std;
typedef long long ll;
const ll N=22e4;

int a[N];
int bz[N];
int n,ans;

int main()
{
	scanf("%d",&n);
	fo(i,1,n)scanf("%d",&a[i]);
	sort(a+1,a+n+1);
	fd(l,30,1){
		int k=1<<l;
		int kt=1;
		fd(i,n,1)if(!bz[i]){
			while(kt<i&&(bz[kt]||a[kt]+a[i]<k))++kt;
			if(kt==i)break;
			if(a[kt]+a[i]==k){
				bz[kt]=bz[i]=1;
				++ans;
			}
		}
	}
	cout<<ans;
}