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<algorithm>
#define LL long long
using namespace std;
LL A[505050];
int n,ans;
bool Tag[2020202];
int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;i++)
		scanf("%lld",&A[i]);
	sort(A+1,A+n+1);
	for (LL x=(1ll<<31);x>0;x>>=1ll){
		int r=n;
		for (int l=1;l<=n;l++){
			if (l>=r) break;
			if (Tag[l]) continue;
			while (r>l&&(Tag[r]||A[l]+A[r]>x)) r--;
			if (l>=r) break;
			if (A[l]+A[r]==x){
				Tag[l]=1; Tag[r]=1; ans++;
			}
		}
	}
	cout<<ans;
}