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<cstdlib>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<map>
using namespace std;

const int N=200005;

int n,t,ans;
int f[N],a[N];
map<int,int> cnt;

int main(){
	int i,j,k;
	scanf("%d",&n);
	for (i=1;i<=n;i++) scanf("%d",&a[i]),cnt[a[i]]++;
	sort(a+1,a+1+n);
	for (i=n;i>=1;i--){
		if (!cnt[a[i]]) continue;
		cnt[a[i]]--;
		for (j=1;1ll*j*2<=1ll*(a[i]+a[i]);j=j*2);
		if (cnt[j-a[i]]){
			ans++;
			cnt[j-a[i]]--;
		}
	}
	printf("%d\n",ans);
	return 0;
}