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>
using namespace std;
const int N=200005;
int to[N],n,x,cnt,ans;
map<int,int> Map;
int cmp(int x,int y){
	return x>y;
}
int main(){
	scanf("%d",&n);
	while (n--){
		scanf("%d",&x);
		if (!Map.count(x))to[++cnt]=x;
		Map[x]++;
	}
	sort(to+1,to+cnt+1,cmp);
	for (int i=1;i<=cnt;i++)
		for (int j=0;j<=30;j++)
			if ((1<<j)>to[i])while (Map[to[i]]>0&&Map[(1<<j)-to[i]]>0){
				if (to[i]*2==(1<<j)&&Map[to[i]]==1)break;
				Map[to[i]]--,Map[(1<<j)-to[i]]--,ans++;
			}
	printf("%d\n",ans);
}
