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 N 200006
using namespace std;
map<int,int>g;
int n,x,c[N],p[36];
int main()
{
	scanf("%d",&n);p[0]=1;
	for(int i=1;i<=n;i++)scanf("%d",&c[i]),g[c[i]]++;
	sort(c+1,c+n+1);
	for(int i=1;i<=30;i++)p[i]=p[i-1]<<1;
	for(int i=30,j=n;i>=1&&j>=1;i--){
		while(c[j]<p[i-1])i--;
		for(;c[j]>=p[i-1]&&j>=1;j--){
			if(g[c[j]]<=0)continue;g[c[j]]--;
			if(g[p[i]-c[j]]>0)g[p[i]-c[j]]--,x++;
		}
	}
	printf("%d\n",x);
}