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;
typedef vector<int>VI;
int n;
VI a;
int work(VI a,int d){
	if(d<0)return 0;
	int i=0,j=a.size()-1,ans=0;
	VI b;
	for(;i<j;++i){
		for(;i<j-1 && a[i]+a[j]>(1<<d);--j);
		if(a[i]+a[j]==(1<<d))++ans,a[i]=a[j--]=-1;
	}
	for(int x:a)if(x!=-1)b.push_back(x);
	ans+=work(b,d-1);return ans;
}
int main(){
	scanf("%d",&n);a.resize(n);for(int&x:a)scanf("%d",&x);
	sort(a.begin(),a.end());
	printf("%d\n",work(a,30));
	return 0;
}