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 rep(i,x,y) for (int i=(x);i<=(y);i++)
using namespace std;
const int N=2e5+5,inf=1e9;
int n,a[N],ans; map<int,int> mp;
int main(){
	scanf("%d",&n);
	rep (i,1,n){
		scanf("%d",&a[i]); mp[a[i]]++;
	}
	sort(a+1,a+1+n,greater<int>());
	rep (i,1,n){
		if (!mp[a[i]]) continue;
		int j;
		for (j=1;j<=inf;j*=2) if (j>a[i]) break;
		mp[a[i]]--;
		if (mp.count(j-a[i])&&mp[j-a[i]]) mp[j-a[i]]--,ans++; else mp[a[i]]++;
	}
	printf("%d\n",ans);
	return 0;
}