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>
int n,ans,a[200100];
std::map<int,int>cnt;
int main(){
	scanf("%d",&n);
	for (register int i=1;i<=n;++i)
		scanf("%d",a+i);
	std::sort(a+1,a+1+n);
	for (register int i=n;i>=1;--i){
		int tem=1,x=a[i],f=0;
		for (register int j=1;j<=30;++j){
			tem<<=1;
			int v=tem-x;
			if (v<0) continue;
			if (!cnt[v]) continue;
			cnt[v]--,ans++,f=1;break;
		}
		if (!f) cnt[x]++;
	}
	printf("%d\n",ans);
}