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 Tp template<typename Ty>
#define Ts template<typename Ty,typename... Ar>
#define Reg register
#define RI Reg int
#define Con const
#define CI Con int&
#define I inline
#define W while
#define N 200000
using namespace std;
int n,a[N+5];map<int,int> s,g;
int main()
{
	RI i;for(scanf("%d",&n),i=1;i<=n;++i) scanf("%d",a+i),++s[a[i]];
	RI ans=0,t=1<<30;for(sort(a+1,a+n+1),i=n;i;--i)
	{
		if(g[a[i]]) {--g[a[i]];continue;}--s[a[i]];
		W((a[i]<<1)<t) t>>=1;s[t-a[i]]&&(--s[t-a[i]],++g[t-a[i]],++ans);
	}return printf("%d\n",ans),0;
}