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<cstdio>
#include<algorithm>
inline void read(int&r)
{
	register char c;r=0;
	do c=getchar();while(c<'0'||c>'9');
	do r=r*10+c-'0',c=getchar();while(c>='0'&&c<='9');
}

int a[200000];
bool b[200000];
int main()
{
	int n,i,j,x,s=0;read(n);
	for(i=0;i<n;i++)read(a[i]);
	std::sort(a,a+n);
	for(i=n;i--;)
		if(!b[i])
		{
			x=(1<<(32-__builtin_clz(a[i])))-a[i];
			j=std::lower_bound(a,a+n,x)-a;
			if(j<i&&a[j]==x&&!b[j])b[j]=true,s++,a[j]--;
		}
	printf("%d\n",s);
}