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 "algorithm"
# include "iostream"
# include "cstdio"
# include "set"

using namespace std;

const int maxm=2e5+10;
const int maxn=31;
int N,A[maxm];
multiset<int> LH;

int main(){
	register int i,j,k,Ans=0;
	scanf("%d",&N);
	for(i=1;i<=N;i++){
		scanf("%d",A+i);
		LH.insert(A[i]);
	}
	while(LH.size()){
		int i=*LH.rbegin();
		LH.erase(--LH.end());
		for(j=30;j;j--){
			k=(1<<j)-i;
			if(LH.find(k)!=LH.end()){
				multiset<int>:: iterator it=LH.lower_bound(k);
				LH.erase(it);
				Ans++;
				break;
			}
		}
	}
	printf("%d",Ans);
	return 0;
}