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 FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
	
using namespace std;
typedef long long ll;
const int MAX_N=2e5;
int N;
ll A[MAX_N];
int main(){
	cin>>N;
	map<ll,int> mp;
	REP(i,N){
		cin>>A[i];
		mp[A[i]]++;
	}
	ll ans=0;
	sort(A,A+N);
	REP(i,N){
		ll a=A[N-1-i];
		ll p2=1;
		while(p2<=a){
			p2<<=1;
		}
		if (a!=p2-a){
			ll tmp=min(mp[a],mp[p2-a]);
			
			ans+=tmp;
			mp[a]-=tmp;
			mp[p2-a]-=tmp;
		}else{
			ans+=mp[a]/2;
			mp[a]=0;
		}
	}
	cout<<ans<<endl;
		
	return 0;
}