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>
using namespace std;
typedef long long ll;
ll f(ll x){
	for(ll i=0;i<40;i++){
		if((1ll<<i)<=x&&x<(1ll<<(i+1))){
			return (1ll<<(i+1));
		}
	}
}
int main() {
	ll n,a[214514];
	map<ll,ll>mp;
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
		mp[a[i]]++;
	}
	sort(a,a+n);
	ll ans=0;
	for(int i=n-1;i>=0;i--){
		ll x=f(a[i]);
		if(mp[x-a[i]]&&mp[a[i]]){
			if(x==2*a[i]){
				if(mp[a[i]]>=2){
					mp[a[i]]-=2;
					ans++;
				}
			}else{
				mp[a[i]]--;
				mp[x-a[i]]--;
				ans++;
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}
