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 lol(i,n) for(int i=0;i<n;i++)
typedef long long ll;

using namespace std;
int main(){
    ll n; cin>>n;
    multiset<ll> S;
    lol(i,n){
	ll a;cin>>a;
	S.insert(a);
    }
    ll ans=0;
    while(S.size()>=2){
	auto i=--S.end();
	ll x=*i;
	S.erase(i);
	ll t; for(t=1;t<=x;t*=2);
	auto j=S.find(t-x);
	if(j!=S.end()){
	    ans++;
	    S.erase(j);
	}
    }
    cout<<ans<<endl;
    return 0;
}
