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 n,a,b;
multiset<ll> s;
int main(){
    cin>>n;
    while(n--)cin>>a,s.insert(a);
    while(s.size()){
        a=*s.rbegin();
        s.erase(s.find(a));
        ll p=1;
        while(p<=a)p*=2;
        if(s.find(p-a)!=s.end())s.erase(s.find(p-a)),b++;
    }
    cout<<b<<'\n';
}