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 <iostream>
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,a,ans;
vector<ll> v;
map<ll,ll> mp;
ll f(ll n){
    ll m=1;
    while(m<=n)m*=2;
    return m-n;
}
int main(void){
    cin>>n;
    for(int i=0;i<n;i++){
        cin>>a;
        mp[a]++;
        v.push_back(a);
    }
    sort(v.begin(),v.end());
    reverse(v.begin(),v.end());
    for(int i=0;i<n;i++){
        if(mp[v[i]]>0)mp[v[i]]--;
        else continue;
        if(mp[f(v[i])]>0){
            mp[f(v[i])]--;
            ans++;
        }
    }
    cout<<ans<<endl;
}
