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;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
int main(){
    int n,ans=0;
    cin>>n;
    vector<int> A(n);
    map<int,int> num;
    rep(i,n) cin>>A[i],num[A[i]]++;
    sort(A.begin(),A.end(),greater<int>());
    rep(i,A.size()){
        num[A[i]]--;
        if(num[A[i]]<0) continue;
        int a=pow(2,int(log2(A[i]))+1)-A[i];
        if(num[a]>0) ans++,num[a]--;
    }
    cout<<ans;
}