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;
int N, ans,a;
multiset<int> S;
int main(){
    cin>>N;
    for (int i=1; i<=N; i++) {
        scanf("%d", &a);
        S.insert(a);
    }
    while (!S.empty()){
        int t = *(--S.end()), k;
        S.erase(--S.end());
        for (k=1; k<=t; k<<=1);
        if (S.find(k-t) != S.end()){
            ans++;
            S.erase(S.find(k-t));
        }
    }
    cout<<ans;
    return 0;
}