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 INCANT cin.tie(0), ios::sync_with_stdio(false), cout << fixed << setprecision(20);

int main(){
    INCANT;
    int n, res = 0;
    map<int, int> cnt;
    cin >> n;
    int a[n];
    
    for(auto& i: a){
        cin >> i;
    }
    sort(a, a + n, greater<int>());

    for(auto& i: a){
        if(cnt[i]){
            cnt[i]--;
            res++;
        }else{
            cnt[(1<<(32 - __builtin_clz(i))) - i]++;
        }
    }

    cout << res;
}
