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>
#define rep(i, n) for(int i = 0; i < (n); i++)
using namespace std;

int getpair(int v){
    int res = 1;
    while(res <= v) res *= 2;
    return res - v;
}

int main(){
    int n, a;
    cin >> n;
    multiset<int> ms;
    rep(_, n){
        scanf("%d", &a);
        ms.insert(a);
    }
    int cnt = 0;
    while(!ms.empty()){
        auto maxv = end(ms);
        ms.erase(--maxv);
        auto p = ms.find(getpair(*maxv));
        if(p != end(ms)){
            ms.erase(p);
            cnt++;
        }
    }
    cout << cnt << "\n";
}