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 main(){
    int N;
    cin >> N;
    multiset<int> st;
    for(int i=0; i<N; i++){
        int a;
        cin >> a;
        st.insert(a);
    }
    int ans = 0;
    while(st.size()){
        auto it = prev(st.end());
        int a = *it;
        st.erase(it);
        int pw = 1;
        while(pw-a <= 0) pw *= 2;
        int b = pw-a;
        auto it2 = st.find(b);
        if(it2 != st.end()){
            ans++;
            st.erase(it2);
        }
    }
    cout << ans << endl;
}