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, a[200004];
multiset<int> s;

int over(int k) {
    int ans = 1;
    while (ans <= k) {
        ans *= 2;
    }
    return ans;
}

int main() {
    cin >> n;
    for (int i=0; i<n; i++) cin >> a[i], s.insert(a[i]);

    sort(a, a+n);
    
    int ans = 0;
    for (int i=n-1; ~i; i--) if (s.find(a[i]) != s.end()) {
        int k = over(a[i]) - a[i];
        s.erase(s.lower_bound(a[i]));
        if (s.find(k) != s.end()) {
            s.erase(s.lower_bound(k)); ans += 1;
        }
    }

    cout << ans;
}