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;

const int maxn = 200005;

int n, a, ans;
multiset < int > b;

signed main () { 
    scanf("%d", &n);
    for (int i = 0; i < n; ++i) {
        scanf("%d", &a);
        b.insert(a);
    }
    while (!b.empty()) {
        int x = *prev(b.end());
        b.erase(prev(b.end()));
        int to = (1 << (int(double(log(double(x))) / log(2.0)) + 1));
        auto it = b.find(to - x);
        if (it != b.end()) {
            b.erase(it);
            ++ans;
        }
    }
    printf("%d\n", ans);
}
