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 = 200010;
int n, a[maxn];
unordered_map<int, int> mp;

int main() {
    cin >> n;
    for (int i = 1; i <= n; i++) {
        cin >> a[i]; mp[a[i]]++;
    }
    sort(a + 1, a + n + 1);
    int ans = 0;
    for (int i = n; i; i--) if (mp[a[i]]) {
        mp[a[i]]--;
        for (long long j = 1; j <= 2e9; j *= 2) {
            if (j > a[i] && mp[j - a[i]]) {
                mp[j - a[i]]--, ans++; break;
            }
        }
    }
    cout << ans << endl;
    return 0;
}