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 <algorithm>
#include <iostream>
#include <vector>
#include <map>
using namespace std;
int MSB1(long long x) { int d = 0; while ((1LL << d) <= x) d++; return d; }

int main() {
    int n; cin >> n;
    vector<int> a(n);
    map<int, int> cnt;
    for (auto &ai: a) cin >> ai, cnt[ai]++;
    sort(a.rbegin(), a.rend());
    int ans = 0;
    for (int val: a) if (cnt[val]) {
        cnt[val]--;
        int rem = (1 << MSB1(val)) - val;
        if (cnt[rem]) ans++, cnt[rem]--;
    }
    cout << ans << endl;
    return 0;
}
