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;
using ll = long long;
constexpr int N = 2e5+5;
int n, a[N];
unordered_map<ll,int> mp;
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> n;
    for(int i = 0; i < n; i++) cin >> a[i];
    sort(a, a+n);
    int ans = 0;
    ll pw = 1ll<<40;
    for(int i = n - 1; i >= 0; i--) {
        if(mp[a[i]]) {
            ans++;
            mp[a[i]]--;
            continue;
        }
        while(pw/2>a[i]) pw/=2;
        mp[pw-a[i]]++;
    }
    cout << ans;
    return 0;
}