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 <iostream>
#include <map>
using namespace std;

int main()
{
    int n;
    cin >> n;
    map<int, int> mp;
    for(int i = 0; i < n; i++){
        int a;
        cin >> a;
        mp[a]++;
    }
    int t = (1 << 30);
    int ans = 0;
    for(auto itr = mp.rbegin(); itr != mp.rend(); itr++){
        int a = itr->first, c = itr->second;
        while(t > a * 2) t /= 2;
        if(t == a * 2) ans += c / 2;
        else{
            ans += min(mp[a], mp[t - a]);
            mp[t - a] -= min(mp[a], mp[t - a]);
        }
    }
    cout << ans << endl;
}
