You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
import java.util.*;

public class PowerOf2 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        long result = 0;
        ArrayList<Long> s2 = new ArrayList<>();
        HashMap<Long, Long> s = new HashMap<>();
        long k = 2;
        while(k < 2000000000) {
            s2.add(k);
            k *= 2;
        }
        for(int i = 0; i < n; i++) {
            long a = in.nextLong();
            result += s.getOrDefault(a, 0L);
            for(int j = 0; j < s2.size(); j++) {
                long b = s2.get(j) - a;
                if (b > 0) s.put(b, s.getOrDefault(b, 0L)+1);
            }
        }
        System.out.println(result);
        in.close();
    }
}