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[] argv) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] input = new int[n];
        for (int i = 0; i < n; i++)
            input[i] = in.nextInt();

        HashMap<Integer, Integer> map = new HashMap<>();

        for (int a : input)
            if (map.containsKey(a))
                map.put(a, map.get(a) + 1);
            else
                map.put(a, 1);

        long result = 0;
        for (int a : input) {
            map.put(a, map.get(a) - 1);
            for (int i = 1; i < 32; i++){
                if (map.containsKey((int) Math.pow(2, i) - a)){
                    result += map.get((int) Math.pow(2, i) - a);
                }
            }
        }
        System.out.println(result);
        in.close();
    }
}