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.ArrayList;
import java.util.HashMap;
import java.util.Scanner;

/**
 *
 * @author Begaiym
 */
public class NewClass3 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
         long y = 0;
         HashMap<Long, Integer> x = new HashMap<Long, Integer>();
       for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        for (int i = 0; i < n; ++i) {
            long s = a[i];
            for (long j = 1; j <= Integer.MAX_VALUE; j *= 2) {
                if (x.containsKey(j - s)) {
                    y += x.get(j - s);
                }
            }
            if (!x.containsKey(s)) {
                x.put(s, 0);
            }
            x.put(s, x.get(s) + 1);
        }
        System.out.println(y);

    }
}
