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.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class PowerOfTwo {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        Map<Integer, Integer> additions = new TreeMap<>();
        long count = 0;
        int i = 0;
        int a = 0;
        while (i != n) {
            a = in.nextInt();
            for (int s = 0; s <= 31; ++s) {
                int r = (1 << s) - a;
                if (additions.containsKey(r)) {
                    count += additions.get(r);
                }
            }
            if (!additions.containsKey(a)) {
                additions.put(a, 1);
            } else additions.put(a, additions.get(a) + 1);
        i++;
        }

        System.out.println(count);
    }
}

