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.HashMap;
import java.util.Scanner;

public class PowersOfTwo {
    public static void main(String [] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int [] arr = new int[n];
        for(int i = 0; i < n; i++) 
            arr[i] = in.nextInt();
        HashMap<Long, Integer> map = new HashMap<Long, Integer>();
        long ans = 0;
        for (int i = 0; i < n; i++) {
            long a = arr[i];
            for (long j = 1; j <= 2000000000; j = j*2){
                if (map.containsKey(j - a))
                    ans += map.get(j - a);
            }
            if (!map.containsKey(a))
                map.put(a, 0);
            map.put(a, map.get(a) + 1);
        }
        System.out.println(ans);
    }
}
