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 Dhrubo
 */
public class Edu15B {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        ArrayList<Long>list = new ArrayList<Long>();
        Long array[] = new Long[32];
        for(int i = 0; i <t;i++)
        {
            list.add(sc.nextLong());
        }
        array[0] = 2L;
        for(int i = 1; i <32;i++)
        {
            array[i] = array[i-1]*2;
        }
        HashMap<Long, Long>map = new HashMap<Long, Long>();
        long count = 0;
        for(int i = 0; i <t;i++)
        {
            for(int j = 0; j<32;j++)
            {
                Long x = array[j]-list.get(i);
                if(map.containsKey(x))
                {
                    count = count+map.get(x);
                }
            }
            if(map.containsKey(list.get(i)))
            {
                map.put(list.get(i), map.get(list.get(i))+1);
            }
            else
            {
                map.put(list.get(i), 1L);
            }
        }
        System.out.println(count);
        
    }
    
}