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 Training {

    public static void main(String [] args){
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        int a[]=new int [200000];

        for(int i=1;i<=n;i++) {
            a[i]=sc.nextInt();
        }

        int b[]=new int[200000];
        b[0]=1;
        for(int i=1;i<32;i++) {
            b[i]=b[i-1]*2;
        }


        HashMap<Integer,Integer> map=new HashMap<>();
        long ans=0;
        int p;
        for(int i=1;i<=n;i++) {
            for(int j=0;j<32;j++) {
                int x=b[j]-a[i];
                if(map.containsKey(x)) ans+=map.get(x);
                //System.out.println(map.get(x));
            }
            if(map.containsKey(a[i])) {
                p=map.get(a[i])+1;
                map.put(a[i],p);
            }
            else map.put(a[i],1);
        }
        System.out.println(ans);
    }
}