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 powers_of_2 {
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        long a[]=new long[n];
        long count=0;
        HashMap<Long ,Integer> m = new HashMap<>();
        for(int i=0;i<n;i++){a[i]=sc.nextLong();}
        long p[]=new long[32];
        p[0]=1;
        for(int i=1;i<32;i++){p[i]=p[i-1]*2;}
        for(int i=0;i<n;i++){
            for(int j=0;j<32;j++){
                long x=p[j]-a[i];
                if(m.containsKey(x))
                    count+=m.get(x);}
            int z=0;
            if(m.containsKey(a[i]))
                z=m.get(a[i]);
            m.put(a[i], z+1);
        }
        System.out.println(count);
    }
}