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 dd {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long ans=0;
        long []pow = new long[36];
        int in=0;
        for(long p =1;p <= (1L<<35);p<<=1){
            pow[in++]=p;
        }
        HashMap<Long,Integer> sum = new HashMap<>();
        for(int i =0;i<n;i++){
            long x = sc.nextLong();
            for(int j =0;j<32;j++){
                ans+=sum.getOrDefault(pow[j]-x,0);
            }
            sum.put(x,sum.getOrDefault(x,0)+1);
        }
        System.out.print(ans);

    }
}