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 R702B {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n=in.nextInt();
        long ans=0;
        ArrayList<Integer>s2=new ArrayList<>();
        HashMap<Integer, Integer>s=new HashMap<>();
        long k=2;
        while(k<(int)2e9) {
            s2.add((int)k);
            k*=2;
        }
        for(int i=0; i<n; i++) {
            int a=in.nextInt();
            ans+=s.getOrDefault(a, 0);
            for(int j=0; j<s2.size(); j++) {
                int b=s2.get(j)-a;
                if (b>0) s.put(b, s.getOrDefault(b, 0)+1);
            }
        }
        System.out.println(ans);
    }
}
