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 PowersOfTwo {

    public static void main(String [] a){
        Scanner in = new Scanner(System.in);
        int n=in.nextInt();
        int ara[]=new int [100010];

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

        int power[]=new int[1000010];
        power[0]=1;
        for(int i=1;i<32;i++) {
            power[i]=power[i-1]*2;
        }

        HashMap<Integer,Integer> hm=new HashMap<Integer, Integer>();
        long res=0;

        for(int i=1;i<=n;i++) {
            for(int j=0;j<32;j++) {
                int x=power[j]-ara[i];
                if(hm.containsKey(x)) {
                    res+=hm.get(x);  }
            }
            if(hm.containsKey(ara[i])){
                hm.put(ara[i],hm.get(ara[i])+1);
            }
            else {
                hm.put(ara[i],1);
            }
        }
        System.out.println(res);
        }
}
