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 a {
	 public static void main(String [] a){
	        Scanner in = new Scanner(System.in);
	        int n=in.nextInt();
	        int ara[]=new int [1000000];

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

	        int power[]=new int[1000000];
	        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);
	        }

}