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.io.*;
    import java.util.*;
    import java.text.*;
    import java.math.*;
    import java.util.regex.*;


    public class Solution {

        public static long mod = 1000000007;
     public static void main(String[] args) throws IOException{



//         BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
         PrintWriter  pw = new PrintWriter(System.out);
         Scanner in = new Scanner(System.in);

        int n = in.nextInt();
        HashMap<Long, Integer> map = new HashMap<>();
         ArrayList<Long> list = new ArrayList<>();
         long k = 1;
         while(k<Math.pow(10, 10))
         {
             list.add(k);
             k *= 2;
         }
         long ans = 0;
         for(int i=0; i<n; i++)
         {
    
             long a = in.nextLong();
           // pw.print(map);
                
             for(int j=0; j<list.size(); j++)
             {
                 if(map.get(list.get(j)-a)!=null)
                 {
                  //  pw.println(map.get(list.get(j) - a)+" "+list.get(j));
                     
                     ans += map.get(list.get(j)-a);
             
                 }
             }
             if(map.get(a)!=null)
                  map.put(a, map.get(a)+1);
             else
                 map.put(a, 1);
             
         }
         
         pw.print(ans);
         
         pw.flush();
         pw.close();

       }
    }
