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.
//http://codeforces.com/problemset/problem/702/B

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Map;

public class PowersofTwo {

    static StreamTokenizer st;
    static PrintWriter out;

    static String next() throws IOException {
        st.nextToken();

        return st.sval;
    }

    static int ri() throws IOException {
        st.nextToken();
        return (int) st.nval;
    }
    

    public static void main(String[] args) throws IOException {
        st = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

        //8
        //0 1 1 1 0 0 0 1
        
        int n = ri();
        int a[] = new int[n];
        ArrayList<Integer> pow = new ArrayList<>();
        Map<Integer,Integer> m = new HashMap<>();
        int p =1;
        for (int i = 0; i <= 30; i++)
        {
            pow.add(p<<i);
        }
        
       // System.out.println(pow.toString());
        long count = 0;
        for (int i = 0; i < n; i++) 
        {
            a[i] = ri();
            

            if (i > 0) 
            {
                for (int j = 0; j < pow.size(); j++)
                {

                    if (pow.get(j) - a[i] > 0 ) 
                    {
                        int num = pow.get(j) - a[i];
                       
                            if(m.get(num)!=null)
                                count+=m.get(num);

                    }
                }
            }
            // 1 1 1 1 1 1 1 1 1 1 
             if(m.get(a[i])==null)
            {
            m.put(a[i], 1);
            }
            else
                m.put(a[i], m.get(a[i])+1);
             
            
        }
               
        
        
       
        
        System.out.println(count);
    



    }
}