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.*;
import java.io.*;

public class Solution{
    
    static class FastReader { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
    
	public static void main (String[] args) {
	    FastReader sc = new FastReader();
	    PrintWriter out = new PrintWriter(System.out);
	    
	    ArrayList<Long> pow2 = new ArrayList<Long>();
	    long val2 = 1;
	    for(int i=1;i<=32;i++){
	        val2*=2;
	        pow2.add(val2);
	    }
	    
	    HashMap<Long, Long> map = new HashMap<Long, Long>();
	    long ans = 0;
	    int n = sc.nextInt();
	    
	    for(int i=0;i<n;i++){
	        long val = sc.nextLong();
	        for(long a : pow2){
	            if(map.containsKey(a-val)){
	                ans+=map.get(a-val);
	            }
	        }
	        Long a = map.get(val);
	        map.put(val, ((a==null)?1L:a+1L) );
	    }
	    
	    out.println(ans);
	    out.close();
	}
}