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.*;
import java.math.*;

public class Main{
  
  static int n, x;
  static long ans;
  static Map<Integer, Integer> M;
  
  public static void main(String args[]) throws Exception{
    // Scanner in = new Scanner(new File("a.in"));
    // PrintWriter out = new PrintWriter(new File("a.out"));
    Scanner in = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
    
    M = new HashMap<Integer, Integer>();
    
    n = in.nextInt();
    
    for(int i = 1; i <= n; i++){
      x = in.nextInt();
      
      for(int j = 1; j <= 30; j++){
        int d = (1 << j) - x;
        if(d > 0 && M.containsKey(d)) ans += M.get(d);
      }

      if(M.containsKey(x)) M.put(x, M.get(x) + 1);
      else M.put(x, 1);
    }
    out.println(ans);
    out.close();
  }
}