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 Powers2 
{

	public static void main(String[] args) throws NumberFormatException, IOException 
	{
		BufferedReader br = new BufferedReader (new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] arr = new int[n];
		HashMap<Integer , Integer> hm = new HashMap<>();
		String[] inp = br.readLine().split(" ");
	
		for(int i=0;i<n;i++)
		{
			arr[i] = Integer.parseInt(inp[i]);
			if(hm.containsKey(arr[i]))
				hm.put(arr[i], hm.get(arr[i])+1);
			else
				hm.put(arr[i], 1);
		}
		Long c=0l;
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<=31;j++)
			{
				int ans =(int)( Math.pow(2, j)) - arr[i];
				if(hm.containsKey(ans))
				{
				if(ans == arr[i])
					c+=hm.get(ans)-1;
				else
					c+=hm.get(ans);
				}
			}
		}
		System.out.println(c/2);
	}

}
