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.*;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		
		int N = Integer.parseInt(bf.readLine());
		
		String line = bf.readLine();
		String[] tmp = line.split(" ");
		
		bf.close();
		
		Set<Integer> powerOf2 = new HashSet<Integer>();
		HashMap<Integer, Integer> freq = new HashMap<>();
		
		for(int i = 0 ; i <= 31 ; i++) powerOf2.add(1 << i);
		
		long ctr = 0;
		
		for(int i = 0 ; i < N ; i++){
			int idx = Integer.parseInt(tmp[i]);
			
			for(Integer it : powerOf2){
				
				if(it-idx >=0){
					Integer pom = freq.get(it - idx);
					if(pom != null){
						ctr += pom;
					}
				}
			}
			
			Integer pom = freq.get(idx);
			if(pom == null) freq.put(idx, 1);
			else freq.put(idx, pom+1);
		}
		
		System.out.println(ctr);
	}
}
