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.Map;
import java.util.Scanner;
import java.util.TreeMap;

public class Main {
	public static void main(String[] argv) {
	
	
	Scanner in = new Scanner(System.in);
	
		int n = in.nextInt();	
	
		int a[] = new int[n];
		Map<Integer, Integer> map = new TreeMap<>();
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
			
			Integer prev = map.get(a[i]);
			if (prev == null)
				prev = 0;
			map.put(a[i], prev + 1);
		}
		long ans = 0;
		for (int i = 0; i < n; i++) {
			Integer cnt = map.get(a[i]);
			map.put(a[i], cnt - 1);
			for (int j = 0; j < 31; j++) {
				int sum = (1 << j) - a[i];
				Integer rem = map.get(sum);
				if (rem != null)
					ans += rem; 
			}
			map.put(a[i], cnt);
		}
		
		System.out.println(ans >> 1L);
	
}
}


