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.HashMap;
import java.util.Scanner;

public class powerTwo {

	public static void main(String[] args) {

		long power[] = new long[35];
		power[0] = 1;
		for (int i = 1; i < 35; i++)
			power[i] = power[i - 1] * 2;

	
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();

		HashMap<Long, Integer> hm = new HashMap<Long, Integer>();

		long counter = 0;

		for (int i = 0; i < n; i++) {
			long x = scan.nextLong();
			for (int j = 0; j < 35; j++) {
				if (hm.containsKey(power[j] - x))
					counter += hm.get(power[j] - x);
			}
			hm.put(x, hm.getOrDefault(x, 0) + 1);
		}
		scan.close();
		System.out.print(counter);
	}
}