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.ArrayList;
import java.util.HashMap;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		ArrayList<Long> bin = new ArrayList<Long>();

		for (long i = 2; i < 2000000000; i *= 2) {
			bin.add(i);
		}

		HashMap<Long, Long> hm = new HashMap<Long, Long>();
		long n = sc.nextInt(), sum = 0;
		for (int i = 0; i < n; i++) {
			long a = sc.nextLong();
			for (long f : bin) {
				if (f > a) {
					if (hm.get(f - a) != null) {
						if (hm.get(f - a) > 0) {
							sum += hm.get(f - a);
						}
					}
				}
			}
			if (hm.get(a) != null) {
				hm.put(a, hm.get(a) + 1);
			} else {
				hm.put(a, (long) 1);
			}

		}
		sc.close();
		System.out.println(sum);
	}
}
