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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.HashMap;
import java.util.HashSet;

public class B {

	// private static Scanner in = new Scanner(System.in);
	private static PrintStream out = System.out;
	private static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	// private static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

	public static void main(String[] args) throws IOException {
		int n = Integer.parseInt(in.readLine());
		String[] s = in.readLine().split(" ");
		HashMap<Long, Integer> data = new HashMap<Long, Integer>();
		long ans = 0;
		for (int i = 0; i < n; ++i) {
			long curr = Long.parseLong(s[i]);
			for (long pow = 1; pow <= 2000000000; pow *= 2)
				if (data.containsKey(pow - curr))
					ans += data.get(pow - curr);
			if (!data.containsKey(curr))
				data.put(curr, 0);
			data.put(curr, data.get(curr) + 1);
		}
		out.println(ans);
	}

}
