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.*;

public class SolutionA {
	public static void main(String[] args) {
		Scanner sr = new Scanner(System.in);
		int n = sr.nextInt();
		long[] arr = new long[n];

		long[] powers = new long[32];
		for (int i = 0; i < 32; i++) {
			if (i == 0) {
				powers[i] = (long)2;
			} else {
				powers[i] = powers[i - 1] * 2;
			}
		}

		HashMap<Long, Long> map = new HashMap<Long, Long>();

		long output = 0;

		for (int i = 0;i < n; i++) {
			arr[i] = sr.nextLong();

			for (int power = 0; power < 32; power++) {
                if (map.containsKey(powers[power] - arr[i])) {
                	output += map.get(powers[power] - arr[i]);
                }
			}

			if (map.containsKey(arr[i])) {
				map.put(arr[i], map.get(arr[i]) + (long)1);
			} else {
				map.put(arr[i], (long)1);
			}
		}

		System.out.println(output);
	}
}