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.Scanner;
import java.util.HashMap;

public class A2 {
	public static void main(String [] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; ++i) {
			a[i] = in.nextInt();
		}
		HashMap<Long, Integer> data = new HashMap<Long, Integer>();
	    long count = 0;
	    for (int i = 0; i < n; i++) {
	      	long num = a[i];
	      	for (long pow = 1; pow <= Integer.MAX_VALUE; pow *= 2) {
	        	if (data.containsKey(pow - num)) {
	          		count += data.get(pow - num);
	        	}
	  		}
		    if (!data.containsKey(num)) {
		    	data.put(num, 0);
		    }
		    data.put(num, data.get(num) + 1);
	    }
	    System.out.println(count);
	}
}