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 B{
	public static void main(String args[]){
		HashMap<Long,Integer> count = new HashMap<Long,Integer>();
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long sum = 0;
		for(int i = 0; i < N; i++){
			long curr = sc.nextLong();

			for(int j = 0; j <= 31; j++){
				if((1L << j) < curr) continue;
				if(count.containsKey((1L<<j) - curr))
					sum += count.get((1L<<j) - curr);
			}

			if(!count.containsKey(curr))
				count.put(curr,1);
			else count.put(curr,1+count.get(curr));
		}
		System.out.println(sum);
	}
}