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.util.HashMap;

public class b {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int N = Integer.parseInt(br.readLine());
		String[] line = br.readLine().split(" ");
		int[] arr = new int[N];
		for(int n = 0; n < N; n++){
			arr[n] = Integer.parseInt(line[n]);
		}
		
		HashMap<Integer, Integer> hm = new HashMap<>();
		
		long ans = 0;
		for(int n = 0; n < N; n++){
			if(hm.containsKey(arr[n])){
				ans += (long)hm.get(arr[n]).intValue();
			}
			for(int pow = 1; pow > 0; pow = pow * 2){
				int num = pow - arr[n];
				if(hm.containsKey(num)){
					hm.replace(num, hm.get(num).intValue() + 1);
				}
				else{
					hm.put(num, 1);
				}
			}
		}
		
		System.out.println(ans);
	}
}
