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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class PowersOfTwo {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		
		long[] pot = new long[33];
		pot[0] = 1L;
		for(int i = 1 ; i < pot.length ; ++i) {
			pot[i] = pot[i - 1] << 1; 
		}
		
		Map<Long,Integer> map = new HashMap<>();
		long ans = 0 ;
		
		for (int i = 0; i < n; i++) {
			long l = scan.nextInt();
			for (int j = 0; j < pot.length; j++) {
				long dif = pot[j] - l;
				if(map.containsKey(dif)) {
					ans += map.get(dif);
				}
		
			}
			
			map.put(l, map.getOrDefault(l, 0) + 1);
			}
		System.out.println(ans);
		
	}
}
