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) {
		Scanner scan = new Scanner(System.in);
		int[] a = new int[32];
		for(int i = 1;i<=30;i++){
			a[i] = 1<<i;
		}
		HashMap<Integer,Integer> hm = new HashMap<Integer,Integer>();
		int n = scan.nextInt();
		int[] b = new int[n];
		for(int i = 0;i<n;i++){
			b[i] = scan.nextInt();
			if(hm.containsKey(b[i]))
				hm.put(b[i], hm.get(b[i])+1);
			else
				hm.put(b[i],1);
		}
		long ans = 0;
		for(int i = 0;i<n;i++){
			for(int j = 1;j<=30;j++){
				if(a[j]<=b[i]) continue;
				int k = a[j]-b[i];
				if(hm.containsKey(k)&&b[i]!=k) ans+=hm.get(k);
				if(hm.containsKey(k)&&b[i]==k) ans += hm.get(k) -1;
			}
		}
		ans/=2;
		System.out.println(ans);
	}
}
