There are N cats. We number them from 1 through N.

Each of the cats wears a hat. Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

* 2 ≤ N ≤ 10^5
* 1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print `Yes` if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print `No` otherwise.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
import java.util.Scanner;

public class Main {

	public static boolean avairable(int[] as, int min, int max) {
		switch(max-min) {
		case 0:
			for(int i=0; i<as.length; i++)
				if(as[i]!=as.length-1&&2*as[i]>as.length)
					return false;
			return true;
		case 1:
			int alone_num=0;
			for(int a: as)
				if(a==min)
					alone_num++;
			return alone_num<max && 2*(max-alone_num)<=as.length-alone_num;
		default:
			return false;
		}
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] as = new int[n];
		int min = n;
		int max = 0;
		for(int i=0; i<n; i++) {
			as[i] = sc.nextInt();
			if(as[i]<min) min = as[i];
			if(as[i]>max) max = as[i];
		}
		sc.close();

		System.out.println(avairable(as, min, max)?"Yes":"No");
	}
}
