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 void main(String[] args) {
		DataSet d = new DataSet();
		d.input();
		int dif = d.max - d.min;
		if(dif>1)
			System.out.println("No");
		else if(dif==1){
			if(2*(d.max-d.q)<=d.p&&d.q<=d.min)
				System.out.println("Yes");
			else System.out.println("No");
		}
		else if(dif==0){
			if(d.max==d.N-1||2*d.max<=d.N)
				System.out.println("Yes");
			else System.out.println("No");
		}
	}

}

class DataSet{
	int N;
	int[] a;
	int max=0,min=1000000;
	int p = 0,q = 0;
	public void input(){
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt();
		a = new int[N];
		for(int i=0;i<N;i++){
			a[i] = sc.nextInt();
			max = Math.max(max, a[i]);
			min = Math.min(min,a[i]);
		}
		for(int i=0;i<N;i++){
			if(a[i]==max) p++;
			if(a[i]==min) q++;
		}
		sc.close();
	}
	
}