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.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int[] a = new int[N];
		for(int i=0; i<N; i++)
			a[i] = sc.nextInt();
		Arrays.sort(a);
		
		System.out.println(isPossible(a) ? "Yes" : "No");
		
		sc.close();
	}
	
	static boolean isPossible(int[] a) {
		int N = a.length;
		if(a[0]+1 < a[N-1]) {
			return false;
			
		} else if(a[0]==a[N-1]) {
			return a[0]*2 <= N || a[0] == N-1;
			
		} else {
			int uniq = 0;
			for(int i=0; i<N; i++)
				if(a[i]==a[0])
					uniq++;
			
			return uniq < a[N-1] && uniq + (a[N-1]-uniq)*2 <= N;
		}
	}
}
