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;

class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		int[] a = new int[N];
		a[0] = sc.nextInt();
		int min = a[0];
		int max = a[0];
		int cnt = 1;
		for(int i=1; i<N; i++){
			a[i] = sc.nextInt();
			if(a[i]<=min){
				min = a[i];
			}
			if(a[i]>=max){
				max = a[i];
			}
			if(a[i]==a[0]){
				cnt++;
			}
		}

		int maxCnt;
		int minCnt;
		if(max-min>1){
			System.out.print("No");
		}else if(max-min==1){
			if(a[0]==max){
				maxCnt = cnt;
				minCnt = N - cnt;
			}else{
				maxCnt = N - cnt;
				minCnt = cnt;
			}
			if(max >= minCnt + 1 && max <= minCnt + maxCnt / 2){
				System.out.print("Yes");
			}else{
				System.out.print("No");
			}
		}else if(max==min){
			if(N==max+1 || N>=max*2){
				System.out.print("Yes");
			}else{
				System.out.print("No");
			}
		}

	}

}
