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];
    int max = 0;
    int min = Integer.MAX_VALUE;
    for(int i = 0; i < N; i++) {
      a[i] = sc.nextInt();
      max = Math.max(max, a[i]);
      min = Math.min(min, a[i]);
    }
    String ans = "No";
    if(max == min) {
      if((max + 1 == N) || (N >= 2 * max)) ans = "Yes";
    } else {
      if(max == min + 1) {
      int s = 0;
      for(int i = 0; i < N; i++) {
        if(a[i] == min) s++;
      }
      if((max > s) && (N >= s + (2 * (max - s)))) ans = "Yes";
      }
    }
    System.out.println(ans);
  }
}