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{
  static int n;
  static int[] a;

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

    n = sc.nextInt();
    a = new int[n];
    for(int i = 0; i < n; i++){
      a[i] = sc.nextInt();
    }

    int max = 0, min = n;
    for(int i = 0; i < n; i++){
      max = Math.max(max, a[i]);
      min = Math.min(min, a[i]);
    }

    if(max - min >= 2){
      System.out.println("No");
      return;
    }

    if(max == min){
      if(max == n - 1 || 2 * max <= n){
        System.out.println("Yes");
      }
      else{
        System.out.println("No");
      }
    }
    else{
      int x = 0, y = 0;
      for(int i = 0; i < n; i++){
        if(a[i] == max){
          ++x;
        }
        if(a[i] == min){
          ++y;
        }
      }
      if(y < max && 2 * (max - y) <= x){
        System.out.println("Yes");
      }
      else{
        System.out.println("No");
      }
    }
  }
}