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();
        TreeMap<Integer, Integer> map = new TreeMap<Integer, Integer>();
        for (int i=0;i<N;i++) {
            int a = sc.nextInt();
            if (map.containsKey(a)) map.put(a, map.get(a)+1);
            else map.put(a, 1);
        }

        boolean flag = false;
        ArrayList<Integer> key = new ArrayList<Integer>(map.keySet());
        ArrayList<Integer> val = new ArrayList<Integer>(map.values());
        int size = key.size();
        if (size==1 && ((val.get(0)-1)==key.get(0) || (long)2*key.get(0)<=val.get(0))) flag=true;
        // if (size==2 && key.get(1)-key.get(0)==1 &&  key.get(0)==val.get(0) && val.get(1)>1) flag=true;
        if (size==2 && key.get(1)-key.get(0)==1 &&  val.get(0)<key.get(1) && 2*(key.get(1)-val.get(0))<=val.get(1)) flag=true;

        if (flag) System.out.println("Yes");
        else System.out.println("No");
    }
}