Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

/**
 * Created by yoshiwaratomohiro on 2017/06/18.
 */
import java.util.Scanner;
public class Main {
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int N=scan.nextInt();
        int[] a=new int[N];
        int max=0;
        int min=N;

        for(int i=0;i<N;i++){
            a[i]=scan.nextInt();
            max=Math.max(a[i],max);
            min=Math.min(a[i],min);
        }
        if(max-min>1){
            System.out.println("No");
        }else if(max==min) {
            int maxcnt = 0;
            for (int i = 0; i < N; i++) {
                if (a[i] == max) {
                    maxcnt++;
                }
            }
            if(max*2<=maxcnt||max==maxcnt-1){
                System.out.println("Yes");
            }else{
                System.out.println("No");
            }
        }else {
                int mincnt=0;
                int maxcnt=0;
                for(int i=0;i<N;i++){
                    if(a[i]==max){
                        maxcnt++;
                    }else{
                        mincnt++;
                    }
                }
                max-=mincnt;
                if(max<1){
                    System.out.println("No");
                }else{
                    if(max*2>maxcnt){
                        System.out.println("No");
                    }else{
                        System.out.println("Yes");
                    }
                }
            }
        }
    }