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: Wrong Answer)

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 min = n;
        int max = 0;
        for(int i = 0; i<n; i++){
            a[i] = sc.nextInt();
            if(a[i] < min) min = a[i];
            if(a[i] > max) max = a[i];
        }
        
        if(max - min >= 2){
            System.out.println("No");
            return;
        }

        if(min == max){
            if(min == 1 || min == n-1){
                System.out.println("Yes");
                return;
            }
            if(n / min >= 2){
                System.out.println("Yes");
                return;
            }
            System.out.println("No");
        }else{
            int nmin = 0;
            for(int ta: a){
                if(ta == min) nmin++;
            }
            int nmax = n - nmin;

            if(max < nmin && (nmin - max)*2 <= nmax){
                System.out.println("Yes");
            }else{
                System.out.println("No");
            }
        }
        
    }
}