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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Linq;
class Solve{
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        int N = int.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        int[] A = new int[N];
        int X = N;
        for(int i=0;i<N;i++){
            A[i] = int.Parse(str[i]);
            X = Math.Min(X,A[i]);
        }
        int S = 0;
        int L = 0;
        for(int i=0;i<N;i++){
            if(A[i] == X){
                S++;
            }
            else if(A[i] == X+1){
                L++;
            }
            else{
                sb.Append("No\n");
                return;
            }
        }
        if(L == 0){
            if(X == N-1 || X*2 <= N){
                sb.Append("Yes\n");
            }
            else{
                sb.Append("No\n");
            }
        }
        else{
            X++;
            if(S+1 <= X && X <= S+L/2){
                sb.Append("Yes\n");   
            }
            else{
                sb.Append("No\n");
            }
        }
    }
}