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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace AtCoder.Grand016
{
    class B
    {
        static void Main(string[] args)
        {

            // 整数の入力
            int catNum = int.Parse( Console.ReadLine() );

            // スペース区切りの整数の入力
            string[] hatNumText = Console.ReadLine().Split( ' ' );

            int[] hatNum = new int[catNum];
            for ( int i = 0; i < catNum; i++ )
            {
                hatNum[i] = int.Parse( hatNumText[i] );
            }


            Array.Sort( hatNum );


            int minHatNum = hatNum[0];
            int maxHatNum = hatNum[hatNum.Length - 1];

            int minHatCnt = 1;
            for ( int i=1; i < catNum; i++ )
            {
                if ( hatNum[i] == minHatNum )
                {
                    minHatCnt++;
                }
                else
                {
                    break;
                }
            }

            int maxHatCnt = 1;
            for ( int i = catNum-2; i >= 0; i-- )
            {
                if ( hatNum[i] == maxHatNum )
                {
                    maxHatCnt++;
                }
                else
                {
                    break;
                }
            }

            string result = "Yes";

            if ( maxHatNum - minHatNum > 1 )
            {
                result = "No";
            }

            if ( maxHatNum >= catNum )
            {
                result = "No";
            }
            
            if ( minHatNum == catNum - 2 && maxHatCnt % 2 != 0 )
            {
                result = "No";
            }

            if ( minHatCnt > 1 )
            {
                result = "No";
            }

            //出力
            Console.WriteLine( result );
            

#if DEBUG
            Console.WriteLine( "press Enter." );
            Console.ReadLine();
#endif

        }
        
    }
}