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.Linq;
using System.Collections.Generic;

namespace AtCoder.Grand016
{
    public class AGC016B_ColorfulHats
    {
        public 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 minHatTypeNum = hatNum[0];
            int maxHatTypeNum = hatNum[hatNum.Length - 1];

            int minCatCnt = hatNum.Count( val => val == minHatTypeNum);
            int maxCatCnt = hatNum.Count( val => val == maxHatTypeNum );
            

            string result = "Yes";

            // 色数に2以上の差が付くことはありえない
            if ( maxHatTypeNum - minHatTypeNum > 1 )
            {
                result = "No";
            }

            if ( minHatTypeNum == maxHatTypeNum )
            {
                // 全員が同じ値
                // 各色に1匹、もしくは各色に２匹以上

                // 各色に２匹以上(x!=N-1)であれば、種類数がN/2を上回ることはない
                if ( minHatTypeNum != catNum - 1 && minHatTypeNum > catNum / 2  )
                {
                    result = "No";
                }

            }
            else
            {
                // xとx-1が混在
                // １匹しかいないのが1～x-1組、残りは２匹以上のグループ
                // ２匹以上のペアはx-単独数できるため、ペアに属する猫は(x-単独数)*2匹以上になる

                // １匹しかいない色数（＝x-1の数）は、1～x-1の範囲内でないとおかしい
                if ( minCatCnt > minHatTypeNum )
                {
                    result = "No";
                }

                // ２匹以上グループの猫数は、(x-単独数)*2匹以上でないとおかしい
                if ( maxCatCnt < (maxHatTypeNum - minCatCnt) * 2 )
                {
                    result = "No";
                }

            }
            
            // 結果出力
            Console.WriteLine( result );
            
        }
        
    }
}