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.IO;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

class Solver
{
    public static void Main()
    {
        string YES = "Yes";
        string NO = "No";
        bool result = false;

        int N = int.Parse(Console.ReadLine().Trim());
        string[] strs = Console.ReadLine().Trim().Split(' ');
        int[] ints = new int[strs.Length];
        for (int i=0; i < strs.Length; i++)
        {
            ints[i] = int.Parse(strs[i]);
        }
        int max = ints.Max();


        Dictionary<int, long> dic = new Dictionary<int, long>(ints.Length);
        long tmp;
        foreach(var i in ints)
        {
            dic.TryGetValue(i, out tmp);
            dic[i] = 1 + tmp;
        }

        if (dic.Count > 2)
        {
            Console.WriteLine(YES);
            return;
        } else if (dic.Count == 1)
        {
            int i = dic.Keys.ToArray()[0];
            result = 1 == i || N == i+1 ;
            Console.WriteLine(result ? YES : NO);
            return;
        }

        // dic.Count == 2であることが保証されている
        int nonUniqKey = Math.Max(dic.Keys.ToArray()[0], dic.Keys.ToArray()[1]);
        int uniqKey = nonUniqKey - 1;
        long nonUniqVal;
        dic.TryGetValue(nonUniqKey,out nonUniqVal);
        long uniqVal = N - nonUniqVal;

        result = result || uniqKey == uniqVal;
        result = result || nonUniqKey >= nonUniqVal/2 + 1 && uniqVal == 1;
        result = result || nonUniqKey >= nonUniqVal/2 + uniqVal && uniqVal < uniqKey;

        Console.WriteLine(result ? YES : NO);
    }
}