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.Collections.Generic;
using System.Linq;

public class Program
{
    public void Solve()
    {
        var sc = new Scanner();
        int N = sc.NextInt();
        int[] A = sc.IntArray();

        // 猫iがかぶっている色が複数個ある -> 全体とn-1匹の種類数は変わらない
        // 1個しか無い　-> 種類が一個減る

        var s = new HashSet<int>();

        foreach (int i in A)
        {
            s.Add(i);
        }

        var tmpAr = s.ToArray();
        if (s.Count > 2)
        {
            Console.WriteLine("No");
        }
        else if (s.Count == 1)
        {
            int count = tmpAr[0];
            // 全猫の色が違う -> count = N-1
            // 全種 2匹以上ずつ -> 1 <= count <= N/2
            bool a = count == N - 1;
            bool b = 1 <= count && count <= N / 2;
            Console.WriteLine(a || b ? "Yes" : "No");
        }
        else
        {
            int countA = tmpAr[0];
            int countB = tmpAr[1];
            if (countA > countB)
            {
                int t = countA;
                countA = countB;
                countB = t;
            }

            if (countA + 1 != countB)
            {
                Console.WriteLine("No");
                return;
            }

            // 1個しか無い帽子をかぶっている猫の数 全体の種類数は +1以上
            int uniqueCount = A.Count(i => i == countA);
            int not = N - uniqueCount;
            bool a = uniqueCount + 1 <= countB;
            bool b = countB <= uniqueCount + not / 2;
            Console.WriteLine(a && b ? "Yes" : "No");
        }
    }

    public static void Main(string[] args)
    {
        new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _pos = 0;
        _line = new string[0];
    }

    const char Separator = ' ';
    private int _pos;
    private string[] _line;

    #region スペース区切りで取得

    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = Console.ReadLine().Split(Separator);
            _pos = 0;
        }

        return _line[_pos++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }

    #endregion

    #region 型変換

    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }

    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }

    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }

    #endregion

    #region 配列取得

    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = Console.ReadLine().Split(Separator);

        _pos = _line.Length;
        return _line;
    }

    public int[] IntArray()
    {
        return ToIntArray(Array());
    }

    public long[] LongArray()
    {
        return ToLongArray(Array());
    }

    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }

    #endregion
}