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;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.AGC_Challenge
{
    class _016_B
    {
        static void Main(string[] args)
        {
            Method(args);
            ReadLine();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            int[] array = ReadInts();
            Array.Sort(array);
            if (array[n - 1] - array[0] > 1)
            {
                WriteLine("No");
                return;
            }

            int multis = 0;
            int alones = 0;
            for(int i = 0; i < n; i++)
            {
                if (array[n - 1] == array[i]) multis++;
                else alones++;
            }
            if (multis == n && array[n - 1] == n - 1)
            {
                WriteLine("Yes");
                return;
            }

            if (multis == 1)
            {
                WriteLine("No");
                return;
            }

            int multiMin = 1;
            int multiMax = multis / 2;
            if(array[n-1]< alones+multiMin
                || array[n - 1] > alones + multiMax)
            {
                WriteLine("No");
                return;
            }
            WriteLine("Yes");
            return;
        }

        private static string Read() { return ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}