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;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());
		long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
    long maxNum = nums.Max();
    long minNum = nums.Min();
    long minCount = 0;//小さい数の猫の数
    long maxCount = 0;

    for(long i = 0; i < n; i++)
    {
      if(nums[i] == minNum) minCount++;
    }
    maxCount = n - minCount;

    if(maxNum - minNum >= 2) Console.WriteLine("No");
    else if(maxNum - minNum == 0)
    {
      if(maxNum <= n/2 || maxNum == n-1) Console.WriteLine("Yes");
      else Console.WriteLine("No");
    }else if(maxNum - minNum == 1)
    {
      if(maxCount == 1) Console.WriteLine("No");
      else if(minCount+1 <= maxNum && maxNum <= minCount + (maxCount/2)) Console.WriteLine("Yes");
      else Console.WriteLine("No");
    }

	}
}