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;

class Solution
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var cat = Console.ReadLine().Split().Select(int.Parse).ToArray();

        var max = cat.Max();
        var maxCount = cat.Count(c => c == max);
        var min = cat.Min();
        var minCount = cat.Count(c => c == min);

        bool ok = false;
        if (max == min)
        {
            // 3 3 3 3 3 3      5 5 5 5 5 5
            // a b c a b c      a b c d e f
            if (2 * max <= n || max == n - 1)
            {
                ok = true;
            }
        }
        else if (max == min + 1)
        {
            // 3 3 4 4 4 4
            // a b c d c d
            if (minCount <= min && 2 * (max - minCount) <= maxCount)
            {
                ok = true;
            }
        }

        Console.WriteLine(ok ? "Yes" : "No");
    }
}