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;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            AGC016.B();
        }

        class AGC016
        {
            public static void A()
            {
                var S = Read.Str();
                int min = 1000;
                for(int i = 0; i < 26; ++i)
                {
                    char c = (char)('a' + i);
                    int prev = -1;
                    int max = -1;
                    for(int j = 0; j < S.Length; ++j)
                    {
                        if (S[j] == c)
                        {
                            max = Math.Max(max, j - prev - 1);
                            prev = j;
                        }
                    }
                    if (max >= 0)
                    {
                        max = Math.Max(max, S.Length - 1 - prev);
                        min = Math.Min(min, max);
                    }
                }
                Console.WriteLine(min);
            }
            public static void B()
            {
                var N = Read.Int();
                var A = Read.IntN();
                var count = new Dictionary<int, int>();
                foreach(var a in A)
                {
                    if (!count.ContainsKey(a)) { count.Add(a, 0); }
                    count[a]++;
                }
                if (count.Count > 2) { Console.WriteLine("No"); return; }
                if (count.Count == 1)
                {
                    var k = count.First().Key;
                    Console.WriteLine(k <= N / 2 || k == N - 1 ? "Yes" : "No");
                    return;
                }
                var ks = count.Keys.OrderBy(x => x).ToArray();
                var k1 = ks[0];
                var k2 = ks[1];
                var v1 = count[k1];
                var v2 = count[k2];
                if (k1 + 1 != k2) { Console.WriteLine("No"); return; }
                Console.WriteLine(1 <= (k2 - v1) && (k2 - v1) <= v2 / 2 ? "Yes" : "No");
            }
            public static void C()
            {
                var H = Read.Int();
                var W = Read.Int();
                var h = Read.Int();
                var w = Read.Int();
                if (H % h + W % w == 0) { Console.WriteLine("No");return; }
                Console.WriteLine("Yes");

                var X = H % h > 0 ? H : W;
                var x = H % h > 0 ? h : w;

                var sum = new long[X + 1];
                sum[X] = 1;
                for (int i = X - x; i > 0; i -= x)
                {
                    sum[i] = sum[i + x] + 1;
                }
                for(int i = x; i < X; ++i)
                {
                    if (sum[i] == 0) { sum[i] = sum[i - x] - 1; }
                }
                var diff = Enumerable.Range(0, X).Select(i => sum[i + 1] - sum[i]).ToArray();

                if (H % h > 0)
                {
                    for(int i = 0; i < H; ++i)
                    {
                        Console.WriteLine(String.Join(" ", Enumerable.Repeat(diff[i], W)));
                    }
                }
                else
                {
                    for (int i = 0; i < H; ++i)
                    {
                        Console.WriteLine(String.Join(" ", diff));
                    }
                }
            }
            public static void D()
            {

            }
            public static void E()
            {

            }
            public static void F()
            {

            }
        }

        class Util
        {
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}