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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map.Entry;

public class Main {
	static ContestScanner in;
	static Writer out;
	public static void main(String[] args) {
		Main main = new Main();
		try {
			in = new ContestScanner();
			out = new Writer();
			main.solve();
			out.close();
			in.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	void solve() throws IOException {
		int n = in.nextInt();
		int[] a = new int[n];
		MultiSet<Integer> set = new MultiSet<>();
		for(int i = 0; i < n; i++) {
			a[i] = in.nextInt();
			set.add(a[i]);
		}
		if(set.size() > 2) {
			System.out.println("No");
			return;
		}
		if(set.size() == 1) {
			if(a[0] == n - 1 || a[0] <= n / 2) {
				System.out.println("Yes");
			} else System.out.println("No");
		} else {
			int aL = 0;
			int aS = n + 1;
			int aLn = 0;
			int aSn = 0;
			for(Entry<Integer, Integer> e: set.entrySet()) {
				int k = e.getKey();
				int v = e.getValue();
				if(k > aL) {
					aL = k;
					aLn = v;
				}
				if(k < aS) {
					aS = k;
					aSn = v;
				}
			}
			if(Math.abs(aL - aS) > 1) {
				System.out.println("No");
				return;
			}
			int groups = aL;
			int groupLower = aSn + 1;
			int groupUpper = aSn + aLn / 2;
			if(groupLower <= groups && groups <= groupUpper) {
				System.out.println("Yes");
			} else {
				System.out.println("No");
			}
		}
	}
}

@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
	@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
	public MultiSet<T> merge(MultiSet<T> set)
	{MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
	for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}

class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
	private BufferedReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new BufferedReader(new InputStreamReader(System.in));}
	public ContestScanner(String filename)throws IOException
	{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
	public void close() throws IOException {in.close();}
}