Today, hedgehog Filya went to school for the very first time! Teacher gave him a homework which Filya was unable to complete without your help.

Filya is given an array of non-negative integers a1, a2, ..., an. First, he pick an integer x and then he adds x to some elements of the array (no more than once), subtract x from some other elements (also, no more than once) and do no change other elements. He wants all elements of the array to be equal.

Now he wonders if it's possible to pick such integer x and change some elements of the array using this x in order to make all elements equal.

Input

The first line of the input contains an integer n (1 ≤ n ≤ 100 000) — the number of integers in the Filya's array. The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109) — elements of the array.

Output

If it's impossible to make all elements of the array equal using the process given in the problem statement, then print "NO" (without quotes) in the only line of the output. Otherwise print "YES" (without quotes).

Examples

Input

5
1 3 3 2 1


Output

YES


Input

5
1 2 3 4 5


Output

NO

Note

In the first sample Filya should select x = 1, then add it to the first and the last elements of the array and subtract from the second and the third elements.
import java.util.*;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.math.MathContext;
import java.text.DecimalFormat;
import java.text.Format;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;

import java.awt.List;
 
 
public class Main {
	public static void main(String[] args) throws Exception{
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}

static class TaskA {
	//public ArrayList<Integer> ar;
	public boolean[] bs;
	
  // GCD && LCM 
	 long gcd(long a ,long b){return b == 0 ? a : gcd(b , a % b);}
	 long lcm(long a , long b){return a*(b/gcd(a, b));}
	
  // Sieve of erothenese
	void sieve(int UB ){
		//ar = new ArrayList();
		bs = new boolean[UB+1];
		bs[0] = bs[1] = true;
		for(int i = 2; i*i <= UB; i++){
			if(!bs[i]){
				for(int j = i*i ; j <= UB ; j += i)
					bs[j] = true;
			}
		}
		// for(int i = 2; i <= UB; i++){
		  //    if(!bs[i])ar.add(i);
		//}
	}
	
	// REverse a String 
	
	String rev(String s){
		return new StringBuilder(s).reverse().toString();
	}
	
	// all pair shortest path
	
	public int[][] ShortestPath(int n , int[][] grid){
		
		for(int k = 1; k <= n; k++){
        	for(int i = 1; i <= n; i++){
        		for(int j = 1; j <= n; j++){
        			grid[i][j] = min(grid[i][j] , grid[i][k] + grid[k][j]);
        		}
        	}
        }
		return grid;
	}
	
	
	/*          SOLUTION  IS RIGHT HERE     */
	
	
	public void solve(int testNumber, InputReader in, PrintWriter out){
		 // n br = new BufferedReader(new InputStreamReader(System.in));
		 // Scanner sc = new Scanner(System.in);
		
		
		int n = in.nextInt();
		HashSet<Integer> hs = new HashSet<>();
		for(int i = 1; i <= n; i++){
			hs.add(in.nextInt());
		}
		if(hs.size() > 3){
			out.println("NO");
			return;
		}
		if(hs.size() <= 2){
			out.println("YES");
			return;
		}
		double[] sum = new double[3]; 
		int i = 0;
		for(int  I : hs)
			sum[i++] = I;
		if(sum[0] == (sum[1]+sum[2])/2   || sum[1] == (sum[0]+sum[2])/2 || sum[2] == (sum[1]+sum[0])/2){
			out.println("YES");
			return;
		}
		out.println("NO");
	}
	
}  

   // union
 static class dsu{
	 int[] union , size;
	 
	 public dsu(int n){
		 union = new int[n+1];
		 size = new int[n+1];
		 for(int i = 0; i <= n; i++){
			 union[i] = i;
			 size[i] = 1;
		 }
	 }
	 public int root(int s){
		 while(s != union[s])
			 s = union[s];
		 return s;
	 }
	 
	 public boolean connected(int a , int b){
	    return root(a) == root(b);
	 }
	 
	 public void union(int a, int b){
		 int ea = root(a);
		 int eb = root(b);
		 if(a == b);
		 else if(size[ea] > size[eb]){
			 union[eb] = ea;
			 size[ea] += size[eb];
		 }else{
			union[ea] = eb;
			size[eb] += size[ea];
		 }
	 }
	 
 }
  // pair class
 static class pair implements Comparable<pair>{
	 int first , second ;
	 public pair(){this.first = 0; this.second = 0;}
	 public pair(int f , int s){
		 this.first = f;
		 this.second = s;
	 }
	@Override
	public int compareTo(pair one) {
		if(this.first < one.first)
			return -1;
		if(this.first > one.first)
			return 1;
		if(this.second < one.second)
			return -1;
		if(this.second > one.second)
		    return 1;
		return 0;
	}
	 
 }
  
 // ||||||| INPUT READER ||||||||
 static class InputReader {
	private byte[] buf = new byte[8000];
	private int index;
	private int total;
	private InputStream in;
	
	public InputReader(InputStream stream){
		in = stream;
	}
	
	public int scan(){
		if(total == -1)
			throw new InputMismatchException();
		if(index >= total){
			index = 0; 
			try{
			total = in.read(buf);
			}catch(IOException e){
			   throw new InputMismatchException();
			}
			if(total <= 0)
				return -1;
		}
		return buf[index++];
	}
	public long scanlong(){
		long integer = 0;
		int n = scan();
		while(isWhiteSpace(n))
			n = scan();
		int neg = 1;
		if(n == '-'){
			neg = -1;
			n = scan();
		}
		while(!isWhiteSpace(n)){
			if(n >= '0' && n <= '9'){
				integer *= 10;
				integer += n - '0';
				n = scan();
			}
			else throw new InputMismatchException();
		}
		return neg*integer;
	}
	
	private int scanInt() {
		int integer = 0;
		int n = scan();
		while(isWhiteSpace(n))
			n = scan();
		int neg = 1;
		if(n == '-'){
			neg = -1;
			n = scan();
		}
		while(!isWhiteSpace(n)){
			if(n >= '0' && n <= '9'){
				integer *= 10;
				integer += n - '0';
				n = scan();
			}
			else throw new InputMismatchException();
		}
		return neg*integer;
	}
	
	public double scandouble(){
		double doubll = 0;
		int n = scan();
		int neg = 1;
		while(isWhiteSpace(n))
			n = scan();
		if(n == '-'){
			neg = -1;
			n = scan();
		}
		while(!isWhiteSpace(n) && n != '.'){
			if(n >= '0' && n <= '9'){
				doubll *= 10;
				doubll += n - '0';
				n = scan();
			}
		}
		if(n == '.'){
			n = scan();
			double temp = 1;
			while(!isWhiteSpace(n)){
				if(n >= '0' && n <= '9'){
					temp /= 10;
					doubll += (n - '0')*temp;
					n = scan();
				}
			}
		}
		return neg*doubll;
	}
	
	private float scanfloat() {
		float doubll = 0;
		int n = scan();
		int neg = 1;
		while(isWhiteSpace(n))
			n = scan();
		if(n == '-'){
			neg = -1;
			n = scan();
		}
		while(!isWhiteSpace(n) && n != '.'){
			if(n >= '0' && n <= '9'){
				doubll *= 10;
				doubll += n - '0';
				n = scan();
			}
		}
		if(n == '.'){
			n = scan();
			double temp = 1;
			while(!isWhiteSpace(n)){
				if(n >= '0' && n <= '9'){
					temp /= 10;
					doubll += (n - '0')*temp;
					n = scan();
				}
			}
		}
		return neg*doubll;
	}
	public String scanstring(){
		StringBuilder sb = new StringBuilder();
		int n = scan();
		while(isWhiteSpace(n))
			n = scan();
		while(!isWhiteSpace(n)){
			sb.append((char)n);
			n = scan();
		}
		return sb.toString();
	}
	
	
	public boolean isWhiteSpace(int n){
		if(n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
			return true;
		return false;
	}
/// Input module 	
	
	public int nextInt(){
	  return scanInt();
	}
	
	public long nextLong(){
		  return  scanlong();
		}
	
	public double nextDouble(){
		  return  scandouble();
		}
	
	public float nextFloat(){
		  return scanfloat();
		}

	public String next(){
		return scanstring();
	}
	
	public int[] readIntArray(int size)  {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextInt();
        }
        return array;
    }
}
 
}