Problem: It's time polar bears Menshykov and Uslada from the zoo of St. Petersburg and elephant Horace from the zoo of Kiev got down to business. In total, there are n tasks for the day and each animal should do each of these tasks. For each task, they have evaluated its difficulty. Also animals decided to do the tasks in order of their difficulty. Unfortunately, some tasks can have the same difficulty, so the order in which one can perform the tasks may vary.

Menshykov, Uslada and Horace ask you to deal with this nuisance and come up with individual plans for each of them. The plan is a sequence describing the order in which an animal should do all the n tasks. Besides, each of them wants to have its own unique plan. Therefore three plans must form three different sequences. You are to find the required plans, or otherwise deliver the sad news to them by stating that it is impossible to come up with three distinct plans for the given tasks.

Input

The first line contains integer n (1 ≤ n ≤ 2000) — the number of tasks. The second line contains n integers h1, h2, ..., hn (1 ≤ hi ≤ 2000), where hi is the difficulty of the i-th task. The larger number hi is, the more difficult the i-th task is.

Output

In the first line print "YES" (without the quotes), if it is possible to come up with three distinct plans of doing the tasks. Otherwise print in the first line "NO" (without the quotes). If three desired plans do exist, print in the second line n distinct integers that represent the numbers of the tasks in the order they are done according to the first plan. In the third and fourth line print two remaining plans in the same form.

If there are multiple possible answers, you can print any of them.

Examples

Input

4
1 3 3 1


Output

YES
1 4 2 3 
4 1 2 3 
4 1 3 2 


Input

5
2 4 1 4 8


Output

NO

Note

In the first sample the difficulty of the tasks sets one limit: tasks 1 and 4 must be done before tasks 2 and 3. That gives the total of four possible sequences of doing tasks : [1, 4, 2, 3], [4, 1, 2, 3], [1, 4, 3, 2], [4, 1, 3, 2]. You can print any three of them in the answer.

In the second sample there are only two sequences of tasks that meet the conditions — [3, 1, 2, 4, 5] and [3, 1, 4, 2, 5]. Consequently, it is impossible to make three distinct sequences of tasks.

Solution (in JAVA):

Solution:


import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
import java.lang.*;


public class P471B{
	static long mod=1000000007;
	
    public static void main(String[] args) throws Exception{           	
    	 InputReader in = new InputReader(System.in);       
    	PrintWriter pw=new PrintWriter(System.out);   
    	
    	//int t=in.readInt();
        //	while(t-->0)
        	//{
        	int n=in.readInt();
    	Pair p[]=new Pair[n];
    	int a1[]=new int[n];
    	int a2[]=new int[n];
    	int a3[]=new int[n];
    	for(int i=0;i<n;i++)
    	{
    		int x=in.readInt();
    		Pair c=new Pair(x,i+1);
    		p[i]=c;
    	}
    	Arrays.sort(p);
    	int f=0;
    	int c=0;
    	if(n>=3)
    	for(int i=0;i<n;i++)
    	{
    		if(c==0&&i+1<n)
    		{
    			if(p[i].a==p[i+1].a)
    		{
    			a1[i]=p[i].b;
    			a2[i]=p[i+1].b;
    			a1[i+1]=p[i+1].b;
    			a2[i+1]=p[i].b;
    			a3[i]=p[i].b;
    			a3[i+1]=p[i+1].b;
    			
    			i++;
    			if(i+1<n&&p[i].a==p[i+1].a)
        		{
    				
        			a3[i]=p[i+1].b;
        			a3[i+1]=p[i].b;
        			//a1[i]=p[i].b;
        			//a2[i]=p[i].b;
        			a1[i+1]=p[i+1].b;
        			a2[i+1]=p[i+1].b;
        			i++;
        			c=2;
    				
        		}
    			else
    			c=1;
    			
    		}
    		else
    		{
    			a1[i]=p[i].b;
    			a2[i]=p[i].b;
    			a3[i]=p[i].b;
    		}
    		}
    		else if(c==1&&i+1<n)
    		{
    			if(p[i].a==p[i+1].a)
        		{
    				
        			a3[i]=p[i+1].b;
        			a3[i+1]=p[i].b;
        			a1[i]=p[i].b;
        			a2[i]=p[i].b;
        			a1[i+1]=p[i+1].b;
        			a2[i+1]=p[i+1].b;
        			i++;
        			c=2;
    				
        		}
    			else
    			{
    				a1[i]=p[i].b;
        			a2[i]=p[i].b;
        			a3[i]=p[i].b;
    			}
    		}
    		else
    		{
    			a1[i]=p[i].b;
    			a2[i]=p[i].b;
    			a3[i]=p[i].b;
    		}
    	}
    	if(c<2)
		   pw.println("NO");	     	
    	else
    	{
    		 pw.println("YES");
    		 for(int x:a1)
    		 {    			 
    			 pw.print(x+" ");
    		 }
    		 pw.println("");
    		 for(int x:a2)
    		 {
    			 pw.print(x+" ");
    		 }
    		 pw.println("");
    		 for(int x:a3)
    		 {
    			 pw.print(x+" ");
    		 }
    	}
    	//}
    	    		
    	
    	pw.close();
    }
    
   
    public static BigInteger fact(int n)
    {
    	BigInteger x=BigInteger.valueOf(1);
    	for(int i=1;i<=n;i++)
    	{
    		x=x.multiply(BigInteger.valueOf(i));
    	}
    	return x;
    }
    /* returns nCr mod m */
   	public static long comb(long n, long r, long m) 
   	{
   		long p1 = 1, p2 = 1;
   		for (long i = r + 1; i <= n; i++) {
   			p1 = (p1 * i) % m;
   		}
   		p2 = factMod(n - r, m);
   		p1 = divMod(p1, p2, m);
   		return p1 % m;
   	}
   /* returns a/b mod m, works only if m is prime and b divides a */
   	public static long divMod(long a, long b, long m) 
   	{
   		long c = powerMod(b, m - 2, m);
   		return ((a % m) * (c % m)) % m;
   	}
   /* calculates factorial(n) mod m */
   	public static long factMod(long n, long m) {
   		long result = 1;
   		if (n <= 1)
   			return 1;
   		while (n != 1) {
   			result = ((result * n--) % m);
   		}
   		return result;
   	}
   /* This method takes a, b and c as inputs and returns (a ^ b) mod c */
   	public static long powerMod(long a, long b, long c) {
   		long result = 1;
   		long temp = 1;
   		long mask = 1;
   		for (int i = 0; i < 64; i++) {
   			mask = (i == 0) ? 1 : (mask * 2);
   			temp = (i == 0) ? (a % c) : (temp * temp) % c;
   			/* Check if (i + 1)th bit of power b is set */
   			if ((b & mask) == mask) {
   				result = (result * temp) % c;
   			}
   		}
   		return result;
   	}
	static boolean isPrime(int number) {
        if (number <= 1) {
            return false;
        }
        if (number <= 3) {
            return true;
        }
        if (number % 2 == 0 || number % 3 == 0) {
            return false;
        }
        int i = 5;
        while (i * i <= number) {
            if (number % i == 0 || number % (i + 2) == 0) {
                return false;
            }
            i += 6;
        }
        return true;
    }
	
public static long gcd(long x,long y)
{
	if(x%y==0)
		return y;
	else
		return gcd(y,x%y);
}
	
public static int gcd(int x,int y)
{
	if(x%y==0)
		return y;
	else 
		return gcd(y,x%y);
}
public static int abs(int a,int b)
{
	return (int)Math.abs(a-b);
}
public static long abs(long a,long b)
{
	return (long)Math.abs(a-b);
}
public static int max(int a,int b)
{
	if(a>b)
		return a;
	else
		return b;
}
public static int min(int a,int b)
{
	if(a>b)
		return b;
	else 
		return a;
}
public static long max(long a,long b)
{
	if(a>b)
		return a;
	else
		return b;
}
public static long min(long a,long b)
{
	if(a>b)
		return b;
	else 
		return a;
}

static boolean isPowerOfTwo (long v) {
	return (v & (v - 1)) == 0;
}
public static long pow(long n,long p,long m)
{
	 long  result = 1;
	  if(p==0)
	    return 1;
	if (p==1)
	    return n;
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    if(result>=m)
	    result%=m;
	    p >>=1;
	    n*=n;
	    if(n>=m)
	    n%=m;
	}
	return result;
}
public static long pow(long n,long p)
{
	long  result = 1;
	  if(p==0)
	    return 1;
	if (p==1)
	    return n;
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;	    
	    p >>=1;
	    n*=n;	    
	}
	return result;

}
static class Pair implements Comparable<Pair>
{
	int a,b;
	Pair (int a,int b)
	{
		this.a=a;
		this.b=b;
	}

	public int compareTo(Pair o) {
		// TODO Auto-generated method stub
		if(this.a!=o.a)
		return Integer.compare(this.a,o.a);
		else
			return Integer.compare(this.b, o.b);
		//return 0;
	}
	public boolean equals(Object o) {
        if (o instanceof Pair) {
            Pair p = (Pair)o;
            return p.a == a && p.b == b;
        }
        return false;
    }
    public int hashCode() {
        return new Integer(a).hashCode() * 31 + new Integer(b).hashCode();
    }
} 
    
static long sort(int a[],int n)
{  	int b[]=new int[n];	
	return mergeSort(a,b,0,n-1);}
static long mergeSort(int a[],int b[],long left,long right)
{ long c=0;if(left<right)
 {   long mid=left+(right-left)/2;
	 c= mergeSort(a,b,left,mid);
	 c+=mergeSort(a,b,mid+1,right);
	 c+=merge(a,b,left,mid+1,right); }	
	return c;	 }
static long merge(int a[],int  b[],long left,long mid,long right)
{long c=0;int i=(int)left;int j=(int)mid; int k=(int)left;
while(i<=(int)mid-1&&j<=(int)right)
{ if(a[i]<=a[j]) {b[k++]=a[i++]; }
else	{ b[k++]=a[j++];c+=mid-i;}}
while (i <= (int)mid - 1)   b[k++] = a[i++]; 
while (j <= (int)right) b[k++] = a[j++];
for (i=(int)left; i <= (int)right; i++) 
	a[i] = b[i];  return c;  }
    
    
   static  class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars)
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                } catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public double readDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, readInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        public long readLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return readString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }

     static class OutputWriter
    {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream)
        {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer)
        {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects)
        {
            for (int i = 0; i < objects.length; i++)
            {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects)
        {
            print(objects);
            writer.println();
        }

        public void close()
        {
            writer.close();
        }

        public void flush()
        {
            writer.flush();
        }

    }
    /* USAGE

    //initialize
        InputReader in 		= new InputReader(System.in);
        OutputWriter out	=	new OutputWriter(System.out);

    //read int
    int i = in.readInt();
    //read string
    String s = in.readString();
    //read int array of size N
    int[] x = IOUtils.readIntArray(in,N);
    //printline
    out.printLine("X");


    //flush output
    out.flush();

    //remember to close the
    //outputstream, at the end
    out.close();

    */
  static   class IOUtils {

        public static int[] readIntArray(InputReader in, int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = in.readInt();
            return array;
    }
    }
//BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	//StringBuilder sb=new StringBuilder("");
	 //InputReader in = new InputReader(System.in);
  // OutputWriter out = new OutputWriter(System.out);
	//PrintWriter pw=new PrintWriter(System.out);
	//String line=br.readLine().trim();
	       	
	//int t=Integer.parseInt(br.readLine());
  //	while(t-->0)
  	//{
  	//int n=Integer.parseInt(br.readLine());
	//long n=Long.parseLong(br.readLine());
	//String l[]=br.readLine().split(" ");
  //int m=Integer.parseInt(l[0]);
	//int k=Integer.parseInt(l[1]);
	//String l[]=br.readLine().split(" ");
	//l=br.readLine().split(" ");
	/*int a[]=new int[n];
	for(int i=0;i<n;i++)
	{
		a[i]=Integer.parseInt(l[i]);
	}*/
	   //System.out.println(" ");	     	
	
	//}
}