Problem: Valera has 2·n cubes, each cube contains an integer from 10 to 99. He arbitrarily chooses n cubes and puts them in the first heap. The remaining cubes form the second heap. 

Valera decided to play with cubes. During the game he takes a cube from the first heap and writes down the number it has. Then he takes a cube from the second heap and write out its two digits near two digits he had written (to the right of them). In the end he obtained a single fourdigit integer — the first two digits of it is written on the cube from the first heap, and the second two digits of it is written on the second cube from the second heap.

Valera knows arithmetic very well. So, he can easily count the number of distinct fourdigit numbers he can get in the game. The other question is: how to split cubes into two heaps so that this number (the number of distinct fourdigit integers Valera can get) will be as large as possible?

Input

The first line contains integer n (1 ≤ n ≤ 100). The second line contains 2·n space-separated integers ai (10 ≤ ai ≤ 99), denoting the numbers on the cubes.

Output

In the first line print a single number — the maximum possible number of distinct four-digit numbers Valera can obtain. In the second line print 2·n numbers bi (1 ≤ bi ≤ 2). The numbers mean: the i-th cube belongs to the bi-th heap in your division.

If there are multiple optimal ways to split the cubes into the heaps, print any of them.

Examples

Input

1
10 99


Output

1
2 1 


Input

2
13 24 13 45


Output

4
1 2 2 1 

Note

In the first test case Valera can put the first cube in the first heap, and second cube — in second heap. In this case he obtain number 1099. If he put the second cube in the first heap, and the first cube in the second heap, then he can obtain number 9910. In both cases the maximum number of distinct integers is equal to one.

In the second test case Valera can obtain numbers 1313, 1345, 2413, 2445. Note, that if he put the first and the third cubes in the first heap, he can obtain only two numbers 1324 and 1345.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
 public class Q1 {

	static ArrayList<Integer> adj[],adj2[];
	static int color[],cc;
	static long mod=1000000007;
	static TreeSet<Integer> ts[];
	static boolean b[],visited[],possible,ans1,ans2;
	static Stack<Integer> s;
	static int totalnodes,colored,min,minc;
	static int c[];
	static long sum[];
	static HashMap<Integer,Integer> hm;
	public static void main(String[] args) throws IOException {
		
		//Scanner sc=new Scanner(System.in);
		in=new InputReader(System.in);
		out=new PrintWriter(System.out);
		int n=in.nextInt();
		int freq[]=new int[101];
		int a[]=new int[2*n];
		Pair pair[]=new Pair[2*n];	
		adj=new ArrayList[100];
		for(int i=0;i<100;i++)
			adj[i]=new ArrayList<>();
		for(int i=0;i<2*n;i++)
		{
			a[i]=in.nextInt();
			pair[i]=new Pair(a[i],i,0);
			freq[a[i]]++;
			adj[a[i]].add(i);
		}
		int ans[]=new int[2*n];
		int ones=0;
		int twos=0;
		boolean flag=true;List<Integer> other=new ArrayList<>();
		for(int i=1;i<100;i++)
		{
			if(freq[i]==1)
			{
				if(flag)
				{
					ones++;flag=false;
					ans[adj[i].get(0)]=1;
				}
				else
				{
					twos++;flag=true;
					ans[adj[i].get(0)]=2;
				}
				adj[i].clear();
			}
			else if(freq[i]!=0)
			{
				ans[adj[i].get(0)]=1;
				ans[adj[i].get(1)]=2;
				ones++;
				twos++;
				for(int j=2;j<adj[i].size();j++)
					other.add(adj[i].get(j));
			}
		}
		out.println(ones*twos);
		for(int i:other)
		{
			if(ones<n)
			{
				ones++;
				ans[i]=1;
			}
			else
			{
				twos++;
				ans[i]=2;
			}
		}
	
		
		for(int r:ans)
		{
			out.print(r+" ");
		}
		out.close();
		}
	
	static InputReader in;
	static PrintWriter out;
 	static void dfs(int i,int parent)
	{
 		if(color[i]!=cc)
 			ans1= false;
 		for(int j:adj[i])
 		{
 			if(j!=parent)
 			{
 				dfs(j,i);
 			}
 		}
		
	}
	/*public static void seive(long n){
		b = new boolean[(int) (n+1)];
	Arrays.fill(b, true);
	
		for(int i = 2;i*i<=n;i++){
			if(b[i]){
				sum[i]=count[i];
			//	System.out.println(sum[i]+" wf");
				for(int p = 2*i;p<=n;p+=i){
					b[p] = false;
					sum[i]+=count[p];  
					//System.out.println(sum[i]);
				}
			}
		
		}
	}*/
	static class Pair implements Comparable<Pair> {
		int i;
		int j;
		int index;
		public Pair(){
			
		}
		public Pair(int u, int v,int index) {
			this.i = u;
			this.j= v;
			this.index=index;
		}
		public int compareTo(Pair other) {
			
			
				return this.i-other.i;
		}
		
		/*public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}*/
	}
	static class Node2{
		Node2 left = null;
		Node2 right = null;
		Node2 parent = null;
		int data;
	}
	
	//binaryStree
	static class BinarySearchTree{
		Node2 root = null;
		int height = 0;
		int max = 0;
		int cnt = 1;
		ArrayList<Integer> parent = new ArrayList<>();
		HashMap<Integer, Integer> hm = new HashMap<>();
		public void insert(int x){
			Node2 n = new Node2();
			n.data = x;
			if(root==null){
				root = n;
			}
			else{
				Node2 temp = root,temp2 = null;
				while(temp!=null){
					temp2 = temp;
					if(x>temp.data) temp = temp.right;
					else temp = temp.left;
				}
				if(x>temp2.data) temp2.right = n;
				else temp2.left = n;
				n.parent = temp2;
				parent.add(temp2.data);
			}
		}
		public Node2 getSomething(int x, int y, Node2 n){
			if(n.data==x || n.data==y) return n;
			else if(n.data>x && n.data<y) return n;
			else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
			else return getSomething(x,y,n.left);
		}
		public Node2 search(int x,Node2 n){
			if(x==n.data){
				max = Math.max(max, n.data);
				return n;
			}
			if(x>n.data){
				max = Math.max(max, n.data);
				return search(x,n.right);
			}
			else{
				max = Math.max(max, n.data);
				return search(x,n.left);
			}
		}
		public int getHeight(Node2 n){
			if(n==null) return 0;
			height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
			return height;
		}
	}
public static void debug(Object... o) {
	System.out.println(Arrays.deepToString(o));
}

public static String rev(String s)
{
	StringBuilder sb=new StringBuilder(s);
	sb.reverse();
	return sb.toString();
}

static long lcm(long a, long b)
{
    return a * (b / gcd(a, b));
}

static long gcd(long a, long b)
{
    while (b > 0)
    {
        long temp = b;
        b = a % b; // % is remainder
        a = temp;
    }
    return a;
}

public static long max(long x, long y, long z){
		if(x>=y && x>=z) return x;
		if(y>=x && y>=z) return y;
		return z;
	}
	static int[] sieve(int n,int[] arr)
	{
	for(int i=2;i*i<=n;i++)
	{
		if(arr[i]==0)
		{
			for(int j=i*2;j<=n;j+=i)
				arr[j]=1;
		}
	}
	return arr;
	}




static class InputReader {

private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
private SpaceCharFilter filter;

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

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

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

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

public int[] nextIntArray(int n) {
	 return nextIntArray(n, 0);
	    }
	    
public int[] nextIntArray(int n, int off) {
	 int[] arr = new int[n + off];
	   for (int i = 0; i < n; i++) {
	    arr[i + off] = nextInt();
	    }
	    return arr;
	    }
	    
public long[] nextLongArray(int n) {
return nextLongArray(n, 0);
	    }
        
	public long[] nextLongArray(int n, int off) {
	 long[] arr = new long[n + off];
	 for (int i = 0; i < n; i++) {
		  arr[i + off] = nextLong();
		 }
 return arr;
	}


public String readString() {
  int c = snext();
  while (isSpaceChar(c)) {
    c = snext();
  }
  StringBuilder res = new StringBuilder();
  do {
    res.appendCodePoint(c);
    c = snext();
  } while (!isSpaceChar(c));
  return res.toString();
}

public String nextLine() {
  int c = snext();
  while (isSpaceChar(c))
    c = snext();
  StringBuilder res = new StringBuilder();
  do {
    res.appendCodePoint(c);
    c = snext();
  } while (!isEndOfLine(c));
  return res.toString();
}

public boolean isSpaceChar(int c) {
  if (filter != null)
    return filter.isSpaceChar(c);
  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}

private boolean isEndOfLine(int c) {
  return c == '\n' || c == '\r' || c == -1;
}

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