Problem: You are given an undirected bipartite graph without multiple edges. You should paint the edges of graph to minimal number of colours, so that no two adjacent edges have the same colour.

Input

The first line contains three integers a, b, m (1 ≤ a, b ≤ 1000, 0 ≤ m ≤ 105), a is the size of the first part, b is the size of the second part, m is the number of edges in the graph.

Each of the next m lines contains two integers x, y (1 ≤ x ≤ a, 1 ≤ y ≤ b), where x is the number of the vertex in the first part and y is the number of the vertex in the second part. It is guaranteed that there are no multiple edges.

Output

In the first line print integer c — the minimal number of colours. The second line should contain m integers from 1 to c — the colours of the edges (in the order they appear in the input).

If there are several solutions, you can print any one of them.

Examples

Input

4 3 5
1 2
2 2
3 2
4 1
4 3


Output

3
1 2 3 1 2

Solution (in JAVA):

Solution:
//package educational.round02;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class F2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	int D;
	
	int[][] doEdgeColoring(boolean[][] g)
	{
		int n = g.length, m = g[0].length;
		D = 0; // maxdeg
		for(int i = 0;i < n;i++){
			int ld = 0;
			for(int j = 0;j < m;j++)if(g[i][j])ld++;
			if(ld > D)D = ld;
		}
		for(int j = 0;j < m;j++){
			int ld = 0;
			for(int i = 0;i < n;i++)if(g[i][j])ld++;
			if(ld > D)D = ld;
		}
		
		int[][] ltocolor = new int[n][D]; // [l][color] = r
		int[][] rtocolor = new int[m][D]; // [r][color] = l 
		int[][] color = new int[n][m]; // [l][r] = color
		
		for(int i = 0;i < n;i++)Arrays.fill(color[i], -1);
		for(int i = 0;i < n;i++)Arrays.fill(ltocolor[i], -1);
		for(int i = 0;i < m;i++)Arrays.fill(rtocolor[i], -1);
		
		boolean[] vedf = new boolean[n];
		boolean[] vedt = new boolean[m];
		int[] routet = new int[n+m];
		for(int f = 0;f < n;f++){
			for(int t = 0;t < m;t++){
				if(g[f][t]){
					int cf = -1, ct = -1;
					for(int j = 0;j < D;j++){
						if(ltocolor[f][j] == -1){
							cf = j;
							break;
						}
					}
					for(int j = 0;j < D;j++){
						if(rtocolor[t][j] == -1){
							ct = j;
							break;
						}
					}
					if(cf == ct){
						color[f][t] = cf;
						ltocolor[f][cf] = t;
						rtocolor[t][cf] = f;
					}else{
						// alternating path
						int rtp = 0;
						routet[rtp++] = f;
						routet[rtp++] = t;
						vedf[f] = true;
						vedt[t] = true;
						while(true){
							// t->nf mf->mt
							int lr = routet[rtp-1];
							if(rtocolor[lr][cf] == -1 || vedf[rtocolor[lr][cf]])break;
							routet[rtp++] = rtocolor[lr][cf];
							vedf[routet[rtp-1]] = true;
							
							int ll = routet[rtp-1];
							if(ltocolor[ll][ct] == -1 || vedt[ltocolor[ll][ct]])break;
							routet[rtp++] = ltocolor[ll][ct];
							vedt[routet[rtp-1]] = true;
						}
						
						for(int j = 0;j < rtp-1;j++){
							if((j&1) == 1){ // r->l cf->ct
								color[routet[j+1]][routet[j]] = ct;
								ltocolor[routet[j+1]][cf] = -1;
								ltocolor[routet[j+1]][ct] = routet[j];
								rtocolor[routet[j]][ct] = routet[j+1];
							}else{ // l->r ct->cf
								color[routet[j]][routet[j+1]] = cf;
								ltocolor[routet[j]][cf] = routet[j+1];
								rtocolor[routet[j+1]][ct] = -1;
								rtocolor[routet[j+1]][cf] = routet[j];
							}
						}
						
						vedf[f] = false;
						for(int j = 0;j < rtp;j++){
							if((j&1) == 1){
								vedt[routet[j]] = false;
							}else{
								vedf[routet[j]] = false;
							}
						}
					}
				}
			}
		}
		return color;
	}
	
	void solve()
	{
		int n = ni(), m = ni(), e = ni();
		int[] from = new int[e];
		int[] to = new int[e];
		boolean[][] g = new boolean[n][m];
		for(int i = 0;i < e;i++){
			from[i] = ni()-1;
			to[i] = ni()-1;
			g[from[i]][to[i]] = true;
		}
		int[][] color = doEdgeColoring(g);
		
//		verify(color, g);
		
		out.println(D);
		for(int i = 0;i < e;i++){
			out.print((color[from[i]][to[i]]+1) + " ");
		}
	}
	
	void verify(int[][] color, boolean[][] g)
	{
		int n = g.length;
		int m = g[0].length;
		boolean[][] lc = new boolean[n][n+m];
		boolean[][] rc = new boolean[m][n+m];
		boolean[] ac = new boolean[D];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < m;j++){
				if(g[i][j]){
					assert 0 <= color[i][j];
					assert color[i][j] < D;
					assert !lc[i][color[i][j]];
					lc[i][color[i][j]] = true;
					assert !rc[j][color[i][j]];
					rc[j][color[i][j]] = true;
					ac[color[i][j]] = true;
				}else{
					assert color[i][j] == -1;
				}
			}
		}
		for(int i = 0;i < D;i++){
			assert ac[i];
		}
	}
	
	static int[][] packD(int n, int[] from, int[] to) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]];
		for (int i = 0; i < from.length; i++) {
			g[from[i]][--p[from[i]]] = to[i];
		}
		return g;
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new F2().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}