Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

F. Edge coloring of bipartite graph

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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* ≤ 10^{5}), *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

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/26/2017 01:21:07 (c3).

Desktop version, switch to mobile version.
User lists

Name |
---|