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D. Coloring Edges

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a directed graph with $$$n$$$ vertices and $$$m$$$ directed edges without self-loops or multiple edges.

Let's denote the $$$k$$$-coloring of a digraph as following: you color each edge in one of $$$k$$$ colors. The $$$k$$$-coloring is good if and only if there no cycle formed by edges of same color.

Find a good $$$k$$$-coloring of given digraph with minimum possible $$$k$$$.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 5000$$$, $$$1 \le m \le 5000$$$) — the number of vertices and edges in the digraph, respectively.

Next $$$m$$$ lines contain description of edges — one per line. Each edge is a pair of integers $$$u$$$ and $$$v$$$ ($$$1 \le u, v \le n$$$, $$$u \ne v$$$) — there is directed edge from $$$u$$$ to $$$v$$$ in the graph.

It is guaranteed that each ordered pair $$$(u, v)$$$ appears in the list of edges at most once.

Output

In the first line print single integer $$$k$$$ — the number of used colors in a good $$$k$$$-coloring of given graph.

In the second line print $$$m$$$ integers $$$c_1, c_2, \dots, c_m$$$ ($$$1 \le c_i \le k$$$), where $$$c_i$$$ is a color of the $$$i$$$-th edge (in order as they are given in the input).

If there are multiple answers print any of them (you still have to minimize $$$k$$$).

Examples

Input

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

Output

1 1 1 1 1 1

Input

3 3 1 2 2 3 3 1

Output

2 1 1 2

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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