13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T729,

You 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.

Coloring Edges

Examples