CF1217D Coloring Edges

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 $ .

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