There is a directed graph consisting of $n$ colored nodes labeled from $0$ to $n - 1$ and $m$ directed edges. You are given a string colors of length $n$, where colors[i] represents the color of the $i^{ ext{th}}$ node, and a two dimensional array edges where edges[j] = [a_j, b_j] indicates a directed edge from node $a_j$ to node $b_j$.

A path in the graph is a sequence of nodes $u_1 o u_2 o \dots o u_k$ such that there exists a directed edge from $u_i$ to $u_{i+1}$ for all $1 \leq i < k$. The color value of a path is defined as the frequency of the most common color appearing among the nodes visited in that path.

Return the maximum color value among all valid paths in the graph. If the graph contains a cycle, return $-1$.

Constraints:

• n $==$ colors.length

• m $==$ edges.length

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ m $\leq 10^5$

• colors consists of lowercase English letters.

• $0 \leq a_j, b_j <$ n

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.