Largest Color Value in a Directed Graph

There is a **directed graph** of `n` colored nodes and `m` edges. The nodes are numbered from `0` to `n - 1`. You are given a string `colors` where `colors[i]` is a lowercase English letter representing the **color** of the `ith` node in this graph (**0-indexed**). You are also given a 2D array `edges` where `edges[j] = [aj, bj]` indicates that there is a **directed edge** from node `aj` to node `bj`. A valid **path** in the graph is a sequence of nodes `x1 -> x2 -> x3 -> ... -> xk` such that there is a directed edge from `xi` to `xi+1` for every `1 <= i < k`. The **color value** of the path is the number of nodes that are colored the **most frequently** occurring color along that path. Return _the **largest color value** of any valid path in the given graph, or _`-1`_ if the graph contains a cycle_.   **Example 1:** **Input:** colors = "abaca", edges = [[0,1],[0,2],[2,3],[3,4]] **Output:** 3 **Explanation:** The path 0 -> 2 -> 3 -> 4 contains 3 nodes that are colored `"a" (red in the above image)`. ``` **Example 2:** **Input:** colors = "a", edges = [[0,0]] **Output:** -1 **Explanation:** There is a cycle from 0 to 0. ```   **Constraints:** - `n == colors.length` - `m == edges.length` - `1 <= n <= 105` - `0 <= m <= 105` - `colors` consists of lowercase English letters. - `0 <= aj, bj < n`