Description: You are given a graph with $$$n$$$ nodes and $$$m$$$ directed edges. One lowercase letter is assigned to each node. We define a path's value as the number of the most frequently occurring letter. For example, if letters on a path are "abaca", then the value of that path is $$$3$$$. Your task is find a path whose value is the largest. Input Format: The first line contains two positive integers $$$n, m$$$ ($$$1 \leq n, m \leq 300\,000$$$), denoting that the graph has $$$n$$$ nodes and $$$m$$$ directed edges. The second line contains a string $$$s$$$ with only lowercase English letters. The $$$i$$$-th character is the letter assigned to the $$$i$$$-th node. Then $$$m$$$ lines follow. Each line contains two integers $$$x, y$$$ ($$$1 \leq x, y \leq n$$$), describing a directed edge from $$$x$$$ to $$$y$$$. Note that $$$x$$$ can be equal to $$$y$$$ and there can be multiple edges between $$$x$$$ and $$$y$$$. Also the graph can be not connected. Output Format: Output a single line with a single integer denoting the largest value. If the value can be arbitrarily large, output -1 instead. Note: In the first sample, the path with largest value is $$$1 \to 3 \to 4 \to 5$$$. The value is $$$3$$$ because the letter 'a' appears $$$3$$$ times.