<p>You are given two <strong>sorted</strong> arrays of distinct integers <code>nums1</code> and <code>nums2</code>.</p>

<p>A <strong>valid<strong><em> </em></strong>path</strong> is defined as follows:</p>

<ul>
	<li>Choose array <code>nums1</code> or <code>nums2</code> to traverse (from index-0).</li>
	<li>Traverse the current array from left to right.</li>
	<li>If you are reading any value that is present in <code>nums1</code> and <code>nums2</code> you are allowed to change your path to the other array. (Only one repeated value is considered in the valid path).</li>
</ul>

<p>The <strong>score</strong> is defined as the sum of unique values in a valid path.</p>

<p>Return <em>the maximum score you can obtain of all possible <strong>valid paths</strong></em>. Since the answer may be too large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/07/16/sample_1_1893.png" style="width: 500px; height: 151px;" />
<pre>
<strong>Input:</strong> nums1 = [2,4,5,8,10], nums2 = [4,6,8,9]
<strong>Output:</strong> 30
<strong>Explanation:</strong> Valid paths:
[2,4,5,8,10], [2,4,5,8,9], [2,4,6,8,9], [2,4,6,8,10],  (starting from nums1)
[4,6,8,9], [4,5,8,10], [4,5,8,9], [4,6,8,10]    (starting from nums2)
The maximum is obtained with the path in green <strong>[2,4,6,8,10]</strong>.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,3,5,7,9], nums2 = [3,5,100]
<strong>Output:</strong> 109
<strong>Explanation:</strong> Maximum sum is obtained with the path <strong>[1,3,5,100]</strong>.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,2,3,4,5], nums2 = [6,7,8,9,10]
<strong>Output:</strong> 40
<strong>Explanation:</strong> There are no common elements between nums1 and nums2.
Maximum sum is obtained with the path [6,7,8,9,10].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums1.length, nums2.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums1[i], nums2[i] &lt;= 10<sup>7</sup></code></li>
	<li><code>nums1</code> and <code>nums2</code> are strictly increasing.</li>
</ul>

class DirectedGraph:

    def __init__(self) -> None:
        self.__adjacency_list: Dict[int, List[int]] = dict()
        self.__in_degree_dict: Dict[int, int] = dict()

    def add_node(self, node: int) -> None:
        if node not in self.__adjacency_list:
            self.__adjacency_list[node] = list()
            self.__in_degree_dict[node] = 0

    def add_edge(self, source_node: int, destination_node: int) -> None:
        self.add_node(node=source_node)
        self.add_node(node=destination_node)
        self.__adjacency_list.get(source_node).append(destination_node)
        self.__in_degree_dict[destination_node] += 1

    def get_zero_indegree_nodes(self) -> List[int]:
        zero_indegree_nodes: List[int] = list()
        node: int
        in_degree: int
        for node, in_degree in self.__in_degree_dict.items():
            if in_degree == 0:
                zero_indegree_nodes.append(node)
        return zero_indegree_nodes

    def get_neighbours(self, node: int) -> List[int]:
        return self.__adjacency_list.get(node)

    def __repr__(self) -> str:
        return f'DirectedGraph({self.__adjacency_list} \n{self.__in_degree_dict})'


class Solution:
    def maxSum(self, nums1: List[int], nums2: List[int]) -> int:
        directed_graph: DirectedGraph = Solution.generate_graph(nums1=nums1, nums2=nums2)
        zero_indegree_nodes: List[int] = directed_graph.get_zero_indegree_nodes()
        if len(zero_indegree_nodes) == 0:
            raise Exception("Not Valid LLs")

        # print(directed_graph)

        max_score_cache: Dict[int, int] = dict()
        visited_dict: Dict[int, bool] = dict()
        max_score: int = 0

        dfs_start_node: int
        for dfs_start_node in zero_indegree_nodes:
            max_score = max(max_score,
                            Solution.get_max_score(node=dfs_start_node, directed_graph=directed_graph, max_score_cache=max_score_cache, visited_dict=visited_dict))
        return max_score % (10**9 + 7)

    @staticmethod
    def generate_graph(nums1: List[int], nums2: List[int]) -> DirectedGraph:
        directed_graph: DirectedGraph = DirectedGraph()
        index_: int
        num: int
        for index_, num in enumerate(nums1):
            if index_ == 0:
                directed_graph.add_node(node=num)
            else:
                directed_graph.add_edge(source_node=nums1[index_-1], destination_node=num)

        for index_, num in enumerate(nums2):
            if index_ == 0:
                directed_graph.add_node(node=num)
            else:
                directed_graph.add_edge(source_node=nums2[index_-1], destination_node=num)
        return directed_graph
        
    @staticmethod
    def get_max_score(node: int, directed_graph: DirectedGraph, max_score_cache: Dict[int, int], visited_dict: Dict[int, bool]) -> int:
        # print(node)
        if visited_dict.get(node, False):
            return max_score_cache.get(node)

        visited_dict[node] = True

        max_score: int = node
        neighbour_node: int
        max_neighbour_score: int = 0
        for neighbour_node in directed_graph.get_neighbours(node=node):
            # print(f'Neigh -> {neighbour_node}')
            max_neighbour_score = max(max_neighbour_score, Solution.get_max_score(node=neighbour_node, directed_graph=directed_graph, max_score_cache=max_score_cache, visited_dict=visited_dict))
        max_score += max_neighbour_score
        max_score_cache[node] = max_score
        return max_score

75800