You are given a positive integer n which is the number of nodes of a 0-indexed directed weighted graph and a 0-indexed 2D array edges where edges[i] = [ui, vi, wi] indicates that there is an edge from node ui to node vi with weight wi.

You are also given a node s and a node array marked; your task is to find the minimum distance from s to any of the nodes in marked.

Return an integer denoting the minimum distance from s to any node in marked or -1 if there are no paths from s to any of the marked nodes.

 

Example 1:

Input: n = 4, edges = [[0,1,1],[1,2,3],[2,3,2],[0,3,4]], s = 0, marked = [2,3]
Output: 4
Explanation: There is one path from node 0 (the green node) to node 2 (a red node), which is 0->1->2, and has a distance of 1 + 3 = 4.
There are two paths from node 0 to node 3 (a red node), which are 0->1->2->3 and 0->3, the first one has a distance of 1 + 3 + 2 = 6 and the second one has a distance of 4.
The minimum of them is 4.

Example 2:

Input: n = 5, edges = [[0,1,2],[0,2,4],[1,3,1],[2,3,3],[3,4,2]], s = 1, marked = [0,4]
Output: 3
Explanation: There are no paths from node 1 (the green node) to node 0 (a red node).
There is one path from node 1 to node 4 (a red node), which is 1->3->4, and has a distance of 1 + 2 = 3.
So the answer is 3.

Example 3:

Input: n = 4, edges = [[0,1,1],[1,2,3],[2,3,2]], s = 3, marked = [0,1]
Output: -1
Explanation: There are no paths from node 3 (the green node) to any of the marked nodes (the red nodes), so the answer is -1.

 

Constraints:

• 2 <= n <= 500
• 1 <= edges.length <= 104
• edges[i].length = 3
• 0 <= edges[i][0], edges[i][1] <= n - 1
• 1 <= edges[i][2] <= 106
• 1 <= marked.length <= n - 1
• 0 <= s, marked[i] <= n - 1
• s != marked[i]
• marked[i] != marked[j] for every i != j
• The graph might have repeated edges.
• The graph is generated such that it has no self-loops.