Minimum Weighted Subgraph With the Required Paths

You are given an integer `n` denoting the number of nodes of a **weighted directed** graph. The nodes are numbered from `0` to `n - 1`. You are also given a 2D integer array `edges` where `edges[i] = [fromi, toi, weighti]` denotes that there exists a **directed** edge from `fromi` to `toi` with weight `weighti`. Lastly, you are given three **distinct** integers `src1`, `src2`, and `dest` denoting three distinct nodes of the graph. Return _the **minimum weight** of a subgraph of the graph such that it is **possible** to reach_ `dest` _from both_ `src1` _and_ `src2` _via a set of edges of this subgraph_. In case such a subgraph does not exist, return `-1`. A **subgraph** is a graph whose vertices and edges are subsets of the original graph. The **weight** of a subgraph is the sum of weights of its constituent edges.   **Example 1:** **Input:** n = 6, edges = [[0,2,2],[0,5,6],[1,0,3],[1,4,5],[2,1,1],[2,3,3],[2,3,4],[3,4,2],[4,5,1]], src1 = 0, src2 = 1, dest = 5 **Output:** 9 **Explanation:** The above figure represents the input graph. The blue edges represent one of the subgraphs that yield the optimal answer. Note that the subgraph [[1,0,3],[0,5,6]] also yields the optimal answer. It is not possible to get a subgraph with less weight satisfying all the constraints. ``` **Example 2:** **Input:** n = 3, edges = [[0,1,1],[2,1,1]], src1 = 0, src2 = 1, dest = 2 **Output:** -1 **Explanation:** The above figure represents the input graph. It can be seen that there does not exist any path from node 1 to node 2, hence there are no subgraphs satisfying all the constraints. ```   **Constraints:** - `3 <= n <= 105` - `0 <= edges.length <= 105` - `edges[i].length == 3` - `0 <= fromi, toi, src1, src2, dest <= n - 1` - `fromi != toi` - `src1`, `src2`, and `dest` are pairwise distinct. - `1 <= weight[i] <= 105`