Second Minimum Time to Reach Destination

A city is represented as a **bi-directional connected** graph with `n` vertices where each vertex is labeled from `1` to `n` (**inclusive**). The edges in the graph are represented as a 2D integer array `edges`, where each `edges[i] = [ui, vi]` denotes a bi-directional edge between vertex `ui` and vertex `vi`. Every vertex pair is connected by **at most one** edge, and no vertex has an edge to itself. The time taken to traverse any edge is `time` minutes. Each vertex has a traffic signal which changes its color from **green** to **red** and vice versa every `change` minutes. All signals change **at the same time**. You can enter a vertex at **any time**, but can leave a vertex **only when the signal is green**. You **cannot wait **at a vertex if the signal is **green**. The **second minimum value** is defined as the smallest value** strictly larger **than the minimum value. - For example the second minimum value of `[2, 3, 4]` is `3`, and the second minimum value of `[2, 2, 4]` is `4`. Given `n`, `edges`, `time`, and `change`, return _the **second minimum time** it will take to go from vertex _`1`_ to vertex _`n`. **Notes:** - You can go through any vertex **any** number of times, **including** `1` and `n`. - You can assume that when the journey **starts**, all signals have just turned **green**.   **Example 1:**         **Input:** n = 5, edges = [[1,2],[1,3],[1,4],[3,4],[4,5]], time = 3, change = 5 **Output:** 13 **Explanation:** The figure on the left shows the given graph. The blue path in the figure on the right is the minimum time path. The time taken is: - Start at 1, time elapsed=0 - 1 -> 4: 3 minutes, time elapsed=3 - 4 -> 5: 3 minutes, time elapsed=6 Hence the minimum time needed is 6 minutes. The red path shows the path to get the second minimum time. - Start at 1, time elapsed=0 - 1 -> 3: 3 minutes, time elapsed=3 - 3 -> 4: 3 minutes, time elapsed=6 - Wait at 4 for 4 minutes, time elapsed=10 - 4 -> 5: 3 minutes, time elapsed=13 Hence the second minimum time is 13 minutes. ``` **Example 2:** **Input:** n = 2, edges = [[1,2]], time = 3, change = 2 **Output:** 11 **Explanation:** The minimum time path is 1 -> 2 with time = 3 minutes. The second minimum time path is 1 -> 2 -> 1 -> 2 with time = 11 minutes. ```   **Constraints:** - `2 <= n <= 104` - `n - 1 <= edges.length <= min(2 * 104, n * (n - 1) / 2)` - `edges[i].length == 2` - `1 <= ui, vi <= n` - `ui != vi` - There are no duplicate edges. - Each vertex can be reached directly or indirectly from every other vertex. - `1 <= time, change <= 103`