You are in a city consisting of n intersections numbered from $0$ to n $- 1$, connected by bidirectional roads. You are given an integer n and a $2$D integer array roads where roads[i] $= [u_i, v_i, {time}_i]$ indicates a bidirectional road between intersections $u_i$ and $v_i$ that takes ${time}_i$ minutes to traverse.

You want to travel from intersection $0$ to intersection n $- 1$ in the shortest amount of time.

Return the number of ways to reach intersection n $- 1$ from intersection $0$ in the minimum possible travel time. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ n $\leq 200$

• n $- 1 \leq$ roads.length $\leq \frac{ {`n`} \times ( {`n`} - 1)}{2}$

• roads[i].length $= 3$

• $0 \leq u_i, v_i \leq$ n $- 1$

• $1 \leq {time}_i \leq 10^9$

• $u_i \neq v_i$

• There is at most one road connecting any two intersections.

• You can reach any intersection from any other intersection.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.