You are given an integer n denoting the number of cities numbered from $0$ to $n - 1$.

Initially, there is a directed road from city i to city $i + 1$ for every $0 \leq i < n - 1$.

You are also given a $2$D integer array queries, where each queries[i] $= [u_i, v_i]$ represents the addition of a new directed road from city u_i to city v_i.

After adding each road, determine the length of the shortest path from city $0$ to city $n - 1$.

Return an array ans where ans[i] is the length of the shortest path from city $0$ to city $n - 1$ after processing the first $i + 1$ queries.

Constraints:

• $3 \leq$ n $\leq 500$

• $1 \leq$ queries.length $\leq 500$

• queries[i].length $= 2$

• $0 \leq$ queries[i][0] $<$ queries[i][1] $<$ n

• $1 <$ queries[i][1] $-$ queries[i][0]

• There are no repeated roads among the queries.

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.