You are given an integer n and a $2 D$ integer array queries.

There are n cities numbered from $0$ to n $- 1$. Initially, there is a unidirectional road from city i to city i $+ 1$ for all $0 \le$ i $<$ n $- 1$.

Each query queries[i] $= [u_i, v_i]$ represents the addition of a new unidirectional road from city $u_i$ to city $v_i$. After processing each query, you need to find the length of the shortest path from city $0$ to city n $- 1$.

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

Constraints:

• $3 \le$ n $\le 10^5$

• $1 \le$ queries.length $\le 10^5$

• queries[i].length $= 2$

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

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

• There are no repeated roads among the queries.

• There are no two queries such that i $\neq$ j and queries[i][0] $<$ queries[j][0] $<$ queries[i][1] $<$ queries[j][1].

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.