You are given an integer n representing the number of vertices in a connected undirected graph, labeled from $0$ to n $- 1$. You are also given a $2$D integer array edges where edges[i] = [node1_i, node2_i] indicates a bidirectional edge between vertex node1_i and vertex node2_i.

The graph contains exactly one cycle.

Return an integer array answer of size n, where answer[i] represents the minimum distance from vertex i to any vertex that belongs to the cycle.

Constraints:

• $3 \leq$ n $\leq 10^5$

• edges.length $= n$

• edges[i].length $= 2$

• $0 \leq$ node1_i, node2_i $\leq$ n $- 1$

• node1_i $\neq$ node2_i

• The graph is connected.

• The graph has exactly one cycle.

• There is at most one edge between any pair of vertices.

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.