You are given a positive integer n representing n nodes in a connected undirected graph, where the nodes are numbered from 0 to n - 1.

You are also given an array edges, where edges[i] = [ui, vi] denotes that there is an edge between nodes ui and vi in the graph.

The distance from a node v to a cycle is the minimum number of edges needed to reach a node in a cycle from node v. If node v is part of a cycle, its distance is 0.

Return an array answer of length n, where answer[i] is the distance from node i to a cycle.

Example 1:

Input: n = 9, edges = [[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,1],[2,7],[7,8]]
Output: [1,0,0,0,1,2,1,1,2]

Example 2:

Input: n = 7, edges = [[0,1],[1,2],[2,0],[2,3],[3,4],[4,5],[5,6]]
Output: [0,0,0,1,2,3,4]

Constraints:

• 3 <= n <= 105
• n <= edges.length <= 2 * n
• edges[i].length == 2
• 0 <= ui, vi <= n - 1
• ui != vi
• There are no repeated edges.
• The graph is connected and has exactly one cycle.