There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree.

Initially, all nodes are unmarked. For each node i:

Return an array times where times[i] is the time when all nodes get marked in the tree, if you mark node i at time t = 0.

Note that the answer for each times[i] is independent, i.e. when you mark node i all other nodes are unmarked.

 

Example 1:

Input: edges = [[0,1],[0,2]]

Output: [2,4,3]

Explanation:

Example 2:

Input: edges = [[0,1]]

Output: [1,2]

Explanation:

Example 3:

Input: edges = [[2,4],[0,1],[2,3],[0,2]]

Output: [4,6,3,5,5]

Explanation:

 

Constraints: