Sum of Distances in a Tree

Statement

Given a connected, undirected tree with n nodes, labeled from $0$ to $n - 1$, and $n - 1$ edges. The edges are provided in an array, where each element edges[i] $= [a_i, b_i]$ represents an edge between nodes $a_i$ and $b_i$.

Your task is to return an array ans of length n, where ans[i] is the total sum of the distances between the $i_{th}$ node and all other nodes in the tree.

Constraints:

• $1 <=$ n $<= 3 * 10^4$

• edges.length $==$ n $- 1$

• edges[i].length $== 2$

• $0 <= a_i, b_i <$ n

• $a_i != b_i$

• The given input represents a valid tree.

Examples