Description

Given a tree of n nodes, return an array where ans[i] is the sum of distances between node i and all other nodes.

Examples

Input:n = 6, edges = [[0,1],[0,2],[2,3],[2,4],[2,5]]
Output:[8,12,6,10,10,10]
Explanation:

Distance sums.

Input:n = 6, edges = [[1]]
Output:[1]
Explanation:

Minimal case with a single-element matrix.

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

In this linear tree (path graph), distance sums are [6, 4, 4, 6]. End nodes have the largest sums.

Constraints

  • 1 ≤ n ≤ 3 × 10⁴

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