You are given an integer n and an undirected tree rooted at node 0 with n nodes numbered from 0 to n - 1. This is represented by a 2D array edges of length n - 1, where edges[i] = [ui, vi] indicates an undirected edge between nodes ui and vi.

You are also given an integer array nums, where nums[i] is the positive integer assigned to node i.

Define a value ti as the number of ancestors of node i such that the product nums[i] * nums[ancestor] is a perfect square.

Return the sum of all ti values for all nodes i in range [1, n - 1].

Note:

 

Example 1:

Input: n = 3, edges = [[0,1],[1,2]], nums = [2,8,2]

Output: 3

Explanation:

i Ancestors nums[i] * nums[ancestor] Square Check ti
1 [0] nums[1] * nums[0] = 8 * 2 = 16 16 is a perfect square 1
2 [1, 0] nums[2] * nums[1] = 2 * 8 = 16
nums[2] * nums[0] = 2 * 2 = 4		 Both 4 and 16 are perfect squares 2

Thus, the total number of valid ancestor pairs across all non-root nodes is 1 + 2 = 3.

Example 2:

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

Output: 1

Explanation:

i Ancestors nums[i] * nums[ancestor] Square Check ti
1 [0] nums[1] * nums[0] = 2 * 1 = 2 2 is not a perfect square 0
2 [0] nums[2] * nums[0] = 4 * 1 = 4 4 is a perfect square 1

Thus, the total number of valid ancestor pairs across all non-root nodes is 1.

Example 3:

Input: n = 4, edges = [[0,1],[0,2],[1,3]], nums = [1,2,9,4]

Output: 2

Explanation:

i Ancestors nums[i] * nums[ancestor] Square Check ti
1 [0] nums[1] * nums[0] = 2 * 1 = 2 2 is not a perfect square 0
2 [0] nums[2] * nums[0] = 9 * 1 = 9 9 is a perfect square 1
3 [1, 0] nums[3] * nums[1] = 4 * 2 = 8
nums[3] * nums[0] = 4 * 1 = 4		 Only 4 is a perfect square 1

Thus, the total number of valid ancestor pairs across all non-root nodes is 0 + 1 + 1 = 2.

 

Constraints: