D. GCD Countingtime limit per test4.5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a tree consisting of n vertices. A number is written on each vertex; the number on vertex i is equal to a_i.Let's denote the function g(x, y) as the greatest common divisor of the numbers written on the vertices belonging to the simple path from vertex x to vertex y (including these two vertices). Also let's denote dist(x, y) as the number of vertices on the simple path between vertices x and y, including the endpoints. dist(x, x) = 1 for every vertex x.Your task is calculate the maximum value of dist(x, y) among such pairs of vertices that g(x, y) > 1.InputThe first line contains one integer n — the number of vertices (1 \le n \le 2 \cdot 10^5).The second line contains n integers a_1, a_2, ..., a_n (1 \le a_i \le 2 \cdot 10^5) — the numbers written on vertices.Then n - 1 lines follow, each containing two integers x and y (1 \le x, y \le n, x \ne y) denoting an edge connecting vertex x with vertex y. It is guaranteed that these edges form a tree.OutputIf there is no pair of vertices x, y such that g(x, y) > 1, print 0. Otherwise print the maximum value of dist(x, y) among such pairs.ExamplesInput32 3 41 22 3Output1Input32 3 41 32 3Output2Input31 1 11 22 3Output0
Input32 3 41 22 3
Output1
['data structures', 'dfs and similar', 'dp', 'number theory', 'trees', '*2000']