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Given a non-empty array of unique positive integers A, consider the following graph:

  • There are A.length nodes, labelled A[0] to A[A.length - 1];
  • There is an edge between A[i] and A[j] if and only if A[i] and A[j] share a common factor greater than 1.

Return the size of the largest connected component in the graph.

Example 1:

Input: [4,6,15,35]
Output: 4

example1

Example 2:

Input: [20,50,9,63]
Output: 2

example2

Example 3:

Input: [2,3,6,7,4,12,21,39]
Output: 8

example3

Note:

  1. 1 <= A.length <= 20000
  2. 1 <= A[i] <= 100000