Divide into Coprime Groups

Problem Background

Special for beginners, ^_^

Problem Description

Given $n$ positive integers, divide them into groups such that any two numbers in the same group are coprime. What is the minimum number of groups needed?

Input Format

The first line is a positive integer $n\;(1 \le n \le 10)$.

The second line contains $n$ positive integers not greater than $10000$.

Output Format

One positive integer: the minimum number of groups needed.

Sample Input

6
14 20 33 117 143 175

Sample Output

3

Constraints

1s, 1024KiB for each test case.