B. Mathtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputJATC's math teacher always gives the class some interesting math problems so that they don't get bored. Today the problem is as follows. Given an integer n, you can perform the following operations zero or more times:  mul x: multiplies n by x (where x is an arbitrary positive integer).  sqrt: replaces n with \sqrt{n} (to apply this operation, \sqrt{n} must be an integer). You can perform these operations as many times as you like. What is the minimum value of n, that can be achieved and what is the minimum number of operations, to achieve that minimum value?Apparently, no one in the class knows the answer to this problem, maybe you can help them?InputThe only line of the input contains a single integer n (1 \le n \le 10^6) — the initial number.OutputPrint two integers: the minimum integer n that can be achieved using the described operations and the minimum number of operations required.ExamplesInput20Output10 2Input5184Output6 4NoteIn the first example, you can apply the operation mul 5 to get 100 and then sqrt to get 10.In the second example, you can first apply sqrt to get 72, then mul 18 to get 1296 and finally two more sqrt and you get 6.Note, that even if the initial value of n is less or equal 10^6, it can still become greater than 10^6 after applying one or more operations.
Input20
Output10 2
['greedy', 'math', 'number theory', '*1500']