CF1062B.Math

JATC'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?

JATC 的数学老师总是给全班同学出一些有趣的数学题，以免他们感到无聊。今天的问题如下：给定一个整数 $n$，你可以执行以下操作零次或多次：

• mul $x$：将 $n$ 乘以 $x$（其中 $x$ 是任意正整数）；
• sqrt：将 $n$ 替换为 $\sqrt{n}$（要执行此操作，$\sqrt{n}$ 必须为整数）。

你可以任意多次执行这些操作。问：所能达到的 $n$ 的最小值是多少？以及达到该最小值所需的最少操作次数是多少？

显然，班上没人知道这道题的答案，也许你能帮帮他们？

The only line of the input contains a single integer $n$ ($1 \le n \le 10^6$) — the initial number.

输入仅有一行，包含一个整数 $n$（$1 \le n \le 10^6$）——初始数字。

Print two integers: the minimum integer $n$ that can be achieved using the described operations and the minimum number of operations required.

输出两个整数：通过所述操作所能达到的最小整数 $n$，以及所需的最少操作次数。

In 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.

在第一个例子中，你可以先执行乘法操作 mul 5 得到 $100$，然后执行开方操作 sqrt 得到 $10$。

在第二个例子中，你可以先执行开方操作 sqrt 得到 $72$，再执行乘法操作 mul 18 得到 $1296$，最后再执行两次开方操作，即可得到 $6$。

注意：即使初始值 $n$ 不超过 $10^6$，在执行一次或多次操作后，其值仍可能超过 $10^6$。