Math

题意翻译

## 题目描述 JATC的数学老师为了不让同学们感到厌倦，总是出一些有趣的题目。今天的题目是这样的： 给定一个整数`n`，您可以对它进行如下操作： * 乘以`x`：把n乘上x（x是任意正整数）。 * 开方：把n的值更新为$\sqrt{n}$ (前提是$\sqrt{n}$必须为整数)。 您可以对这些操作进行零次至任意次。那么n可以达到的最小值是多少 ？达到最小值需要进行操作的次数又是多少？ 显然，班里没有同学能够解决这个问题，您能够帮帮他吗？ ## 输入格式 输入一行，包含一个整数$n(1\le n\le 10^6)$——最初的数字。 ## 输出格式 输出两个整数：按照题目描述，n可以达到的最小整数，以及所需的操作次数。 ## 说明 在样例1中，可以先乘上5得到100，再开方得到10。 在样例2中，可以先开方得到72，再乘18得到1296，最后再开方两次，最终得到6。 注意，即使$n$小于等于$10^6$，它仍然可以在一次或数次操作后超过$10^6$。

题目描述

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?

输入输出格式

输入格式

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

输出格式

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

输入输出样例

输入样例 #1

20

输出样例 #1

10 2

输入样例 #2

5184

输出样例 #2

6 4

说明

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.