#P1062B. Math

    ID: 3020 Type: RemoteJudge 1000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>greedymathnumber theory*1500

Math

No submission language available for this problem.

Description

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 nn, you can perform the following operations zero or more times:

  • mul xx: multiplies nn by xx (where xx is an arbitrary positive integer).
  • sqrt: replaces nn with n\sqrt{n} (to apply this operation, n\sqrt{n} must be an integer).

You can perform these operations as many times as you like. What is the minimum value of nn, 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?

The only line of the input contains a single integer nn (1n1061 \le n \le 10^6) — the initial number.

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

Input

The only line of the input contains a single integer nn (1n1061 \le n \le 10^6) — the initial number.

Output

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

Samples

Sample Input 1

20

Sample Output 1

10 2

Sample Input 2

5184

Sample Output 2

6 4

Note

In the first example, you can apply the operation mul 55 to get 100100 and then sqrt to get 1010.

In the second example, you can first apply sqrt to get 7272, then mul 1818 to get 12961296 and finally two more sqrt and you get 66.

Note, that even if the initial value of nn is less or equal 10610^6, it can still become greater than 10610^6 after applying one or more operations.