PTIME - Prime Time


For your math homework this week your teacher gave you five large numbers and asked you to find their prime factors. However these numbers aren't nearly large enough for someone with knowledge of programming like yourself. So you decide to take the factorial of each of these numbers. Recall that N! (N factorial) is the product of the integers from 1 through N (inclusive). It’s your job now to create a program to help you do your homework.

Input

Each test case contains a number N (2 ≤ N ≤ 10000).

Output

The output should contain a line representing the prime factorization of the factorial given number, which should be of the form: p1^e1 * p2^e2 * ... * pk^ek where p1, p2, ..., pk are the distinct prime factors of the factorial of the given number in increasing order, and e1, e2, ..., ek are their exponents.

Example

Input:
10

Output:
2^8 * 3^4 * 5^2 * 7^1

hide comments
jaans: 2012-06-21 22:27:44

@ :D :: i read upto EOF and got AC :)

:D: 2012-06-21 22:27:44

It's pretty unclear how many test cases are per file. One or some read until EOF? Please clarify.

MR. BEAN : 2012-06-21 22:27:44

enjoyed solving it :)

devu: 2012-06-21 22:27:44

cant really get why i am getting wa!!
Could you please cleck my soln..my submission id is 7176656.

Gaurav: 2012-06-21 22:27:44

@problem setter pls chk my soln..i dnt understand why it is giving WA..pls


Added by:Amlesh Jayakumar
Date:2012-06-19
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:DWITE Programming Contest 2012 (Own Problem)