##### DWITE, January 2012, Problem 2

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 ( factorial) is the product of the integers from through . It's your job now to create a program to help you do your homework.

The input will contain 5 test cases. Each test case contains a number .

The output will contain 5 lines of output, each representing the prime factorization of the given number, which should be of the form: where are the distinct prime factors of the given number in increasing order, and are their exponents.

#### Sample Input

```
2
3
5
10
20
```

#### Sample Output

```
2^1
2^1 * 3^1
2^3 * 3^1 * 5^1
2^8 * 3^4 * 5^2 * 7^1
2^18 * 3^8 * 5^4 * 7^2 * 11^1 * 13^1 * 17^1 * 19^1
```

Problem Resource: DWITE

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