primefactorization

Problem Description

Given an integer n where 2 ≤ n < 1012, factorize it into its prime factors.

Input

A single integer, n

For 100% of the testcases, n < 1012
For 50% of the testcases, n < 106
For 30% of the testcases, n < 103

Output

On each line, output the prime factors of n in sorted order, with its power indicated. (See Sample Output)

Sample Input 1

120

Sample Output 1

2^3
3^1
5^1

Sample Input 2

331

Sample Output 2

331^1

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Compile Errors


							
Time Limit: 1 Seconds
Memory Limit: 256MB
No. of ACs: 140
Your best score: 0
Source: Dunjudge Archive

Subtask Score
1 100
2 0