It is a well-known fact that every natural number has a unique prime factorization. That is, you can uniquely express each natural number as:
Where are prime numbers. For example, and .
In general, finding the prime factorization of large numbers is difficult to do (and serves as a basis for many cryptographic systems). However, in some special cases it is easy to find a number’s prime factorization.
One such case is when a number is a power of a smaller number. Given a number , can you figure out the prime factorization of ?
Each test case contains one integer .
For each test case, output, on one line, the prime factorization of the number.
2^6 * 3^6
2^1185230361009024 * 3^790153574006016 * 11^592615180504512 * 31^987691967507520