It is a well-known fact that every natural number has a unique prime factorization. That is, you can uniquely express each natural number ~N~ as:

$$\displaystyle N = P_1^{M_1} \times P_2^{M_2} \times \ldots \times P_K^{M_K} $$

Where ~P_1 < P_2 < \ldots < P_K~ are prime numbers. For example, ~28 = 2^2 \times 7~ and ~3645 = 3^6 \times 5~.

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 ~N~, can you figure out the prime factorization of ~N^N~?

Input

Each test case contains one integer ~N~ ~(2 \le N \le 2^{47})~.

Output

For each test case, output, on one line, the prime factorization of the number.

Sample Input

6

Sample Output

2^6 * 3^6

Sample Input

197538393501504

Sample Output

2^1185230361009024 * 3^790153574006016 * 11^592615180504512 * 31^987691967507520