# Prime Factors

Webster defines prime as:

prime (prim) n.[ME, fr. MF, fem. of prin first, L primus; akin to L prior] 1 :first in time: original 2 a : having no factor except itself and one 3 is a   number b : having no common factor except one 12 and 25 are relatively   3 a : first in rank, authority or significance : principal b : having the highest quality or value   television time [from Webster's New Collegiate Dictionary]

The most relevant definition for this problem is 2a: An integer g>1 is said to be prime if and only if its only positive divisors are itself and one (otherwise it is said to be composite). For example, the number 21 is composite; the number 23 is prime. Note that the decompositon of a positive number g into its prime factors, i.e.,

is unique if we assert that fi > 1 for all i and for i<j.

One interesting class of prime numbers are the so-called Mersenne primes which are of the form 2p- 1. Euler proved that 231 - 1 is prime in 1772 -- all without the aid of a computer.

## Input

The input will consist of a sequence of numbers. Each line of input will contain one number g in the range -231 < g <231, but different of -1 and 1. The end of input will be indicated by an input line having a value of zero.

## Output

For each line of input, your program should print a line of output consisting of the input number and its prime factors. For an input number , where each fi is a prime number greater than unity (with for i<j), the format of the output line should be

When g < 0, if , the format of the output line should be

## Sample Input

-190
-191
-192
-193
-194
195
196
197
198
199
200
0


## Sample Output

-190 = -1 x 2 x 5 x 19
-191 = -1 x 191
-192 = -1 x 2 x 2 x 2 x 2 x 2 x 2 x 3
-193 = -1 x 193
-194 = -1 x 2 x 97
195 = 3 x 5 x 13
196 = 2 x 2 x 7 x 7
197 = 197
198 = 2 x 3 x 3 x 11
199 = 199
200 = 2 x 2 x 2 x 5 x 5


Miguel Revilla
2000-05-19