Problem
It is known that any natural number can be represented as the sum of at most four squares of natural numbers. Vasya decided to come up with a similar statement for cubes - he wants to know how many cubes are enough to represent any number. His first working hypothesis is eight.
It turned out that almost all the numbers that Vasya could come up with can be represented as a sum of no more than eight cubes. However, the number 239, for example, does not allow such a representation. Now Vasya wants to find some other such numbers, and also, perhaps, some pattern in the representations of all other numbers, in order to put forward a hypothesis about the form of all numbers that are not represented as the sum of eight cubes.
Help Vasya write a program that would check if it is possible to represent a given natural number as a sum of no more than eight cubes of natural numbers, and if possible, find some such representation.
Input
A natural number is entered
N <= 2*10
9.
Imprint
It is required to print no more than eight natural numbers, whose cubes add up to N. If the required representation does not exist, then the word
IMPOSSIBLE.
should be output to the output file
Examples
| # |
Input |
Output |
| 1 |
239 |
IMPOSSIBLE |
| 2 |
17 |
2 2 1 |