Summation of Four Primes

The Problem

A prime number is an integer larger than 1 which is divisible by no positive integers other than 1 and itself.

Waring's prime number conjecture states that every odd integer is either prime or the sum of three primes. Goldbach's conjecture is that every even integer is the sum of two primes. Both problems have been open for over 200 years.

In this problem you have a slightly less demanding task. Find a way to express a given integer as the sum of exactly four primes.

Input File:

Each input case consists of one integer n (1 ≤ n ≤ 10000000) on its own line. Input is terminated by end of file.

Output File: primes.out

Each input n will generate one line of output. The output line should start with the number n, followed by a colon(:), followed by a space. If there is no solution to the problem, the rest of the line should contain Impossible. If there is a solution, the rest of the line should contain the four prime numbers that sum up to n (in any order). There should be one blank space between each pair of prime numbers.

There can be multiple solutions. Any good solution will be accepted.




24: 3 11 3 7
36: 3 7 13 13
46: 11 11 17 7