Goldbach Conjecture

Input file: goldbach.in
Output file: goldbach.out

The Problem

The Goldbach conjecture states that any positive even number greater than 4 can be expressed as the sum of two prime numbers. This conjecture has never been completely proven, but it has been demonstrated by computer to be true for a wide range of even numbers.

Given an even number greater than 4, find two prime numbers which sum to it. For purposes of this problem, 1 is not considered a prime number.

Each line of program output consists of exctly three entites: the original input number and the two primes which sum to that number, with spaces separating the numbers as shown below.

Input

6
8
10
100

Output

6  3  3
8  3  5
10  5  5
100  47  53