Problem F
Önnur tilgáta Goldbachs
Languages
en
is
The integer
There is a famous conjecture about primes, Goldbach’s conjecture, which says:
All even integers greater thancan be written as the sum of two primes.
This conjecture is from the year 1742. To this day no one has proved it nor found a counterexample. We considered making you prove it, but that would be too easy.
Instead we introduced a harder conjecture known as Goldbach’s second conjecture:
All odd numbers greater thancan be written as the sum of three primes.
In this problem we provide the odd integer
Input
The input contains one odd integer
Output
Print three primes separated by spaces such that their sum
is
Explanation of Sample Inputs
In the first sample
Scoring
The solution will be tested on input data of varying difficulty and the data is divided into groups as shown in the table below. The solution will then be scored according to how many groups are solved.
Group |
Points |
Constraints |
1 |
20 |
|
2 |
25 |
|
3 |
25 |
|
4 |
30 |
|
Sample Input 1 | Sample Output 1 |
---|---|
7 |
2 2 3 |
Sample Input 2 | Sample Output 2 |
---|---|
65 |
2 2 61 |