A sheikh had to pay three men with a batch of 21 equal wine casks, seven of them being full, seven half-full, and seven empty. How could Beremiz do the distribution, in such a way that each man received the same number of casks and the same amount of wine?

Input

Input consists in several natural numbers n, all between 2 and 10^{6}.

Output

For every n, print a line with “n:”. Then, print in three lines any way to divide n full casks, n half-full casks and n empty casks among three men, so that each one receives n casks and the same total amount of wine. The i-th line must contain, separated by spaces, the number of full casks, half-full casks and empty casks that correspond to the i-th man. Follow the format of the samples exactly.

Public test cases

**Input**

7 7 9

**Output**

7: 3 1 3 2 3 2 2 3 2 7: 3 1 3 3 1 3 1 5 1 9: 3 3 3 3 3 3 3 3 3

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Spanish
- Other languages
- Spanish
- Official solutions
- C++
- User solutions
- C++