Problem Statement

H has been asked to create test cases based on the following constraints.
$a+b+c = N$ and $a \le b \le c$ (where $a,b,c,N$ are positive integers)
Find all possible test cases,
- in ascending order of $a$,
- and, for equal $a$, in ascending order of $b$.

The output is large, so please use a fast output function or the like.

Input

$N$

The input consists of $N$ given on one line.
- Constraints
$3 \le N \le 3000$

Output

Output $a,b,c$ separated by spaces, with test cases separated by newlines.
A newline is required at the end of the output.

Sample

3

1 1 1

10

1 1 8
1 2 7
1 3 6
1 4 5
2 2 6
2 3 5
2 4 4
3 3 4