Denomination Combinations

Problem Background

Special for beginners, ^_^

Problem Description

Use $1$-jiao, $2$-jiao, and $5$-jiao coupons to make up $n$ jiao. Let $a, b, c$ be the numbers of $1$-jiao, $2$-jiao, and $5$-jiao coupons used, respectively. List all possible combinations of $a, b, c$.

The output order is: first by $c$ in increasing order; if $c$ is the same, then by $b$ in increasing order.

Input Format

One integer $n$ ($1 \le n \le 100$), the amount in jiao to be made up.

Output Format

Output several lines, each line in the form:

i a b c

The first column $i$ is the current line number (starting from 001, a fixed width of $3$ characters, zero-padded on the left if shorter). The following three columns $a, b, c$ are the numbers of $1$-jiao, $2$-jiao, and $5$-jiao coupons (each fixed at $12$ characters wide, padded with spaces on the left).

Sample Input

10

Sample Output

001         10           0           0
002           8           1           0
003           6           2           0
004           4           3           0
005           2           4           0
006           0           5           0
007           5           0           1
008           3           1           1
009           1           2           1
010           0           0           2

Constraints

Time limit: 1s, memory limit: 1024KiB for each test case.

Hint

Each of $a, b, c$ is right-aligned in a field of width $12$; the line number $i$ is zero-padded to width $3$.