Roast Chicken

Problem Background

Piggy Hanke got himself a chicken.

Problem Description

Piggy Hanke especially loves eating roast chicken (they are both livestock, why fry each other alive!). Hanke eats chicken in a peculiar way — why peculiar? Because he has $10$ seasonings (mustard, cumin, etc.), and each seasoning can be added in an amount from $1$ to $3$ grams. The deliciousness of any roast chicken is the sum of the amounts of all seasonings.

Now Hanke wants to know: given a target deliciousness $n$, output all the combination schemes for the $10$ seasonings.

Input Format

One positive integer $n$, representing the target deliciousness.

Output Format

The first line: the total number of schemes.

From the second line to the end: $10$ numbers per line, representing the amount of each seasoning used, listed in lexicographic order.

If there is no valid scheme, just output a single $0$ on the first line.

Sample Input

11

Sample Output

10
1 1 1 1 1 1 1 1 1 2
1 1 1 1 1 1 1 1 2 1
1 1 1 1 1 1 1 2 1 1
1 1 1 1 1 1 2 1 1 1
1 1 1 1 1 2 1 1 1 1
1 1 1 1 2 1 1 1 1 1
1 1 1 2 1 1 1 1 1 1
1 1 2 1 1 1 1 1 1 1
1 2 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1

Constraints

For $100\%$ of the test data, $n \le 10000$.