Table 1

Time limit1sMemory limit512 MB

Summary

Construct an N by N digit grid (2 <= N <= 10) so every row, column, and main diagonal reads as a distinct multiple of M with no leading zero.

Level: Medium7 of 10
Topics: Backtracking, Brute force, Math, Implementation
Solved: No attempts yet

Problem

For a given integer M, build a square table with N rows and N columns (2 ≤ N ≤ 10) filled with decimal digits, subject to the following restrictions. The N-digit numbers formed by the digits in each row (left to right), each column (top to bottom), and each main diagonal (top to bottom) must all be multiples of M, must not start with the digit 0, and must be distinct within the table.

For example, a valid table for M = 2 is

2 3 4
5 6 6
8 2 0

The following tables are not valid for M = 2:

because N < 2;

2 0
4 8

because the numbers in the last column and on one of the main diagonals start with the digit 0;

2 3 4
5 8 8
2 0 2

because the number 482 appears twice in the table.

This task is not always solvable. For example, it is unsolvable for M = 10.

Input

The first line contains one value of M.

Output

The first line must contain N, the number of rows and columns in the table. The i+1-st line (1 ≤ i ≤ N) must contain the N elements of the i-th row, separated by spaces.

Constraints

M = 3

Hint

It is known that at least one solution exists for each given test input.

Examples1

Example 1
Input
```
2
```
Expected output
```
3
2 3 4
5 6 6
8 2 0
```