1476. Table

单点时限: 2.0 sec

内存限制: 256 MB

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

4

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 is present twice in the table.

It is not always possible to solve this task. For example, the task is unsolvable for M = 10.

输入格式

You are given one value of M.

输出格式

You must find a valid table for each test case and write it into the corresponding output. The first line of a output must contain N, the number of rows and columns in the table. The i+1-st line of the output (1 ≤ i ≤ N) must contain the elements of the i-th row of the table as N digits, separated by spaces.

样例

Input
2
Output
3
2 3 4
5 6 6
8 2 0

1 人解决,1 人已尝试。

1 份提交通过,共有 11 份提交。

9.4 EMB 奖励。

创建: 16 年,9 月前.

修改: 6 年,8 月前.

最后提交: 3 年,5 月前.

来源: BOI 2003

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