Time limit時間制限 : 4sec / Memory limitメモリ制限 : 256MB

Alice has a box locked with `n` digits dial lock. Each dial of the lock can be set to a digit from `0` to `9`.
Unfortunately, she forgot the passcode (of `n` digits). Now she will try all possible combinations of digits to unlock the key.

She can do one of the following procedure each time.

- Choose
`1`dial and add`1`to that digit. (If the digit chosen was`9`, it will be`0`). - Choose
`1`dial and subtract`1`from that digit. (If the digit chosen was`0`, it will be`9`).

Curiously, she wants to try all combinations even if she found the correct passcode during the trials. But it is a hard work to try all the `10^n` combinations.
Help her by showing the way how to make the procedure less as possible.

Initially, the combination of digits of the lock is set to `00..0`.

Calculate `m`, the minimum number of procedures to try all combinations of digits, and show the `m+1` combinations of digits after each procedures, including the initial combination `00..0`.
If there are more than one possible answer, you may choose any one of them.

Checking if the current combination of digits matches the passcode doesn't count as a procedure.

Input is given in the following format.

n

- On the first line, you will be given
`n (1 \leq n \leq 5)`, the number of digits of the dial lock.

On the first line, output `m`, the minimum number of procedures to try all combinations of digits.

On the following `m+1` lines, output the combination of digits that appears during the trial in order.
If there are more than `1` possible answer, you may choose any one of them.
Make sure to insert a line break at the end of the last line.

1

9 0 1 2 3 4 5 6 7 8 9

Don't forget to output the minimum number of procedures `9` on the first line.

On the following lines, note that you have to output `m+1` lines including the initial combination `0`.

2

99 00 01 02 03 04 05 06 07 08 09 19 18 17 16 15 14 13 12 11 10 20 21 22 23 24 25 26 27 28 29 39 38 37 36 35 34 33 32 31 30 40 41 42 43 44 45 46 47 48 49 59 58 57 56 55 54 53 52 51 50 60 61 62 63 64 65 66 67 68 69 79 78 77 76 75 74 73 72 71 70 80 81 82 83 84 85 86 87 88 89 99 98 97 96 95 94 93 92 91 90