Problem

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

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.

Output

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.

Input Example 1

1

Output Example 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 $0$.

Input Example 2

2

Output Example 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