Problem statement

Of the string set $ S $ that meets the following conditions, configure $ 1 $ with the largest number of elements.

• The length of the string contained in $ S $ is $ 1 $ or more and $ N $ or less.
• The lengths of the strings contained in $ S $ are different.
• The string contained in $ S $ consists only of the characters 0 and1.
• For any $ 2 $ string contained in $ S $, one is not a substring of the other.

However, the substring of the string $ x $ is the string obtained by removing more than $ 0 $ characters from the beginning and end of $ x $.

Constraint

• $1 \ leq N \ leq 300$
• $ N $ is an integer

input

Input is given from standard input in the following format.

$ N $

output

Output $ 1 $ of the string set $ S $ that satisfies the condition with the maximum number of elements. There may be multiple such $ S $, but any output will be correct.

Specifically, output in the following format.

Output $ K $, the number of elements of $ S $, on the $ 1 $ line.

Output all $ S $ elements from the $ 2 $ line to the $ K + 1 $ line. Print $ 1 $ of $ S $ elements on each line.

$ K $
$ S_1 $
$ S_2 $
$\$
$ S_K $

Input example 1

2

Output example 1

2
0
11

The string set $\\ {0, 11 \\}$ is the set with the largest number of elements that meets the conditions.

Input example 2

1

Output example 2

1
0

Example

Input

2

Output

2
0
11

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见题面