String Set

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 and 1.
• 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.

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

---

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

inputFormat

input

Input is given from standard input in the following format.

$N$

outputFormat

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.

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

---

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

样例

2

2
0
11

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