#include "iostream"
#include "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"
#include "ctime"

using namespace std;

//constexpr long long int MOD = 1000000007;
//constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;
//constexpr long long int MOD = 998244353;
constexpr long double EPS = 1e-8;


int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	int N;
	cin >> N;
	if (N == 1) {
		cout << 1 << endl;
		cout << 1 << endl;
		return 0;
	}
	if (N == 2) {
		cout << 2 << endl;
		cout << 0 << endl;
		cout << 11 << endl;
		return 0;
	}
	cout << N - 1 << endl;
	for (int i = 2; i <= N; i++) {
		cout << 0;
		for (int j = 0; j < i - 2; j++)cout << 1;
		cout << 0 << endl;
	}
}

### Prompt

Generate a cpp solution to the following problem:

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

### Response

```cpp
#include "iostream"
#include "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"
#include "ctime"

using namespace std;

//constexpr long long int MOD = 1000000007;
//constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;
//constexpr long long int MOD = 998244353;
constexpr long double EPS = 1e-8;


int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	int N;
	cin >> N;
	if (N == 1) {
		cout << 1 << endl;
		cout << 1 << endl;
		return 0;
	}
	if (N == 2) {
		cout << 2 << endl;
		cout << 0 << endl;
		cout << 11 << endl;
		return 0;
	}
	cout << N - 1 << endl;
	for (int i = 2; i <= N; i++) {
		cout << 0;
		for (int j = 0; j < i - 2; j++)cout << 1;
		cout << 0 << endl;
	}
}

```