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
#define _CRT_SECURE_NO_WARNINGS
#include<iostream>
#include<sstream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<climits>
#include<cmath>
#include<string>
#include<vector>
#include<set>
#include<map>
#include<queue>
#include<numeric>
#include<functional>
#include<algorithm>
#include<bitset>
#include<tuple>
#include<unordered_set>
#include<unordered_map>
#include<random>
#include<array>
#include<cassert>
using namespace std;
#define INF (1<<29)
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define all(v) v.begin(),v.end()
#define uniq(v) v.erase(unique(all(v)),v.end())





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


	int n;
	cin >> n;
	if (n==1) {
		cout << 1 << endl;
		cout << "0" << endl;
	}
	else if (n==2) {
		cout << 2 << endl;
		cout << "0" << endl;
		cout << "11" << endl;
	}
	else {
		cout << n - 1 << endl;
		for (int i = 2; i <= n;i++) {
			cout << '0';
			rep(j, i - 2)cout << '1';
			cout << '0';
			cout << endl;
		}
	}




	return 0;
}
