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
//    _        _   __
//   (_)      | | / /
//    __ ___  | |/ / ___    ____
//   | |/ _ `\|   | / _ `\ / _  \
//   | | (_) | |\ \| (_) || (_) |
//   | |\__,_|_| \_\___,_|\____/
// _/ |
//|__/
#pragma GCC optimize("O3")
#include<bits/stdc++.h>
#define endl '\n'
#define mod 1000000007LL
#define lowbit(x) (x&-x)
using namespace std;
using ll = long long;


int main(){
	ios::sync_with_stdio(false);cin.tie(NULL);
	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=0;i<n-1;i++){
			cout<<1;
			for(int j=0;j<i;j++){
				cout<<0;
			}
			cout<<1;
			cout<<endl;
		}
	}
	return 0;
}
/*
1000001
100001
10001
1001
101
11

3

111
11
0
*/
