#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long int ull;
typedef long long int ll;
typedef pair<ll,ll> pll;
typedef pair<int,int> pii;
typedef long double D;
//typedef complex<D> P;
#define F first
#define S second
const ll MOD=1000000007;
//const ll MOD=998244353;

template<typename T,typename U>istream & operator >> (istream &i,pair<T,U> &A){i>>A.F>>A.S; return i;}
template<typename T>istream & operator >> (istream &i,vector<T> &A){for(auto &I:A){i>>I;} return i;}
template<typename T,typename U>ostream & operator << (ostream &o,const pair<T,U> &A){o<<A.F<<" "<<A.S; return o;}
template<typename T>ostream & operator << (ostream &o,const vector<T> &A){int i=A.size(); for(auto &I:A){o<<I<<(--i?" ":"");} return o;}


int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll N;
  cin>>N;
  if(N==1){cout<<1<<endl<<1<<endl;}
  else if(N==2){cout<<2<<endl<<0<<endl<<11<<endl;}
  else{
    cout<<N-1<<endl;
    for(int i=2;i<=N;i++){
      cout<<0;
      for(int j=1;j+1<i;j++){cout<<1;}
      cout<<0<<endl;
    }
  }

  return 0;
}


### Prompt

Construct a Cpp code solution to the problem outlined:

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<bits/stdc++.h>
using namespace std;
typedef unsigned long long int ull;
typedef long long int ll;
typedef pair<ll,ll> pll;
typedef pair<int,int> pii;
typedef long double D;
//typedef complex<D> P;
#define F first
#define S second
const ll MOD=1000000007;
//const ll MOD=998244353;

template<typename T,typename U>istream & operator >> (istream &i,pair<T,U> &A){i>>A.F>>A.S; return i;}
template<typename T>istream & operator >> (istream &i,vector<T> &A){for(auto &I:A){i>>I;} return i;}
template<typename T,typename U>ostream & operator << (ostream &o,const pair<T,U> &A){o<<A.F<<" "<<A.S; return o;}
template<typename T>ostream & operator << (ostream &o,const vector<T> &A){int i=A.size(); for(auto &I:A){o<<I<<(--i?" ":"");} return o;}


int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll N;
  cin>>N;
  if(N==1){cout<<1<<endl<<1<<endl;}
  else if(N==2){cout<<2<<endl<<0<<endl<<11<<endl;}
  else{
    cout<<N-1<<endl;
    for(int i=2;i<=N;i++){
      cout<<0;
      for(int j=1;j+1<i;j++){cout<<1;}
      cout<<0<<endl;
    }
  }

  return 0;
}


```