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
// warm heart, wagging tail,and a smile just for you!
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//                                            ███████████       ██╬╬╬╬╬████╬╬████╬╬╬╬╬██
//                                      █████████╬╬╬╬╬████████████╬╬╬╬╬██╬╬╬╬╬╬███╬╬╬╬╬██
//                               ████████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬██╬╬╬╬╬╬╬██
//                             ████╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████████╬╬╬╬╬╬╬╬╬╬╬██
//                           ███╬╬╬█╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬███╬╬╬╬╬╬╬█████
//                         ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬████████╬╬╬╬╬██
//                       ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬╬╬╬╬███
//                     ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬██
//                 ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬████
//     █████████████╬╬╬╬╬╬╬╬██╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬██████
//   ████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬██████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████╬╬╬╬╬╬╬███████████╬╬╬╬╬╬╬╬██╬╬╬██╬╬╬██
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████╬╬╬╬╬╬╬╬╬╬╬█╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬██
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬▓▓▓▓▓▓╬╬╬████╬╬████╬╬╬╬╬╬╬▓▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬███
// ██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██████▓▓▓▓▓▓▓╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬▓▓▓▓▓▓▓██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██╬╬╬╬█████
// ███╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████████
//   ███╬╬╬╬╬╬╬╬╬╬╬╬╬█████╬╬╬╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬███╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬██
//       ██████████████  ████╬╬╬╬╬╬███████████████████████████╬╬╬╬╬██╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬╬████
//                         ███████                           █████  ███████████████████  
//
#include "bits/stdc++.h"
using namespace std;
#define INF (1<<30)
#define LINF (1LL<<60)
#define fs first
#define sc second
#define int long long
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define RFOR(i,a,b) for(int i = (b-1);i>=(a);--i)
#define REP(i,n)  FOR(i,0,(n))
#define RREP(i,n) RFOR(i,0,(n))
#define ITR(itr,mp) for(auto itr = (mp).begin(); itr != (mp).end(); ++itr)
#define RITR(itr,mp) for(auto itr = (mp).rbegin(); itr != (mp).rend(); ++itr)
#define range(i,a,b) ((a)<=(i) && (i)<(b))
#define debug(x)  cout << #x << " = " << (x) << endl
#define SP << " " << 
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
#define MSB(x) (63-__builtin_clzll(x))
#define pcnt(x) (__builtin_popcountll(x))
#define parity(i,j) (i&(1LL<<j))
typedef pair<int,int> P;
typedef tuple<int,int,int> T;
typedef vector<int> vec;
typedef vector<vector<int>> mat;

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

  int n;
  cin >> n;

  if(n==1){
    cout << 1 << endl << 1 << endl;
  }
  else if(n==2){
    cout << 2 << endl << 1 << endl << "00" << endl;
  }
  else{
    cout << n-1 << endl;
    REP(i,n-1){
      cout << 1;
      REP(_,i) cout << 0;
      cout << 1 << endl;
    }
  }

  return 0;
}
