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
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<int,int>;
constexpr ll INF = 9e18;
constexpr int inf = 1e9;
const double INFD = 1e100;
const ll mod = 1000000007;
const double PI = 3.1415926535897932384626433832795028841971;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
};
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
};

// intやllをstringに変換
template<typename T> inline string toString(const T &a){
  ostringstream oss;
  oss << a;
  return oss.str();
};
// ---------------------------------------------------------------------------

int main(){
  int N;
  cin >> N;
  if(N == 1){
    cout << 1 << endl;
    cout << 0 << endl;
    return 0;
  }
  if(N == 2){
    cout << 2 << endl;
    cout << 0 << endl;
    cout << 11 << endl;
    return 0;
  }
  cout << N-1 << endl;
  for(int i=0; i<N-1; i++){
    string S = "";
    S += '1';
    S += string(i,'0');
    S += '1';
    cout << S << endl;
  }
  return 0;
}

