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>
#define rep(i,a,...) for(int i = (a)*(strlen(#__VA_ARGS__)!=0);i<(int)(strlen(#__VA_ARGS__)?__VA_ARGS__:(a));++i)
#define per(i,a,...) for(int i = (strlen(#__VA_ARGS__)?__VA_ARGS__:(a))-1;i>=(int)(strlen(#__VA_ARGS__)?(a):0);--i)
#define foreach(i, n) for(auto &i:(n))
#define pii pair<int, int>
#define pll pair<long long, long long>
#define all(x) (x).begin(), (x).end()
#define bit(x) (1ll << (x))
using ll = long long;
//const ll MOD = (ll)1e9+7;
const ll MOD = 998244353;
const int INF = (ll)1e9+7;
const ll INFLL = (ll)1e18;
using namespace std;
template<class t>
using vvector = vector<vector<t>>;
template<class t>
using vvvector = vector<vector<vector<t>>>;
template<class t>
using priority_queuer = priority_queue<t, vector<t>, greater<t>>;
template<class t, class u> bool chmax(t &a, u b){if(a<b){a=b;return true;}return false;}
template<class t, class u> bool chmin(t &a, u b){if(a>b){a=b;return true;}return false;}
#ifdef DEBUG
#define debug(x) cout<<"LINE "<<__LINE__<<": "<<#x<<" = "<<x<<endl;
#else
#define debug(x) (void)0
#endif

ll modpow(ll x, ll b){
  ll res = 1;
  while(b){
    if(b&1)res = res * x % MOD;
    x = x * x % MOD;
    b>>=1;
  }
  return res;
}

ll modinv(ll x){
  return modpow(x, MOD-2);
}

bool was_output = false;
template<class t>
void output(t a){
  if(was_output)cout << " ";
  cout << a;
  was_output = true;
}
void outendl(){
  was_output = false;
  cout << endl;
}
ll in(){
  ll res;
  scanf("%lld", &res);
  return res;
}

template<class t>
istream& operator>>(istream&is, vector<t>&x){
  for(auto &i:x)is >> i;
  return is;
}

template<class t, class u>
istream& operator>>(istream&is, pair<t, u>&x){
  is >> x.first >> x.second;
  return is;
}

template<class t>
void in(t&x){
  cin >> x;
}

string func(int n){
  string res = "1";
  rep(i,n-2)res+="0";
  res+="1";
  return res;
}

int main(){
  int n = in();
  if(n==1){
    cout << 1 << endl;
    cout << "1" << endl;
    return 0;
  }
  if(n==2){
    cout << 2 << endl;
    cout << "11" << endl;
    cout << "0" << endl;
    return 0;
  }
  cout << n-1 << endl;
  rep(i,2,n+1){
    cout << func(i) << endl;
  }

  return 0;
}

