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;
#define rep(i,N) for(int i=0;i<int(N);++i)
#define rep1(i,N) for(int i=1;i<int(N);++i)
#define all(a) (a).begin(),(a).end()
#define print(v) { cerr<<#v<<": [ "; for(auto _ : v) cerr<<_<<", "; cerr<<"]"<<endl; }
#define printpair(v) { cerr<<#v<<": [ "; for(auto _ : v) cerr<<"{"<<_.first<<","<<_.second<<"}"<<", "; cerr<<"]"<<endl; }
#define dump(x) cerr<<#x<<": "<<x<<endl;
#define bit(k) (1LL<<(k))
#define Yes "Yes"
#define No "No"
#define YES "YES"
#define NO "NO"
typedef long long ll;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vec<T>>;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

const int INF = (ll)1e9;
const ll INFLL = (ll)1e18+1;
const ll MOD = (ll)1e9+7;
const double PI = acos(-1.0);
/*
const int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
const int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
const string dir = "DRUL";
*/

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);

    int N;
    cin >> N;
    if(N == 1){
        cout << 1 << endl;
        cout << 1 << endl;
        return 0;
    }
    if(N == 2){
        cout << 2 << endl;
        cout << 0 << endl;
        cout << 11 << endl;
        return 0;
    }
    cout << N - 1 << endl;
    vec<string> ans(N-1, "");
    for(int i = 0; i < N - 1;++i){
        rep(j, i+2){
            if(j == 0)ans[i].push_back('1');
            else if(j == i+1)ans[i].push_back('1');
            else{
                ans[i].push_back('0');
            }
        }
    }
    rep(i,N-1){
        cout << ans[i] << endl;
    }
}
