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<iostream>
#include<algorithm>
#include<vector>
#include<string>
#include<utility>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<functional>
#include<math.h>
using namespace std;
#define N (1000000000+7)
#define INF 1e16
typedef long long ll;
typedef pair<ll,ll> P;
 

int main(void){
    int n;
    cin>>n;
    if(n==1){
        cout<<1<<endl;
        cout<<0<<endl;
        return 0;
    }
    else{
        if(n==2){
            cout<<2<<endl;
            cout<<0<<endl;
            cout<<11<<endl;
        }
        else{
            vector<string>ans;
            string s="";
            ans.push_back("00");
            for(ll i=0;i<n-2;i++){
                s.push_back('1');
                ans.push_back("0"+s+"0");
            }
            cout<<ans.size()<<endl;
            for(int i=0;i<ans.size();i++){
                cout<<ans[i]<<endl;
            }
        }
    }
    return 0;
}
