#include <bits/stdc++.h>
#define be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin>>n;
    vector<string> s;
    string t;
    s.pb("11");
    s.pb("101");
    s.pb("0100");
    if(n==1){
    	cout << "1" <<endl;
    	cout << "0" <<endl;
    	return 0;
    }
    if(n==2||n==3){
    	cout << "2" <<endl;
    	cout <<"0" <<endl;
     	cout << "11" <<endl;
     	return 0;
    }
    t="0";
    for(int i=0;i<=n-5;i++){
    	t+="0";
    	s.pb("1"+t+"10");
    }
    cout << s.size() <<endl;
    for(auto i:s){
    	cout << i<<endl;
    }

    return 0;
}


### Prompt

Please create a solution in cpp to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
#define be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin>>n;
    vector<string> s;
    string t;
    s.pb("11");
    s.pb("101");
    s.pb("0100");
    if(n==1){
    	cout << "1" <<endl;
    	cout << "0" <<endl;
    	return 0;
    }
    if(n==2||n==3){
    	cout << "2" <<endl;
    	cout <<"0" <<endl;
     	cout << "11" <<endl;
     	return 0;
    }
    t="0";
    for(int i=0;i<=n-5;i++){
    	t+="0";
    	s.pb("1"+t+"10");
    }
    cout << s.size() <<endl;
    for(auto i:s){
    	cout << i<<endl;
    }

    return 0;
}


```