#include<bits/stdc++.h>
using namespace std;
#define fs first
#define sc second
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<int,int> P;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<typename T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
const LL mod=998244353;
const LL LINF=1LL<<62;
const int INF=1<<30;
int dx[]={1,0,-1,0,1,-1,1,-1};
int dy[]={0,1,0,-1,1,-1,-1,1};




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


### Prompt

Develop a solution in Cpp to the problem described below:

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>
using namespace std;
#define fs first
#define sc second
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<int,int> P;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template<typename T> T gcd(T a,T b){return b?gcd(b,a%b):a;}
const LL mod=998244353;
const LL LINF=1LL<<62;
const int INF=1<<30;
int dx[]={1,0,-1,0,1,-1,1,-1};
int dy[]={0,1,0,-1,1,-1,-1,1};




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


```