#include <algorithm>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using namespace std;
#define rep(i, n) for(int i = 0; (i) < (n); (i)++)
#define FOR(i, m, n) for(int i = (m); (i) < (n); (i)++)
#define All(v) (v).begin(), (v).end()
#define MP make_pair
#define pb push_back
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1 << 30;
const ll LINF = 1LL << 61;
const int MOD = 1e9 + 7;

int main() {
    int N;
    cin >> N;
    set<string> S;
    if(N == 1) {
        cout << 1 << endl;
        cout << 0 << endl;
    } else if(N == 2) {
        cout << 2 << endl;
        cout << 0 << endl;
        cout << 11 << endl;
    } else {
        cout << N - 1 << endl;
        cout << 11 << endl;
        string s = "1";
        rep(i, N - 2) {
            s = s + '0';
            cout << s + '1' << endl;
        }
    }
    return 0;
}

### Prompt

Generate a cpp solution 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 <algorithm>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using namespace std;
#define rep(i, n) for(int i = 0; (i) < (n); (i)++)
#define FOR(i, m, n) for(int i = (m); (i) < (n); (i)++)
#define All(v) (v).begin(), (v).end()
#define MP make_pair
#define pb push_back
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1 << 30;
const ll LINF = 1LL << 61;
const int MOD = 1e9 + 7;

int main() {
    int N;
    cin >> N;
    set<string> S;
    if(N == 1) {
        cout << 1 << endl;
        cout << 0 << endl;
    } else if(N == 2) {
        cout << 2 << endl;
        cout << 0 << endl;
        cout << 11 << endl;
    } else {
        cout << N - 1 << endl;
        cout << 11 << endl;
        string s = "1";
        rep(i, N - 2) {
            s = s + '0';
            cout << s + '1' << endl;
        }
    }
    return 0;
}

```