#include <bits/stdc++.h>  // clang-format off
using namespace std;
using Int = long long;
#define REP_(i, a_, b_, a, b, ...) for (int i = (a), lim_i = (b); i < lim_i; i++)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
struct SetupIO { SetupIO() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(13); } } setup_io;
#ifndef _MY_DEBUG
#define dump(...)
#endif  // clang-format on

/**
 *    author:  knshnb
 *    created: Fri Mar 20 14:03:30 JST 2020
 **/

signed main() {
    Int n;
    cin >> n;
    if (n == 1) {
        cout << "1\n0\n";
    } else if (n == 2) {
        cout << "2\n0\n11\n";
    } else {
        cout << n - 1 << endl;
        REP(i, 2, n + 1) {
            cout << 1;
            REP(j, i - 2) cout << 0;
            cout << "1\n";
        }
    }
}


### 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>  // clang-format off
using namespace std;
using Int = long long;
#define REP_(i, a_, b_, a, b, ...) for (int i = (a), lim_i = (b); i < lim_i; i++)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
struct SetupIO { SetupIO() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(13); } } setup_io;
#ifndef _MY_DEBUG
#define dump(...)
#endif  // clang-format on

/**
 *    author:  knshnb
 *    created: Fri Mar 20 14:03:30 JST 2020
 **/

signed main() {
    Int n;
    cin >> n;
    if (n == 1) {
        cout << "1\n0\n";
    } else if (n == 2) {
        cout << "2\n0\n11\n";
    } else {
        cout << n - 1 << endl;
        REP(i, 2, n + 1) {
            cout << 1;
            REP(j, i - 2) cout << 0;
            cout << "1\n";
        }
    }
}


```