#include<iostream>
#include<vector>
#include<string>
#define rep(i, start, end) for (int i = (int)start; i < (int)end; ++i)
#define rrep(i, start, end) for (int i = (int)start - 1; i >= (int)end; --i)
#define all(x) (x).begin(), (x).end()
using namespace std;
using ll = long long;
template<typename T> inline bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return 0;}
template<typename T> inline bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return 0;}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;
    if (N == 1) {
        cout << 1 << endl << 0 << endl;
    }
    else if (N == 2) {
        cout << 2 << endl << 0 << endl << 11 << endl;
    }
    else {
        cout << N - 1 << endl;
        rep(i, 0, N - 1) {
            cout << 0;
            rep(j, 0, i) {
                cout << 1;
            }
            cout << 0 << endl;
        }
    }
    return 0;
}

### Prompt

Create a solution in CPP for 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<iostream>
#include<vector>
#include<string>
#define rep(i, start, end) for (int i = (int)start; i < (int)end; ++i)
#define rrep(i, start, end) for (int i = (int)start - 1; i >= (int)end; --i)
#define all(x) (x).begin(), (x).end()
using namespace std;
using ll = long long;
template<typename T> inline bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return 0;}
template<typename T> inline bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return 0;}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;
    if (N == 1) {
        cout << 1 << endl << 0 << endl;
    }
    else if (N == 2) {
        cout << 2 << endl << 0 << endl << 11 << endl;
    }
    else {
        cout << N - 1 << endl;
        rep(i, 0, N - 1) {
            cout << 0;
            rep(j, 0, i) {
                cout << 1;
            }
            cout << 0 << endl;
        }
    }
    return 0;
}

```