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
#include<bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x...) do { cout << "\033[32;1m " << #x << " -> "; err(x); } while (0)
void err() { cout << "\033[39;0m" << endl; }
template<template<typename...> class T, typename t, typename... A>
void err(T<t> a, A... x) { for (auto v: a) cout << v << ' '; err(x...); }
template<typename T, typename... A>
void err(T a, A... x) { cout << a << ' '; err(x...); }
#else
#define dbg(...)
#endif
typedef long long ll;
typedef pair<int,int> pi;
typedef vector<int> vi;
template<class T> using vc=vector<T>;
template<class T> using vvc=vc<vc<T>>;
template<class T> void mkuni(vector<T>&v)
{
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}
ll rand_int(ll l, ll r) //[l, r]
{
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
    return uniform_int_distribution<ll>(l, r)(gen);
}
template<class T>
void print(T x,int suc=1)
{
    cout<<x;
    if(suc==1) cout<<'\n';
    else cout<<' ';
}
template<class T>
void print(const vector<T>&v,int suc=1)
{
    for(int i=0;i<v.size();i++)
    print(v[i],i==(int)(v.size())-1?suc:2);
}
int main()
{
    int n;
    cin>>n;
    if(n==1)
    {
        cout<<"1\n0\n";
    }
    else if(n==2)
    {
        cout<<2<<'\n'<<0<<'\n'<<"11\n";
    }
    else{
        cout<<n-1<<'\n';
        cout<<"00\n";
        for(int i=1;i<=n-2;i++)
        {
            cout<<'0';
            for(int j=0;j<i;j++) cout<<'1';
            cout<<'0';
            cout<<'\n';
        }
    }
}
