#include "prison.h"
#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace std;
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
vi splits = {3,3,3,3,3,2,2,1,2,2};
int n;
vector<pii> sp;
pii nxt_lr(int l, int r, int s, int val)
{
sp = {};
int siz_ = (r-l+1)/splits[s];
int add_ = (r-l+1) - splits[s]*siz_;
rep(i,add_)
{
sp.pb({l,l+siz_});
l += siz_+1;
}
rep(i,splits[s]-add_)
{
sp.pb({l,l+siz_-1});
l += siz_;
}
pii new_pair = {-1,-1};
forall(it,sp)
{
if(val >= it.ff && val <= it.ss)
{
new_pair = it;
}
}
return new_pair;
}
int what_print(int val, int num)
{
int l = 1;
int r = n;
int cur_del = 0;
rep(s,siz(splits))
{
l++;
r--;
pii new_pair = nxt_lr(l,r,s,val);
forall(it,sp)
{
if(val >= it.ff && val <= it.ss)
{
new_pair = it;
}
}
if(cur_del+splits[s] < num)
{
l = new_pair.ff;
r = new_pair.ss;
cur_del += splits[s];
}
else
{
int k = num-cur_del-1;
if(num == 0 || (val >= sp[k].ff && val <= sp[k].ss))
{
pii new_pair2;
if(num != 0)
{
if(val == sp[k].ff) return -1;
if(val == sp[k].ss) return -2;
new_pair2 = nxt_lr(new_pair.ff+1,new_pair.ss-1,s+1,val);
}
else
{
new_pair2 = nxt_lr(l,r,0,val);
}
int beg_num = (num != 0 ? cur_del+splits[s]+1 : 1);
rep(k,10)
{
if(new_pair2.ff == sp[k].ff) break;
beg_num++;
}
return beg_num;
}
else
{
if(val < sp[k].ff)
{
return -1;
}
return -2;
}
}
}
}
vector<vi> devise_strategy(int N)
{
n = N;
vector<vi> ans;
vi zero(n+1);
zero[0] = 0;
zero[1] = -1;
zero[n] = -2;
rep2(i,2,n-1)
{
zero[i] = what_print(i,0);
}
int cur_max = 0;
rep2(i,2,n-1) cur_max = max(cur_max,zero[i]);
ans.pb(zero);
int cur_print = 1;
while(cur_print <= cur_max)
{
int cur_del = 0;
vi p;
p.pb(0);
rep(s,siz(splits))
{
p[0] ^= 1;
if(cur_del+splits[s] >= cur_print)
{
break;
}
cur_del+=splits[s];
}
rep2(i,1,n)
{
int pr = what_print(i,cur_print);
if(pr != -1 && pr != -2) p.pb(pr);
else
{
if(pr == -1)
{
if(p[0] == 1) pr = -2;
}
else
{
if(p[0] == 1) pr = -1;
}
p.pb(pr);
}
}
ans.pb(p);
rep2(i,1,n) cur_max = max(cur_max,p[i]);
cur_print++;
}
return ans;
}
