#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
https://youtu.be/RwrBLp8AvJA?t=17698
edi
*/
const int MOD = 1e9 + 7;
const int N = 6e3 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "prison.h"
vector<int> dp(N,inf1), best(N);
int ptr = 1;
vector<vector<int>> ans;
map<int,int> mp[25];
int n;
void go(int l, int r, int p, int d, int bag){
if(l > r) return;
ans[p][0] = bag;
int len = r-l+1;
if(len <= 2){
return;
}
int segs = best[len];
int seg_len = (len-2)/segs;
int curr = l+1;
int seg = 1;
while(curr < r){
if(!mp[d].count(seg)){
mp[d][seg] = ptr++;
}
int nxt = mp[d][seg];
for(int j = curr; j <= curr+seg_len-1; ++j){
ans[p][j] = nxt;
}
for(int j = l; j <= curr; ++j){
ans[nxt][j] = -((bag^1)+1);
}
for(int j = curr+seg_len-1; j <= r; ++j){
ans[nxt][j] = -(bag+1);
}
go(curr,curr+seg_len-1,nxt,d+1,bag^1);
curr += seg_len;
seg++;
}
}
vector<vector<int>> devise_strategy(int n_) {
n = n_;
dp[0] = dp[1] = dp[2] = 0;
for(int i = 3; i < N; ++i){
rep1(j,min(i-2,20)){
int val = j+dp[ceil2(i-2,j)];
if(val < dp[i]){
best[i] = j;
dp[i] = val;
}
}
}
int mx_val = -1;
rep(i,N){
if(dp[i] <= 20){
mx_val = i;
}
}
ans = vector<vector<int>>(21,vector<int>(mx_val+1));
ans[0][1] = -1;
ans[0][mx_val] = -2;
go(1,mx_val,0,0,0);
rep(i,21){
while(sz(ans[i]) > n+1){
ans[i].pop_back();
}
}
// rep(i,sz(ans)){
// rep(j,n+1){
// cout << ans[i][j] << " ";
// }
// cout << endl;
// }
return ans;
}
