#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 = 5e3 + 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;
int n;
void go(int l, int r, int p, int bag){
if(l > r) return;
ans[p][0] = bag;
rep1(j,l){
ans[p][j] = -(bag+1);
}
for(int j = r; j <= n; ++j){
ans[p][j] = -((bag^1)+1);
}
int len = r-l+1;
if(len <= 2){
return;
}
int segs = best[len];
int len1 = (len-2)/segs;
int len2 = ceil2(len-2,segs);
int cnt1 = (len-2)/len1;
int cnt2 = (len-2)%len1;
cnt1 -= cnt2;
assert(cnt1+cnt2 == segs);
int curr = l+1;
rep1(i,cnt1){
for(int j = curr; j <= curr+len1-1; ++j){
ans[p][j] = ptr;
}
go(curr,curr+len1-1,ptr++,bag^1);
curr += len1;
}
rep1(i,cnt2){
for(int j = curr; j <= curr+len1-1; ++j){
ans[p][j] = ptr;
}
go(curr,curr+len2-1,ptr++,bag^1);
curr += len2;
}
}
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;
}
}
}
ans = vector<vector<int>>(n+1,vector<int>(n+1));
go(1,n,0,0);
return ans;
}
