// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h>
#include "prison.h"
using namespace std;
#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 5005;
int n;
vector<vi> ans;
vector<vi> nans;
int sp[MAXN], dp[MAXN], nxt[MAXN];
void solve(int c, int clo, int chi, int lo, int hi, int cp, int len) {
ans[c][0] = cp;
REP (i, lo, clo) {
ans[c][i] = -cp - 1;
}
REP (i, chi + 1, hi + 1) {
ans[c][i] = -(cp ^ 1) - 1;
}
if (chi - clo <= 1) {
ans[c][clo] = -cp - 1; ans[c][chi] = -(cp ^ 1) - 1;
return;
}
int need = (len - 3) / sp[len] + 1;
ans[c][clo] = -cp - 1; ans[c][chi] = -(cp ^ 1) - 1;
int nlo = clo + 1;
REP (i, nxt[c], nxt[c] + need) {
int nhi = min(chi - 1, nlo + sp[len] - 1);
REP (j, nlo, nhi + 1) {
ans[c][j] = i;
}
ans[i][clo] = -(cp ^ 1) - 1; ans[i][chi] = -cp - 1;
solve(i, nlo, nhi, clo + 1, chi - 1, cp ^ 1, sp[len]);
nlo = nhi + 1;
}
}
vector<vi> devise_strategy(int n) {
::n = n;
if (n == 2) {
ans.resize(1, vi(3, 0));
ans[0][1] = -1; ans[0][2] = -2;
return ans;
}
REP (i, 0, 3) {
dp[i] = 0;
sp[i] = i;
}
REP (i, 3, n + 1) {
dp[i] = i;
int ptr = 0;
REP (j, 0, i) {
while (ptr < i && dp[ptr] <= j) {
ptr++;
}
int need = (i - 3) / (ptr - 1) + 1;
if (mnto(dp[i], j + need)) {
sp[i] = ptr - 1;
}
}
cerr << i << ": " << dp[i] << ' ' << sp[i] << '\n';
}
nxt[0] = 1;
int tmp = 1;
int tn = n;
while (tn >= 3) {
int need = (tn - 3) / sp[tn] + 1;
REP (i, tmp, tmp + need) {
nxt[i] = tmp + need;
}
tmp += need;
tn = sp[tn];
}
ans = vector<vi>(tmp, vi(n + 1, 0));
ans[0][0] = 0; ans[0][1] = -1; ans[0][n] = -2;
int need = (n - 3) / sp[n] + 1;
int lo = 2;
REP (i, 1, 1 + need) {
int hi = min(n - 1, lo + sp[n] - 1);
REP (j, lo, hi + 1) {
ans[0][j] = i;
}
ans[i][1] = -2; ans[i][n] = -1;
solve(i, lo, hi, 2, n - 1, 1, sp[n]);
lo = hi + 1;
}
cerr << SZ(ans) - 1 << '\n';
return ans;
}
