#ifndef Nhoksocqt1
#include "prison.h"
#endif // Nhoksocqt1
#include<bits/stdc++.h>
using namespace std;
#define inf 0x3f3f3f3f
#define sz(x) int((x).size())
#define fi first
#define se second
typedef long long ll;
typedef pair<int, int> ii;
template<class X, class Y>
inline bool maximize(X &x, const Y &y) {return (x < y ? x = y, 1 : 0);}
template<class X, class Y>
inline bool minimize(X &x, const Y &y) {return (x > y ? x = y, 1 : 0);}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int Random(int l, int r) {
return uniform_int_distribution<int>(l, r)(rng);
}
const int MAXN = 5003;
const int MOD = 3;
int pw[20];
int ans[MAXN][MAXN], nArr;
vector<vector<int>> devise_strategy(int _N) {
nArr = _N;
for (int i = 0; i <= max(26, nArr); ++i) {
ans[i][0] = 0;
for (int j = 1; j <= nArr; ++j)
ans[i][j] = -1;
}
pw[0] = 1;
int MAX_EXPO(0);
while(pw[MAX_EXPO] * MOD <= 5000) {
++MAX_EXPO;
pw[MAX_EXPO] = pw[MAX_EXPO - 1] * MOD;
}
int x(0), cnt(0);
ans[0][0] = cnt & 1;
for (int j = 1; j <= nArr; ++j)
ans[0][j] = x + 1 + j / pw[MAX_EXPO] % MOD;
x += MOD;
for (int i = MAX_EXPO; i > 0; --i) {
++cnt;
for (int j = 0; j < MOD; ++j)
ans[x - j][0] = cnt & 1;
for (int j = 1; j <= nArr; ++j) {
for (int k = 0; k < MOD; ++k) {
if(j / pw[i] % MOD != k) {
ans[x - MOD + k + 1][j] = ((cnt & 1) ^ (j / pw[i] % MOD > k)) ? -2 : -1;
} else
if(i == 1 && (j / pw[i - 1] % MOD == 0 || j / pw[i - 1] % MOD == MOD - 1)) {
ans[x - MOD + k + 1][j] = ((cnt & 1) ^ (j / pw[i - 1] % MOD == 0)) ? -1 : -2;
} else {
ans[x - MOD + k + 1][j] = x + 1 + j / pw[i - 1] % MOD - (i == 1);
}
}
}
x += (i > 1) * MOD + (i == 1) * (MOD - 2);
}
++cnt;
for (int j = 1; j <= nArr; ++j) {
for (int k = 1; k + 1 < MOD; ++k) {
if(j / pw[0] % MOD != k) {
ans[x - MOD + k + 2][j] = ((cnt & 1) ^ (j / pw[0] % MOD > k)) ? -2 : -1;
} else {
ans[x - MOD + k + 2][j] = 0;
}
}
}
vector<vector<int>> res;
for (int i = 0; i <= x; ++i) {
vector<int> p;
for (int j = 0; j <= nArr; ++j)
p.push_back(ans[i][j]);
res.push_back(p);
}
return res;
}
#ifdef Nhoksocqt1
int main(void) {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#define TASK "prison"
if(fopen(TASK".inp", "r")) {
freopen(TASK".inp", "r", stdin);
freopen(TASK".out", "w", stdout);
}
int _N;
cin >> _N;
vector<vector<int>> ans = devise_strategy(_N);
cout << "X USED: " << sz(ans) - 1 << '\n';
for (int i = 0; i < sz(ans); ++i) {
for (int j = 0; j < sz(ans[i]); ++j)
cout << ans[i][j] << ' ';
cout << '\n';
}
for (int A = 1; A <= _N; ++A) {
for (int B = 1; B <= _N; ++B) {
if(A == B)
continue;
int x(0);
while(1) {
int y = ans[x][0] ? B : A;
x = ans[x][y];
//cout << x << ' ' << y << '\n';
if(x == -1) {
if(A < B) {
cout << "OK WITH PAIR " << A << ' ' << B << " !!\n";
break;
} else {
cout << "WRONG WITH PAIR " << A << ' ' << B << " !!\n";
exit(1);
}
} else
if(x == -2) {
if(A > B) {
cout << "OK WITH PAIR " << A << ' ' << B << " !!\n";
break;
} else {
cout << "WRONG WITH PAIR " << A << ' ' << B << " !!\n";
exit(1);
}
}
}
}
}
return 0;
}
#endif // Nhoksocqt1
