#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> devise_strategy(int N) {
auto factors_for_sum = [](int sum) {
vector<int> r;
if (sum == 2) return vector<int>{2};
if (sum == 3) return vector<int>{3};
int q = sum / 3;
int rem = sum % 3;
if (rem == 0) {
r.assign(q, 3);
} else if (rem == 1) {
r.assign(q - 1, 3);
r.push_back(4);
} else {
r.assign(q, 3);
r.push_back(2);
}
return r;
};
vector<int> base;
for (int sum = 2;; ++sum) {
vector<int> cand = factors_for_sum(sum);
long long prod = 1;
for (int v : cand) prod *= v;
if (prod >= N) {
base = cand;
break;
}
}
int L = (int)base.size();
vector<int> place(L, 1), offset(L);
for (int i = L - 2; i >= 0; --i) {
place[i] = place[i + 1] * base[i + 1];
}
int x = 0;
for (int i = 0; i < L; ++i) {
offset[i] = x + 1;
x += base[i];
}
auto digit = [&](int value, int pos) {
int z = value - 1;
return (z / place[pos]) % base[pos];
};
auto id = [&](int pos, int d) {
return offset[pos] + d;
};
vector<vector<int>> s(x + 1, vector<int>(N + 1, 0));
s[0][0] = 0;
for (int j = 1; j <= N; ++j) {
s[0][j] = id(0, digit(j, 0));
}
for (int pos = 0; pos < L; ++pos) {
for (int d = 0; d < base[pos]; ++d) {
int st = id(pos, d);
bool inspectB = (pos % 2 == 0);
s[st][0] = inspectB ? 1 : 0;
for (int j = 1; j <= N; ++j) {
int cur = digit(j, pos);
if (cur < d) {
s[st][j] = inspectB ? -2 : -1;
} else if (cur > d) {
s[st][j] = inspectB ? -1 : -2;
} else {
if (pos + 1 == L) {
s[st][j] = -1;
} else {
s[st][j] = id(pos + 1, digit(j, pos + 1));
}
}
}
}
}
return s;
}
