#include <bits/stdc++.h>
using namespace std;
using i32 = int;
using i64 = long long;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
#define OVERRIDE4(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, l, r) for (i32 i = (i32)(l); i < (i32)(r); ++i)
#define REP(...) OVERRIDE4(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, l, r) for (i32 i = (i32)(r)-1; i >= (i32)(l); --i)
#define PER(...) OVERRIDE4(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32) size(x)
void dbg(i32 x) { cerr << x; }
void dbg(i64 x) { cerr << x; }
template <typename T, typename U>
void dbg(pair<T, U> p) {
cerr << '(' << p.first << ", " << p.second << ')';
}
template <typename T>
void dbg(V<T> arr) {
cerr << '[';
REP(i, LEN(arr)) {
if (i) {
cerr << ", ";
}
dbg(arr[i]);
}
cerr << ']';
}
template <typename T, size_t N>
void dbg(array<T, N> arr) {
cerr << '[';
REP(i, LEN(arr)) {
if (i) {
cerr << ", ";
}
dbg(arr[i]);
}
cerr << ']';
}
void debug() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug(Head head, Tail... tail) {
dbg(head);
cerr << ", ";
debug(tail...);
}
#ifdef DEBUGF
#define DBG(...) \
do { \
cerr << #__VA_ARGS__ << " : "; \
debug(__VA_ARGS__); \
} while (false)
#else
#define DBG(...) (void)0
#endif
#include "prison.h"
VV<i32> devise_strategy(i32 n) {
array<i32, 8> l = {3, 3, 3, 3, 3, 2, 2, 2};
array<i32, 9> sum;
sum[0] = 0;
REP(i, 8) {
sum[i + 1] = sum[i] + l[i];
}
array<i32, 9> div;
div[8] = 1;
PER(i, 8) {
div[i] = div[i + 1] * l[i] + 2;
}
i32 m = accumulate(ALL(l), 0);
V<i32> stage(m + 1, 0);
REP(i, 8) {
REP(j, sum[i] + 1, sum[i + 1] + 1) {
stage[j] = i + 1;
}
}
DBG(sum, div, stage);
VV<i32> table(m + 1, V<i32>(n + 1));
REP(i, m + 1) {
table[i][0] = stage[i] % 2;
}
table[0][1] = -1;
REP(j, 2, n + 1) {
table[0][j] = 1 + (j - 2) / div[1];
}
REP(i, 1, m + 1) {
if (stage[i] == 8) {
break;
}
i32 tr_q = i - sum[stage[i] - 1] - 1;
REP(j, 1, n + 1) {
i32 cur = j - 1;
i32 ret = -3;
i32 quot = -1;
REP(k, stage[i]) {
if (cur == 0) {
ret = (table[i][0] == 0 ? -1 : -2);
break;
}
if (cur == div[k] - 1) {
ret = (table[i][0] == 0 ? -2 : -1);
break;
}
--cur;
quot = cur / div[k + 1];
cur %= div[k + 1];
}
if (ret != -3) {
table[i][j] = ret;
continue;
}
if (quot < tr_q) {
table[i][j] = (table[i][0] == 0 ? -1 : -2);
continue;
}
if (quot > tr_q) {
table[i][j] = (table[i][0] == 0 ? -2 : -1);
continue;
}
if (cur == 0) {
table[i][j] = (table[i][0] == 0 ? -1 : -2);
continue;
}
if (cur == div[stage[i]] - 1) {
table[i][j] = (table[i][0] == 0 ? -2 : -1);
continue;
}
--cur;
quot = cur / div[stage[i] + 1];
table[i][j] = 1 + sum[stage[i]] + quot;
}
}
DBG(table[19][0]);
DBG(table[19][4999]);
DBG(table[19][5000]);
REP(i, m + 1) {
if (stage[i] != 8) {
continue;
}
i32 tr_q = i - sum[stage[i] - 1] - 1;
DBG(i, tr_q, table[i][0]);
REP(j, 1, n + 1) {
i32 cur = j - 1;
i32 ret = -3;
i32 quot = -1;
REP(k, stage[i]) {
if (i == m && j >= n - 1) {
DBG(cur);
}
if (cur == 0) {
ret = (table[i][0] == 0 ? -1 : -2);
break;
}
if (cur == div[k] - 1) {
ret = (table[i][0] == 0 ? -2 : -1);
break;
}
--cur;
quot = cur / div[k + 1];
cur %= div[k + 1];
if (i == m && j >= n - 1) {
DBG(quot);
}
}
if (j == n) {
DBG(cur);
}
if (ret != -3) {
table[i][j] = ret;
continue;
}
if (quot < tr_q) {
table[i][j] = (table[i][0] == 0 ? -1 : -2);
continue;
}
if (quot > tr_q) {
table[i][j] = (table[i][0] == 0 ? -2 : -1);
continue;
}
table[i][j] = 0;
}
}
DBG(div);
DBG(sum);
DBG(stage);
DBG(table[0][5000]);
DBG(table[1][5000]);
DBG(table[2][5000]);
DBG(table[3][5000]);
return table;
}
