#include "robot.h"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <vector>
using namespace std;
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python!
// pairs
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
#define mp make_pair
#define f first
#define s second
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
using vi = V<int>;
using vb = V<bool>;
using vl = V<ll>;
using vd = V<db>;
using vs = V<str>;
using vpi = V<pi>;
using vpl = V<pl>;
using vpd = V<pd>;
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define pb push_back
#define eb emplace_back
#define ft front()
#define bk back()
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
tcT > int upb(V<T> &a, const T &b) { return int(ub(all(a), b) - bg(a)); }
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define rep(a) F0R(_, a)
#define each(a, x) for (auto &a : x)
const int MOD = (int)1e9 + 7; // 998244353;
const int MX = (int)2e5 + 5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1, 0, -1, 0}, dy[4]{0, 1, 0, -1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until
// USACO updates ...
return x == 0 ? 0 : 31 - __builtin_clz(x);
} // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
ll cdiv(ll a, ll b) {
return a / b + ((a ^ b) > 0 && a % b);
} // divide a by b rounded up
ll fdiv(ll a, ll b) {
return a / b - ((a ^ b) < 0 && a % b);
} // divide a by b rounded down
tcT > bool ckmin(T &a, const T &b) {
return b < a ? a = b, 1 : 0;
} // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) {
return a < b ? a = b, 1 : 0;
} // set a = max(a,b)
tcTU > T fstTrue(T lo, T hi, U f) {
++hi;
assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo) / 2;
f(mid) ? hi = mid : lo = mid + 1;
}
return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
--lo;
assert(lo <= hi); // assuming f is decreasing
while (lo < hi) { // find first index such that f is true
T mid = lo + (hi - lo + 1) / 2;
f(mid) ? lo = mid : hi = mid - 1;
}
return lo;
}
tcT > void remDup(vector<T> &v) { // sort and remove duplicates
sort(all(v));
v.erase(unique(all(v)), end(v));
}
tcTU > void safeErase(T &t, const U &u) {
auto it = t.find(u);
assert(it != end(t));
t.erase(it);
}
inline namespace IO {
#define SFINAE(x, ...) \
template <class, class = void> struct x : std::false_type {}; \
template <class T> struct x<T, std::void_t<__VA_ARGS__>> : std::true_type {}
SFINAE(DefaultI, decltype(std::cin >> std::declval<T &>()));
SFINAE(DefaultO, decltype(std::cout << std::declval<T &>()));
SFINAE(IsTuple, typename std::tuple_size<T>::type);
SFINAE(Iterable, decltype(std::begin(std::declval<T>())));
template <class T> constexpr char Space(const T &) {
return (Iterable<T>::value or IsTuple<T>::value) ? '\n' : ' ';
}
template <auto &is> struct Reader {
template <class T> void Impl(T &t) {
if constexpr (DefaultI<T>::value) is >> t;
else if constexpr (Iterable<T>::value) {
for (auto &x : t) Impl(x);
} else if constexpr (IsTuple<T>::value) {
std::apply([this](auto &...args) { (Impl(args), ...); }, t);
} else static_assert(IsTuple<T>::value, "No matching type for read");
}
template <class... Ts> void read(Ts &...ts) { ((Impl(ts)), ...); }
};
template <class... Ts> void re(Ts &...ts) { Reader<cin>{}.read(ts...); }
#define def(t, args...) \
t args; \
re(args);
template <auto &os, bool debug> struct Writer {
string comma() const { return debug ? "," : ""; }
template <class T> void Impl(T const &t) const {
if constexpr (DefaultO<T>::value) os << t;
else if constexpr (Iterable<T>::value) {
if (debug) os << '{';
int i = 0;
for (auto &&x : t)
((i++) ? (os << comma() << Space(x), Impl(x)) : Impl(x));
if (debug) os << '}';
} else if constexpr (IsTuple<T>::value) {
if (debug) os << '(';
std::apply(
[this](auto const &...args) {
int i = 0;
(((i++) ? (os << comma() << " ", Impl(args)) : Impl(args)),
...);
},
t);
if (debug) os << ')';
} else static_assert(IsTuple<T>::value, "No matching type for print");
}
template <class T> void ImplWrapper(T const &t) const {
if (debug) os << "\033[0;31m";
Impl(t);
if (debug) os << "\033[0m";
}
template <class... Ts> void print(Ts const &...ts) const {
((Impl(ts)), ...);
}
template <class F, class... Ts>
void print_with_sep(const std::string &sep, F const &f,
Ts const &...ts) const {
ImplWrapper(f), ((os << sep, ImplWrapper(ts)), ...), os << '\n';
}
void print_with_sep(const std::string &) const { os << '\n'; }
};
template <class... Ts> void pr(Ts const &...ts) {
Writer<cout, false>{}.print(ts...);
}
template <class... Ts> void ps(Ts const &...ts) {
Writer<cout, false>{}.print_with_sep(" ", ts...);
}
} // namespace IO
inline namespace Debug {
template <typename... Args> void err(Args... args) {
Writer<cerr, true>{}.print_with_sep(" | ", args...);
}
void err_prefix(str func, int line, string args) {
cerr << "\033[0;31m\u001b[1mDEBUG\033[0m"
<< " | "
<< "\u001b[34m" << func << "\033[0m"
<< ":"
<< "\u001b[34m" << line << "\033[0m"
<< " - "
<< "[" << args << "] = ";
}
#ifdef LOCAL
#define dbg(args...) err_prefix(__FUNCTION__, __LINE__, #args), err(args)
#else
#define dbg(...)
#endif
const auto beg_time = std::chrono::high_resolution_clock::now();
// https://stackoverflow.com/questions/47980498/accurate-c-c-clock-on-a-multi-core-processor-with-auto-overclock?noredirect=1&lq=1
double time_elapsed() {
return chrono::duration<double>(std::chrono::high_resolution_clock::now() -
beg_time)
.count();
}
} // namespace Debug
inline namespace FileIO {
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
cout << fixed << setprecision(12);
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for old USACO
}
} // namespace FileIO
void program_pulibot() {
const int Z_max = 13;
const str dirs = "WSEN";
FOR(H, -2, Z_max + 1)
FOR(W, -2, Z_max + 1)
FOR(S, -2, Z_max + 1) FOR(E, -2, Z_max + 1) FOR(N, -2, Z_max + 1) {
AR<int, 4> vals{W, S, E, N};
auto marked = [&](int d) {
assert(0 <= d && d <= 3);
return 6 <= vals.at(d) && vals.at(d) <= 9;
};
auto is_child = [&](int d) {
if (!(2 <= vals.at(d) && vals.at(d) <= 9)) return false;
return (vals.at(d) - 2) % 4 == (d ^ 2);
};
bool done = 0;
auto det = [&](int Z, char A) {
string actions = "HWSENT";
assert(0 <= Z && Z <= Z_max);
assert(actions.find(A) != string::npos);
assert(!done);
done = 1;
set_instruction({H, W, S, E, N}, Z, A);
};
auto dir = [&](int x) { return 2 + x; };
bool is_source = W == -2 && N == -2;
bool is_dest = E == -2 && S == -2;
if (H == 0) {
if (is_source) {
det(dir(3), 'H');
} else {
int targ = 0;
F0R(i, 4) if (vals[i] > 0) targ = i;
if (is_dest) {
det(1, dirs.at(targ));
} else {
det(dir(targ), dirs.at(targ));
}
}
goto done;
}
// if (H == 1) {
// F0R(d, 4) if (is_child(d)) {
// det(1, d);
// }
// }
if (2 <= H && H <= 13) {
int par_val = vals.at((H - 2) % 4);
if (par_val == 1 || 10 <= par_val) { // kill the subtree
F0R(d, 4) if (is_child(d)) {
det(10 + (H - 2) % 4, dirs.at(d));
goto done;
}
det(0, dirs.at((H - 2) % 4));
goto done;
}
}
if (any_of(all(vals), [](int val) { return val == 1; })) {
// set to 1 and move to parent
if (2 <= H && H <= 9) {
F0R(d, 4) if (is_child(d)) {
det((H - 2) % 4 + 10, dirs.at(d));
goto done;
}
det(1, is_source ? 'T' : dirs.at((H - 2) % 4));
} else if (10 <= H && H <= 13) {
det(1, is_source ? 'T' : dirs.at((H - 2) % 4));
}
goto done;
} else if (2 <= H && H <= 5) { // mark all children
F0R(d, 4) if (is_child(d) && !marked(d)) {
det(H, dirs.at(d));
goto done;
}
if (is_source) {
det(H + 4, 'H');
} else {
det(H + 4, dirs.at(H - 2));
}
goto done;
} else if (6 <= H && H <= 9) { // unmark all children
F0R(d, 4) {
if (vals.at(d) == 0) {
det(H, dirs.at(d));
goto done;
} else if (is_child(d) && marked(d)) {
det(H, dirs.at(d));
goto done;
}
}
if (is_source) {
det(H - 4, 'H');
} else {
det(H - 4, dirs.at(H - 6));
}
goto done;
}
done:;
}
// set_instruction({0, -2, -1, 0, -2}, 1, 'E');
// set_instruction({0, 1, -1, 0, -2}, 1, 'E');
// set_instruction({0, 1, 0, -2, -2}, 1, 'S');
// set_instruction({0, -1, -2, -2, 1}, 1, 'T');
}
