#include "obstacles.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
#define sz(x) int(size(x))
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) rbegin(x), rend(x)
#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(const V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
tcT > int upb(const 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 = 998244353; // 1e9+7;
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_64
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 <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, bool print_nd> struct Writer {
string comma() const { return debug ? "," : ""; }
template <class T> constexpr char Space(const T &) const {
return print_nd && (Iterable<T>::value or IsTuple<T>::value) ? '\n' : ' ';
}
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, true>{}.print(ts...);
}
template <class... Ts> void ps(Ts const &...ts) {
Writer<cout, false, true>{}.print_with_sep(" ", ts...);
}
} // namespace IO
inline namespace Debug {
template <typename... Args> void err(Args... args) {
Writer<cerr, true, false>{}.print_with_sep(" | ", args...);
}
template <typename... Args> void errn(Args... args) {
Writer<cerr, true, 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)
#define dbgn(args...) err_prefix(__FUNCTION__, __LINE__, #args), errn(args)
#else
#define dbg(...)
#define dbgn(args...)
#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
/**
* Description: 1D range minimum query. If TL is an issue, use
* arrays instead of vectors and store values instead of indices.
* Source: KACTL
* Verification:
* https://cses.fi/problemset/stats/1647/
* http://wcipeg.com/problem/ioi1223
* https://pastebin.com/ChpniVZL
* Memory: O(N\log N)
* Time: O(1)
*/
tcT > struct RMQ { // floor(log_2(x))
int level(int x) { return 31 - __builtin_clz(x); }
V<T> v;
V<vi> jmp;
int cmb(int a, int b) {
return v[a] == v[b] ? min(a, b) : (v[a] < v[b] ? a : b);
}
void init(const V<T> &_v) {
v = _v;
jmp = {vi(sz(v))};
iota(all(jmp[0]), 0);
for (int j = 1; 1 << j <= sz(v); ++j) {
jmp.pb(vi(sz(v) - (1 << j) + 1));
F0R(i, sz(jmp[j]))
jmp[j][i] = cmb(jmp[j - 1][i], jmp[j - 1][i + (1 << (j - 1))]);
}
}
int index(int l, int r) {
assert(l <= r);
int d = level(r - l + 1);
return cmb(jmp[d][l], jmp[d][r - (1 << d) + 1]);
}
T query(int l, int r) { return v[index(l, r)]; }
};
int N, M;
using U = uint64_t;
V<U> hsh;
const int big = 1e9 + 1;
RMQ<int> rmq_l, rmq_r;
void initialize(std::vector<int> T, std::vector<int> H) {
N = sz(T);
M = sz(H);
vi l_to_r(M, -1), r_to_l(M, -1);
map<pi, int> ivals;
set<pair<int, pi>> remaining_ivals;
auto add_interval = [&](int l, int r, int h) {
dbg("ADD INTERVAL", l, r, h);
ivals[{l, r}] = h;
remaining_ivals.ins({h, {l, r}});
l_to_r.at(l) = r;
r_to_l.at(r) = l;
};
auto del_ival = [&](int l, int r) {
dbg("DEL IVAL", l, r);
auto it = ivals.find({l, r});
assert(it != end(ivals));
int h = it->s;
ivals.erase(it);
auto it2 = remaining_ivals.find({h, {l, r}});
if (it2 != end(remaining_ivals))
remaining_ivals.erase(it2);
dbg("DONE IVAL");
return h;
};
dbg("XX");
priority_queue<pi, vpi, greater<pi>> H_todo;
// min H in range
for (int r = 0; r < M;) {
if (H.at(r) >= T.at(0)) {
H_todo.push({H.at(r), r});
++r;
continue;
}
int l = r;
int min_H = H.at(l);
while (r + 1 < sz(H) && T.at(0) > H.at(r + 1)) {
++r;
ckmin(min_H, H.at(r));
}
add_interval(l, r, min_H);
++r;
}
dbg("AA");
vpi bounded;
int min_T = T.at(0);
RMQ<int> rmq_H;
rmq_H.init(H);
vi lbound(M, big), rbound(M, big);
auto set_bounds = [&](int i) {
dbg("BEFORE", i, sz(H));
lbound.at(i) =
fstTrue(0, i, [&](int l) { return rmq_H.query(l, i) >= min_T; });
rbound.at(i) =
-lstTrue(i, M - 1, [&](int r) { return rmq_H.query(i, r) >= min_T; });
dbg("AFTER", i);
};
F0R(i, N) {
ckmin(min_T, T.at(i));
// dbg("DOING", i);
while (sz(remaining_ivals) && rbegin(remaining_ivals)->f >= T.at(i)) {
dbg("KILL", *rbegin(remaining_ivals));
bounded.pb(rbegin(remaining_ivals)->s);
remaining_ivals.erase(prev(end(remaining_ivals)));
}
while (sz(H_todo) && H_todo.top().f < T.at(i)) {
int l = H_todo.top().s;
int r = H_todo.top().s;
set_bounds(l);
int h = H_todo.top().f;
H_todo.pop();
// dbg("PROC", l, r, h);
if (l > 0 && r_to_l.at(l - 1) != -1) {
int l1 = r_to_l.at(l - 1);
// dbg("GOT", l1, l - 1);
ckmin(h, del_ival(l1, l - 1));
r_to_l.at(l - 1) = -1;
l = l1;
}
if (r < M - 1 && l_to_r.at(r + 1) != -1) {
int r1 = l_to_r.at(r + 1);
// dbg("GOT", r + 1, r1);
ckmin(h, del_ival(r + 1, r1));
l_to_r.at(r + 1) = -1;
r = r1;
}
add_interval(l, r, h);
}
}
while (sz(remaining_ivals)) {
bounded.pb(rbegin(remaining_ivals)->s);
remaining_ivals.erase(prev(end(remaining_ivals)));
}
rmq_l.init(lbound);
rmq_r.init(rbound);
hsh.rsz(M + 1);
for (auto [l, r] : bounded) {
U u = rng();
hsh.at(l) ^= u;
hsh.at(r + 1) ^= u;
}
F0R(i, M) hsh.at(i + 1) ^= hsh.at(i);
// dbg("BB");
// dbg(bounded);
}
bool can_reach(int L, int R, int S, int D) {
// assert(L == 0 && R == M - 1);
if (S > D)
swap(S, D);
if (D <= S + 1)
return true;
if (hsh.at(S) != hsh.at(D))
return false;
if (rmq_l.query(S + 1, D - 1) <= L) {
return false;
}
if (-rmq_r.query(S + 1, D - 1) >= R) {
return false;
}
return true;
}
