#include "worldmap.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 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: wraps a lambda so it can call itself
* Source: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
*/
namespace std {
template <class Fun> class y_combinator_result {
Fun fun_;
public:
template <class T>
explicit y_combinator_result(T &&fun) : fun_(std::forward<T>(fun)) {}
template <class... Args> decltype(auto) operator()(Args &&...args) {
return fun_(std::ref(*this), std::forward<Args>(args)...);
}
};
template <class Fun> decltype(auto) y_combinator(Fun &&fun) {
return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun));
}
} // namespace std
void y_comb_demo() {
cout << y_combinator([](auto gcd, int a, int b) -> int {
return b == 0 ? a : gcd(b, a % b);
})(20, 30)
<< "\n"; // outputs 10
}
std::vector<std::vector<int>> create_map(int N, int M, std::vector<int> A,
std::vector<int> B) {
std::vector<std::vector<int>> ans(2 * N, std::vector<int>(2 * N, 0));
V<vi> adj(N + 1);
vi vis(N + 1);
for (int i = 0; i < M; ++i) {
adj.at(A.at(i)).pb(B.at(i));
adj.at(B.at(i)).pb(A.at(i));
}
auto fill_diag = [&](int d, int v) {
dbg("FILL DIAG", d, v);
F0R(x, 2 * N) {
int y = d - x;
if (0 <= y && y < 2 * N)
ans.at(x).at(y) = v;
}
};
int glob_diag = 0;
int cnt = 0;
auto dfs = y_combinator([&](auto self, int v) -> void {
// dbg("DFS", v);
vis.at(v) = ++cnt;
int diag = glob_diag + 1;
glob_diag += 3;
fill_diag(diag - 1, v);
fill_diag(diag, v);
fill_diag(diag + 1, v);
int x = max(0, diag - 2 * N + 1);
for (int w : adj.at(v)) {
// dbg("DOING", v, w);
if (!vis.at(w)) {
self(w);
fill_diag(glob_diag, v);
++glob_diag;
} else if (vis.at(w) < vis.at(v)) {
// dbg("HELLO", diag, x, diag - x);
// dbg("EDGE", v, w);
// dbg("SET", x, diag - x, w);
assert(0 <= diag - x && diag - x < 2 * N);
ans.at(x).at(diag - x) = w;
++x;
}
}
// dbg("HI", v);
});
dfs(1);
while (glob_diag < 4 * N) {
fill_diag(glob_diag, 1);
++glob_diag;
}
assert(cnt == N);
// dbg(glob_diag);
// assert(glob_diag == 4 * N);
return ans;
}
