#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python!
using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
#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>;
tcT> using PR = pair<T,T>;
// pairs
#define mp make_pair
#define f first
#define s second
// 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 ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front
#define rtn return
#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)); }
// 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 = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 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; }
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 erase(T& t, const U& u) { // don't erase
auto it = t.find(u); assert(it != end(t));
t.erase(it); } // element that doesn't exist from (multi)set
#define tcTUU tcT, class ...U
inline namespace Helpers {
//////////// is_iterable
// https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
// this gets used only when we can call begin() and end() on that type
tcT, class = void> struct is_iterable : false_type {};
tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
decltype(end(declval<T>()))
>
> : true_type {};
tcT> constexpr bool is_iterable_v = is_iterable<T>::value;
//////////// is_readable
tcT, class = void> struct is_readable : false_type {};
tcT> struct is_readable<T,
typename std::enable_if_t<
is_same_v<decltype(cin >> declval<T&>()), istream&>
>
> : true_type {};
tcT> constexpr bool is_readable_v = is_readable<T>::value;
//////////// is_printable
// // https://nafe.es/posts/2020-02-29-is-printable/
tcT, class = void> struct is_printable : false_type {};
tcT> struct is_printable<T,
typename std::enable_if_t<
is_same_v<decltype(cout << declval<T>()), ostream&>
>
> : true_type {};
tcT> constexpr bool is_printable_v = is_printable<T>::value;
}
inline namespace Input {
tcT> constexpr bool needs_input_v = !is_readable_v<T> && is_iterable_v<T>;
tcTUU> void re(T& t, U&... u);
tcTU> void re(pair<T,U>& p); // pairs
// re: read
tcT> typename enable_if<is_readable_v<T>,void>::type re(T& x) { cin >> x; } // default
tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; } // complex
tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i); // ex. vectors, arrays
tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i) {
each(x,i) re(x); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); } // read multiple
// rv: resize and read vectors
void rv(size_t) {}
tcTUU> void rv(size_t N, V<T>& t, U&... u);
template<class...U> void rv(size_t, size_t N2, U&... u);
tcTUU> void rv(size_t N, V<T>& t, U&... u) {
t.rsz(N); re(t);
rv(N,u...); }
template<class...U> void rv(size_t, size_t N2, U&... u) {
rv(N2,u...); }
// dumb shortcuts to read in ints
void decrement() {} // subtract one from each
tcTUU> void decrement(T& t, U&... u) { --t; decrement(u...); }
#define ints(...) int __VA_ARGS__; re(__VA_ARGS__);
#define int1(...) ints(__VA_ARGS__); decrement(__VA_ARGS__);
}
inline namespace ToString {
tcT> constexpr bool needs_output_v = !is_printable_v<T> && is_iterable_v<T>;
// ts: string representation to print
tcT> typename enable_if<is_printable_v<T>,str>::type ts(T v) {
stringstream ss; ss << fixed << setprecision(15) << v;
return ss.str(); } // default
tcT> str bit_vec(T t) { // bit vector to string
str res = "{"; F0R(i,sz(t)) res += ts(t[i]);
res += "}"; return res; }
str ts(V<bool> v) { return bit_vec(v); }
template<size_t SZ> str ts(bitset<SZ> b) { return bit_vec(b); } // bit vector
tcTU> str ts(pair<T,U> p); // pairs
tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v); // vectors, arrays
tcTU> str ts(pair<T,U> p) { return "("+ts(p.f)+", "+ts(p.s)+")"; }
tcT> typename enable_if<is_iterable_v<T>,str>::type ts_sep(T v, str sep) {
// convert container to string w/ separator sep
bool fst = 1; str res = "";
for (const auto& x: v) {
if (!fst) res += sep;
fst = 0; res += ts(x);
}
return res;
}
tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v) {
return "{"+ts_sep(v,", ")+"}"; }
// for nested DS
template<int, class T> typename enable_if<!needs_output_v<T>,vs>::type
ts_lev(const T& v) { return {ts(v)}; }
template<int lev, class T> typename enable_if<needs_output_v<T>,vs>::type
ts_lev(const T& v) {
if (lev == 0 || !sz(v)) return {ts(v)};
vs res;
for (const auto& t: v) {
if (sz(res)) res.bk += ",";
vs tmp = ts_lev<lev-1>(t);
res.ins(end(res),all(tmp));
}
F0R(i,sz(res)) {
str bef = " "; if (i == 0) bef = "{";
res[i] = bef+res[i];
}
res.bk += "}";
return res;
}
}
inline namespace Output {
template<class T> void pr_sep(ostream& os, str, const T& t) { os << ts(t); }
template<class T, class... U> void pr_sep(ostream& os, str sep, const T& t, const U&... u) {
pr_sep(os,sep,t); os << sep; pr_sep(os,sep,u...); }
// print w/ no spaces
template<class ...T> void pr(const T&... t) { pr_sep(cout,"",t...); }
// print w/ spaces, end with newline
void ps() { cout << "\n"; }
template<class ...T> void ps(const T&... t) { pr_sep(cout," ",t...); ps(); }
// debug to cerr
template<class ...T> void dbg_out(const T&... t) {
pr_sep(cerr," | ",t...); cerr << endl; }
void loc_info(int line, str names) {
cerr << "Line(" << line << ") -> [" << names << "]: "; }
template<int lev, class T> void dbgl_out(const T& t) {
cerr << "\n\n" << ts_sep(ts_lev<lev>(t),"\n") << "\n" << endl; }
#ifdef LOCAL
#define dbg(...) loc_info(__LINE__,#__VA_ARGS__), dbg_out(__VA_ARGS__)
#define dbgl(lev,x) loc_info(__LINE__,#x), dbgl_out<lev>(x)
#else // don't actually submit with this
#define dbg(...) 0
#define dbgl(lev,x) 0
#endif
}
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
// 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
}
}
#include "parks.h"
/**
* Description: Disjoint Set Union with path compression
* and union by size. Add edges and test connectivity.
* Use for Kruskal's or Boruvka's minimum spanning tree.
* Time: O(\alpha(N))
* Source: CSAcademy, KACTL
* Verification: *
*/
struct DSU {
vi e; void init(int N) { e = vi(N,-1); }
int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
bool sameSet(int a, int b) { return get(a) == get(b); }
int size(int x) { return -e[get(x)]; }
bool unite(int x, int y) { // union by size
x = get(x), y = get(y); if (x == y) return 0;
if (e[x] > e[y]) swap(x,y);
e[x] += e[y]; e[y] = x; return 1;
}
};
/**template<class T> T kruskal(int N, vector<pair<T,pi>> ed) {
sort(all(ed));
T ans = 0; DSU D; D.init(N); // edges that unite are in MST
each(a,ed) if (D.unite(a.s.f,a.s.s)) ans += a.f;
return ans;
}*/
int construct_roads(std::vector<int> X, std::vector<int> Y) {
int N = sz(X);
vpi pos(N);
F0R(i,N) pos[i] = mp(X[i],Y[i]);
vi inds(N); iota(all(inds),0);
sort(all(inds), [&](int a, int b) { return pos[a] < pos[b]; });
map<pi,int> pos_to_ind;
DSU D; D.init(N);
set<pi> used;
vi U,V,A,B;
auto tri = [&](pi loc, int u, int v) {
if (used.count(loc)) return;
used.ins(loc);
D.unite(u,v);
U.pb(u), V.pb(v);
A.pb(loc.f), B.pb(loc.s);
};
auto add_x_edge = [&](int x, int y) {
int ny = y+((x+y)&2 ? 1 : -1);
tri({x+1,ny},pos_to_ind[{x,y}],pos_to_ind[{x+2,y}]);
};
auto add_y_edge = [&](int x, int y) {
int nx = x+((x+y)&2 ? -1 : 1);
tri({nx,y+1},pos_to_ind[{x,y}],pos_to_ind[{x,y+2}]);
};
F0R(i,N) {
int v = inds[i];
pi p = pos[v];
pos_to_ind[p] = v;
if (pos_to_ind.count({p.f-2,p.s})) add_x_edge(p.f-2,p.s);
if (pos_to_ind.count({p.f,p.s-2})) add_y_edge(p.f,p.s-2);
}
if (D.size(0) != N) return 0;
build(U,V,A,B);
// if (x.size() == 1) {
// build({}, {}, {}, {});
// return 1;
// }
// std::vector<int> u, v, a, b;
// u.push_back(0);
// v.push_back(1);
// a.push_back(x[0]+1);
// b.push_back(y[0]-1);
// build(u, v, a, b);
return 1;
}
