This documentation is automatically generated by competitive-verifier/competitive-verifier
#include "../../../../template/template.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"
#include "../../../../data-structure/others/AreaofUnionofRectangles.hpp"
using S = lint;
int main() {
cin.tie(0)->sync_with_stdio(0);
int n;
in(n);
vector<lint> x1(n), x2(n), y1(n), y2(n);
rep(i, n) {
in(x1[i], y1[i], x2[i], y2[i]);
}
AreaofUnionofRectangles t(x1, x2, y1, y2);
out(t.ans());
}
#line 2 "template/template.hpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using ull = unsigned long long;
using ld = long double;
using int128 = __int128_t;
#define all(x) (x).begin(), (x).end()
#define uniqv(v) v.erase(unique(all(v)), v.end())
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP1(i, n) for (auto i = std::decay_t<decltype(n)>{}; (i) != (n); ++(i))
#define REP2(i, l, r) for (auto i = (l); (i) != (r); ++(i))
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define logfixed(x) cout << fixed << setprecision(10) << x << endl;
ostream &operator<<(ostream &dest, __int128_t value) {
ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(ios_base::badbit);
}
}
return dest;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != (int)v.size() ? " " : "");
}
return os;
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &set_var) {
for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
os << *itr;
++itr;
if (itr != set_var.end()) os << " ";
itr--;
}
return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &set_var) {
for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
os << *itr;
++itr;
if (itr != set_var.end()) os << " ";
itr--;
}
return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
os << itr->first << " -> " << itr->second << "\n";
}
return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const unordered_map<T, U> &map_var) {
for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
os << itr->first << " -> " << itr->second << "\n";
}
return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &pair_var) {
os << pair_var.first << " " << pair_var.second;
return os;
}
void out() { cout << '\n'; }
template <class T, class... Ts>
void out(const T &a, const Ts &...b) {
cout << a;
(cout << ... << (cout << ' ', b));
cout << '\n';
}
void outf() { cout << '\n'; }
template <class T, class... Ts>
void outf(const T &a, const Ts &...b) {
cout << fixed << setprecision(14) << a;
(cout << ... << (cout << ' ', b));
cout << '\n';
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
inline void in(void) { return; }
template <typename First, typename... Rest>
void in(First &first, Rest &...rest) {
cin >> first;
in(rest...);
return;
}
template <typename T>
bool chmax(T &a, const T &b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T>
bool chmin(T &a, const T &b) {
if (a > b) {
a = b;
return true;
}
return false;
}
vector<lint> dx8 = {1, 1, 0, -1, -1, -1, 0, 1};
vector<lint> dy8 = {0, 1, 1, 1, 0, -1, -1, -1};
vector<lint> dx4 = {1, 0, -1, 0};
vector<lint> dy4 = {0, 1, 0, -1};
#pragma endregion
#line 2 "verify/LibraryChecker/data-structure/others/AreaofUnionofRectangles.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"
#line 1 "data-structure/segment-tree/LazySegmentTree.hpp"
template <class S,
auto op,
auto e,
class F,
auto mapping,
auto composition,
auto id>
struct lazy_segtree {
private:
unsigned int seg_bit_ceil(unsigned int n) {
unsigned int x = 1;
while (x < (unsigned int)(n)) x *= 2;
return x;
}
public:
static_assert(std::is_convertible_v<decltype(op), std::function<S(S, S)>>,
"op must work as S(S, S)");
static_assert(std::is_convertible_v<decltype(e), std::function<S()>>,
"e must work as S()");
static_assert(
std::is_convertible_v<decltype(mapping), std::function<S(F, S)>>,
"mapping must work as F(F, S)");
static_assert(
std::is_convertible_v<decltype(composition), std::function<F(F, F)>>,
"compostiion must work as F(F, F)");
static_assert(std::is_convertible_v<decltype(id), std::function<F()>>,
"id must work as F()");
lazy_segtree() : lazy_segtree(0) {}
explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
size = (int)seg_bit_ceil((unsigned int)(_n));
log = __builtin_ctz((unsigned int)size);
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
S sml = e(), smr = e();
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() { return d[1]; }
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <bool (*g)(S)>
int max_right(int l) {
return max_right(l, [](S x) { return g(x); });
}
template <class G>
int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
template <bool (*g)(S)>
int min_left(int r) {
return min_left(r, [](S x) { return g(x); });
}
template <class G>
int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
std::vector<S> d;
std::vector<F> lz;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
void all_apply(int k, F f) {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) {
all_apply(2 * k, lz[k]);
all_apply(2 * k + 1, lz[k]);
lz[k] = id();
}
};
#line 3 "data-structure/others/AreaofUnionofRectangles.hpp"
using Sa = pair<int, long long>;
using Fa = int;
Sa opa(Sa a, Sa b) {
if (a.first < b.first) return a;
if (a.first > b.first) return b;
return {a.first, a.second + b.second};
}
Sa ea() {
return {1e9 + 1e5, 0};
}
Sa mappinga(Fa f, Sa x) {
return {x.first + f, x.second};
}
Fa compositiona(Fa f, Fa g) {
return f + g;
}
Fa ida() {
return 0;
}
class AreaofUnionofRectangles {
private:
vector<long long> x1, x2, y1, y2;
int n;
lint res = 0;
public:
AreaofUnionofRectangles(const vector<long long> &xl, const vector<long long> &xr, const vector<long long> &yl, const vector<long long> &yr) {
x1 = xl;
x2 = xr;
y1 = yl;
y2 = yr;
n = x1.size();
vector<int> cmp(n * 2);
vector<tuple<long long, int, int, int>> q(n * 2);
for (int i = 0; i < n; i++) {
cmp[i * 2] = y1[i];
cmp[i * 2 + 1] = y2[i];
}
sort(cmp.begin(), cmp.end());
cmp.erase(unique(cmp.begin(), cmp.end()), cmp.end());
for (int i = 0; i < n; i++) {
int idx1 = distance(cmp.begin(), lower_bound(cmp.begin(), cmp.end(), y1[i]));
int idx2 = distance(cmp.begin(), lower_bound(cmp.begin(), cmp.end(), y2[i]));
q[i * 2] = {x1[i], 1, idx1, idx2};
q[i * 2 + 1] = {x2[i], -1, idx1, idx2};
}
sort(q.begin(), q.end());
int siz = cmp.size() - 1;
vector<Sa> v(siz);
for (int i = 0; i < siz; i++) {
v[i] = {0, cmp[i + 1] - cmp[i]};
}
lazy_segtree<Sa, opa, ea, Fa, mappinga, compositiona, ida> seg(v);
long long prev = get<0>(q[0]);
for (int i = 0; i < n * 2; i++) {
long long x = get<0>(q[i]);
int f = get<1>(q[i]);
long long l = get<2>(q[i]);
long long r = get<3>(q[i]);
long long h = x - prev;
long long w = cmp[siz] - cmp[0];
Sa pr = seg.all_prod();
if (pr.first == 0) w -= pr.second;
res += h * w;
prev = x;
seg.apply(l, r, f);
}
}
lint ans() {
return res;
}
};
#line 4 "verify/LibraryChecker/data-structure/others/AreaofUnionofRectangles.test.cpp"
using S = lint;
int main() {
cin.tie(0)->sync_with_stdio(0);
int n;
in(n);
vector<lint> x1(n), x2(n), y1(n), y2(n);
rep(i, n) {
in(x1[i], y1[i], x2[i], y2[i]);
}
AreaofUnionofRectangles t(x1, x2, y1, y2);
out(t.ans());
}