#include "seats.h"
#include <bits/stdc++.h>
#define fi first
#define se second
#define mp make_pair
#define TASK ""
#define bit(x) (1LL << (x))
#define getbit(x, i) (((x) >> (i)) & 1)
#define ALL(x) (x).begin(), (x).end()
using namespace std;
template <typename T1, typename T2> bool mini(T1 &a, T2 b) {
if (a > b) {a = b; return true;} return false;
}
template <typename T1, typename T2> bool maxi(T1 &a, T2 b) {
if (a < b) {a = b; return true;} return false;
}
mt19937_64 rd(chrono::steady_clock::now().time_since_epoch().count());
int rand(int l, int r) {
return l + rd() % (r - l + 1);
}
const int N = 1e6 + 5;
const int oo = 1e9;
const long long ooo = 1e18;
const int mod = 1e9 + 7; // 998244353;
const long double pi = acos(-1);
typedef tuple <int, int, int, int> pir;
pair <int, int> st[N << 2];
int lz[N << 2];
set <int> sr[N], sc[N];
int minx[N];
int miny[N];
int maxx[N];
int maxy[N];
int x[N];
int y[N];
int a[N];
int n,m,sz,ans;
void dolazy(int id) {
for (int i = (id << 1); i <= (id << 1 | 1); i++) {
lz[i] += lz[id];
st[i].fi += lz[id];
}
lz[id] = 0;
}
void build(int id, int l, int r) {
if (l == r) {
st[id].se = 1;
return;
}
int mid = (l + r) >> 1;
build(id << 1, l, mid);
build(id << 1 | 1, mid + 1, r);
}
void update(int id, int l, int r, int u, int v, int val) {
if (l > v || r < u)
return;
if (l >= u && r <= v) {
lz[id] += val;
st[id].fi += val;
return;
}
int mid = (l + r) >> 1;
dolazy(id);
update(id << 1, l, mid, u, v, val);
update(id << 1 | 1, mid + 1, r, u, v, val);
st[id] = st[id << 1];
if (st[id].fi > st[id << 1 | 1].fi)
st[id] = st[id << 1 | 1];
else if (st[id].fi == st[id << 1 | 1].fi)
st[id].se += st[id << 1 | 1].se;
}
void update(int l, int r, int val) {
update(1, 0, sz - 1, l, r, val);
}
int getmin() {
return st[1].se;
}
bool check(int i) {
int dx = maxx[i] - minx[i] + 1;
int dy = maxy[i] - miny[i] + 1;
return (dx * dy == i + 1);
}
void give_initial_chart(int H, int W, vector<int> R, vector<int> C) {
n = H;
m = W;
sz = n * m;
build(1, 0, sz - 1);
for (int i = 0; i < n * m; i++) {
x[i] = R[i], y[i] = C[i];
sr[x[i]].insert(i);
sc[y[i]].insert(i);
minx[i] = maxx[i] = x[i];
miny[i] = maxy[i] = y[i];
a[y[i]] = i;
}
for (int i = 0; i + 1 < n * m; i++)
update(max(a[i], a[i + 1]), sz - 1, -1);
for (int i = 0; i < n * m; i++) {
if (i > 0) {
mini(minx[i], minx[i - 1]);
mini(miny[i], miny[i - 1]);
maxi(maxx[i], maxx[i - 1]);
maxi(maxy[i], maxy[i - 1]);
}
ans += check(i);
}
for (int i = 0; i < sz; i++)
update(i, i, i);
}
int sub2() {
vector <int> events;
for (int i = 0; i < n; i++)
events.push_back(*sr[i].begin());
for (int i = 0; i < m; i++)
events.push_back(*sc[i].begin());
sort(ALL(events));
int minx = oo, maxx = -oo, miny = oo, maxy = -oo;
int res = 0;
for (int it = 0; it < (int) events.size(); it++) {
if (it + 1 == (int) events.size()) {
res++;
break;
}
int i = events[it];
int j = events[it + 1];
mini(minx, x[i]);
mini(miny, y[i]);
maxi(maxx, x[i]);
maxi(maxy, y[i]);
int t = (maxx - minx + 1) * (maxy - miny + 1);
res += (i <= t && t <= j);
}
return res;
}
int sub3(int l, int r) {
if (l > r)
swap(l, r);
for (int i = l; i <= r; i++) {
ans -= check(i);
minx[i] = maxx[i] = x[i];
miny[i] = maxy[i] = y[i];
if (i > 0) {
mini(minx[i], minx[i - 1]);
mini(miny[i], miny[i - 1]);
maxi(maxx[i], maxx[i - 1]);
maxi(maxy[i], maxy[i - 1]);
}
ans += check(i);
}
return ans;
}
void add(int i, int val) {
int pos = y[i];
if (pos > 0)
update(max(a[pos - 1], a[pos]), sz - 1, val);
if (pos + 1 < sz)
update(max(a[pos], a[pos + 1]), sz - 1, val);
}
int sub4() {
return getmin();
}
int swap_seats(int l, int r) {
sr[x[l]].erase(l);
sr[x[r]].erase(r);
sc[y[l]].erase(l);
sc[y[r]].erase(r);
add(l, 1);
add(r, 1);
swap(x[l], x[r]);
swap(y[l], y[r]);
swap(a[y[l]], a[y[r]]);
add(l, -1);
add(r, -1);
sr[x[l]].insert(l);
sr[x[r]].insert(r);
sc[y[l]].insert(l);
sc[y[r]].insert(r);
if (n == 1)
return sub4();
if (max(n, m) <= 1000)
return sub2();
if (abs(l - r) <= 10000)
return sub3(l, r);
return -1;
}
//#include "grader.cpp"
