#include "bits/extc++.h"
using namespace std;
template <typename T>
void dbgh(const T& t) {
cerr << t << endl;
}
template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
cerr << t << " | ";
dbgh(u...);
}
#ifdef DEBUG
#define dbg(...) \
cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
dbgh(__VA_ARGS__);
#else
#define dbg(...)
#define cerr \
if (false) \
cerr
#endif
#define endl "\n"
#define long int64_t
#define sz(x) int((x).size())
const int dx[] = {0, 0, -1, 1}, dy[] = {-1, 1, 0, 0};
struct Node {
int mn, cnt;
void apply_lazy(int x) {
mn += x;
}
Node operator+(const Node& n) const {
if (mn < n.mn) {
return *this;
} else if (n.mn < mn) {
return n;
}
return {mn, cnt + n.cnt};
}
};
struct DS {
int n;
vector<Node> v;
vector<int> lazy;
DS() {}
DS(int n): n(n), v(4 * n, {0, 1}), lazy(4 * n) {
build(1, 0, n - 1);
}
void build(int o, int l, int r) {
if (l == r) {
return;
}
int mid = (l + r) / 2, lc = o * 2, rc = lc + 1;
build(lc, l, mid);
build(rc, mid + 1, r);
v[o] = v[lc] + v[rc];
}
void update(int o, int l, int r, int ql, int qr, int x) {
if (ql <= l && r <= qr) {
lazy[o] += x;
v[o].apply_lazy(x);
return;
}
int mid = (l + r) / 2, lc = o * 2, rc = lc + 1;
if (ql <= mid) {
update(lc, l, mid, ql, qr, x);
}
if (mid < qr) {
update(rc, mid + 1, r, ql, qr, x);
}
v[o] = v[lc] + v[rc];
v[o].apply_lazy(lazy[o]);
}
void update(int l, int r, int x) {
if (l > r) {
return;
}
update(1, 0, n - 1, l, r, x);
}
int query() const {
return v[1].cnt;
}
} ds;
int n, m;
vector<vector<int>> arr;
vector<pair<int, int>> pos;
bool ibs(int x, int y) {
return 0 <= x && x < n && 0 <= y && y < m;
}
void update1(int x, int y, int v) {
int ans = n * m;
auto go = [&](int x, int y) -> void {
if (ibs(x, y)) {
ans = min(ans, arr[x][y]);
}
};
go(x - 1, y);
go(x, y - 1);
ds.update(arr[x][y], ans - 1, v);
}
void update2(int x, int y, int v) {
int adj[4];
for (int i = 0; i < 4; i++) {
int cx = x + dx[i], cy = y + dy[i];
if (ibs(cx, cy)) {
adj[i] = arr[cx][cy];
} else {
adj[i] = 1e9;
}
}
sort(begin(adj), end(adj));
ds.update(adj[1], arr[x][y] - 1, v);
}
void update(int x, int y, int v) {
update1(x, y, v);
update2(x, y, v);
}
void set_pos(int u) {
auto& [x, y] = pos[u];
arr[x][y] = u;
}
void give_initial_chart(int _n, int _m, vector<int> r, vector<int> c) {
n = _n;
m = _m;
ds = DS(n * m);
pos.resize(n * m);
arr.resize(n, vector<int>(m));
for (int i = 0; i < n * m; i++) {
pos[i] = {r[i], c[i]};
set_pos(i);
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
update(i, j, 1);
}
}
}
int swap_seats(int u, int v) {
set<pair<int, int>> changed;
for (auto& [x, y] : {pos[u], pos[v]}) {
changed.emplace(x, y);
for (int i = 0; i < 4; i++) {
int cx = x + dx[i], cy = y + dy[i];
if (ibs(cx, cy)) {
changed.emplace(cx, cy);
}
}
}
for (auto& [x, y] : changed) {
update(x, y, -1);
}
swap(pos[u], pos[v]);
set_pos(u);
set_pos(v);
for (auto& [x, y] : changed) {
update(x, y, 1);
}
return ds.query();
}
