#include <bits/stdc++.h>
using namespace std;
#define pi pair<int, int>
#define X first
#define Y second
int h, w;
int r[1000005];
int c[1000005];
pair<int, int> pref_mx[1000005], pref_mn[1000005];
int small_change = 0;
struct ST{
pair<pi, pi> st[8000005];
pair<pi, pi> comb(pair<pi, pi> x, pair<pi, pi> y) {
pair<pi, pi> ret;
ret.X.X = max(x.X.X, y.X.X);
ret.X.Y = max(x.X.Y, y.X.Y);
ret.Y.X = min(x.Y.X, y.Y.X);
ret.Y.Y = min(x.Y.Y, y.Y.Y);
return ret;
}
void Build(int node, int ll, int rr) {
if (ll == rr) {
st[node] = {{r[ll], c[ll]}, {r[ll], c[ll]}};
return;
}
int mid = ll + rr >> 1;
Build(node * 2, ll, mid);
Build(node * 2 + 1, mid + 1, rr);
st[node] = comb(st[node * 2], st[node * 2 + 1]);
}
void Set(int node, int l, int r, int x, pi val) {
if (l == r) {
st[node].X = st[node].Y = val;
return;
}
int mid = l + r >> 1;
if (x <= mid) Set(node * 2, l, mid, x, val);
else Set(node * 2 + 1, mid + 1, r, x, val);
st[node] = comb(st[node * 2], st[node * 2 + 1]);
}
pair<pi, pi> Get(int node, int l, int r, int ql, int qr) {
if (l > r || l > qr || r < ql) return {{0, 0}, {1e9, 1e9}};
if (ql <= l && r <= qr) return st[node];
int mid = l + r >> 1;
return comb(Get(node * 2, l, mid, ql, qr), Get(node * 2 + 1, mid + 1, r, ql, qr));
}
} ST;
void give_initial_chart(int H, int W, vector<int> R, vector<int> C) {
h = H, w = W;
for (int i = 0; i < h * w; i++) {
r[i] = R[i];
c[i] = C[i];
}
if (H + W <= 2000) ST.Build(1, 0, h * w - 1);
else {
pref_mx[0] = pref_mn[0] = {r[0], c[0]};
for (int i = 1; i < h * w; i++) {
pref_mx[i].first = max(pref_mx[i - 1].first, r[i]);
pref_mx[i].second = max(pref_mx[i - 1].second, c[i]);
pref_mn[i].first = min(pref_mn[i - 1].first, r[i]);
pref_mn[i].second = min(pref_mn[i - 1].second, c[i]);
}
for (int i = 0; i < h * w; i++) {
if ((pref_mx[i].first - pref_mn[i].first + 1) * (pref_mx[i].second - pref_mn[i].second + 1) == i + 1) {
small_change++;
}
}
}
}
int swap_seats(int a, int b) {
if (h + w <= 2000) {
swap(r[a], r[b]);
swap(c[a], c[b]);
ST.Set(1, 0, h * w - 1, a, {r[a], c[a]});
ST.Set(1, 0, h * w - 1, b, {r[b], c[b]});
int pos = 0, ans = 0;
while (pos < h * w) {
pair<pi, pi> rect = ST.Get(1, 0, h * w - 1, 0, pos);
int P = (rect.X.X - rect.Y.X + 1) * (rect.X.Y - rect.Y.Y + 1);
assert(P > pos);
if (P == pos + 1) ans++, pos++;
else pos = P - 1;
}
return ans;
} else {
if (h * w <= 10000) {
swap(r[a], r[b]);
swap(c[a], c[b]);
int ans = 0;
pair<int, int> mn, mx;
mx = mn = {r[0], c[0]};
for (int i = 0; i < h * w; i++) {
mx.first = max(mx.first, r[i]);
mx.second = max(mx.second, c[i]);
mn.first = min(mn.first, r[i]);
mn.second = min(mn.second, c[i]);
if ((mx.first - mn.first + 1) * (mx.second - mn.second + 1) == i + 1) {
ans++;
}
}
return ans;
} else {
if (a > b) swap(a, b);
for (int i = a; i <= b; i++) {
if ((pref_mx[i].first - pref_mn[i].first + 1) * (pref_mx[i].second - pref_mn[i].second + 1) == i + 1) {
small_change--;
}
}
swap(r[a], r[b]);
swap(c[a], c[b]);
for (int i = a; i <= b; i++) {
if (i == 0) pref_mx[i] = pref_mn[i] = {r[i], c[i]};
else {
pref_mx[i].first = max(pref_mx[i - 1].first, r[i]);
pref_mx[i].second = max(pref_mx[i - 1].second, c[i]);
pref_mn[i].first = min(pref_mn[i - 1].first, r[i]);
pref_mn[i].second = min(pref_mn[i - 1].second, c[i]);
}
}
for (int i = a; i <= b; i++) {
if ((pref_mx[i].first - pref_mn[i].first + 1) * (pref_mx[i].second - pref_mn[i].second + 1) == i + 1) {
small_change++;
}
}
return small_change;
}
}
}
