#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define ff first
#define ss second
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define replr(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define reprl(i, a, b) for (int i = int(a); i >= int(b); --i)
#define rep(i, n) for (int i = 0; i < int(n); ++i)
#define mkp(a, b) make_pair(a, b)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<PII> VPI;
typedef vector<VI> VVI;
typedef vector<VVI> VVVI;
typedef vector<VPI> VVPI;
typedef pair<ll, ll> PLL;
typedef vector<ll> VL;
typedef vector<PLL> VPL;
typedef vector<VL> VVL;
typedef vector<VVL> VVVL;
typedef vector<VPL> VVPL;
template<class T> T setmax(T& a, T b) {if (a < b) return a = b; return a;}
template<class T> T setmin(T& a, T b) {if (a < b) return a; return a = b;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template<class T>
using indset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "seats.h"
struct RECTANGLE {
int mnx, mxx, mny, mxy;
RECTANGLE() {
mnx = mny = +2e9;
mxx = mxy = -2e9;
}
void addcell(int x, int y) {
setmin(mnx, x);
setmax(mxx, x);
setmin(mny, y);
setmax(mxy, y);
}
int area() {
if (mnx == +2e9) return -1;
return (mxx-mnx+1) * (mxy-mny+1);
}
};
namespace TEST4 {
int n, m;
VPI tex;
int ans;
vector<RECTANGLE> pref;
void give_initial_chart(int H, int W, VI R, VI C) {
n = H;
m = W;
rep(i, n*m) tex.pb({R[i], C[i]});
pref = vector<RECTANGLE>(n*m+1);
replr(i, 1, n*m) {
pref[i] = pref[i-1];
auto[x, y] = tex[i-1];
pref[i].addcell(x, y);
ans += (i == pref[i].area());
}
}
int swap_seats(int a, int b) {
swap(tex[a], tex[b]);
replr(i, min(a, b)+1, max(a, b)+1) {
ans -= (i == pref[i].area());
pref[i] = pref[i-1];
auto[x, y] = tex[i-1];
pref[i].addcell(x, y);
ans += (i == pref[i].area());
}
return ans;
}
}
/*SEGTREE*/
template<int DEFAULT, typename COMPORATOR>
struct SEGTREE {
int n;
VI tree;
COMPORATOR comp;
int BEST(int a, int b) {
if (comp(a, b)) return a;
return b;
}
SEGTREE(){}
SEGTREE(int sz) {
n = 1;
while (n < sz) n *= 2;
tree = VI(2*n, DEFAULT);
}
void upd(int N, int L, int R, int i, int s) {
if (i < L || i > R) return;
if (L == R) {
tree[N] = s;
return;
}
int M = (L + R) / 2;
upd(2*N+1, L, M, i, s);
upd(2*N+2, M+1, R, i, s);
tree[N] = BEST(tree[2*N+1], tree[2*N+2]);
}
int query(int N, int L, int R, int x) {
if (!comp(tree[N], x)) return -1;
if (L == R) return L;
int M = (L + R) / 2;
if (comp(tree[2*N+1], x)) return query(2*N+1, L, M, x);
if (comp(tree[2*N+2], x)) return query(2*N+2, M+1, R, x);
return -1;
}
void upd(int i, int s) {
upd(0, 0, n-1, i, s);
}
int query(int x) {
int ret = query(0, 0, n-1, x);
if (ret == -1) return 2e9;
return ret;
}
};
namespace TEST3 {
int n, m;
VPI tex;
SEGTREE<(int)+2e9, less<int>> flx, fly;
SEGTREE<(int)-2e9, greater<int>> fgx, fgy;
void give_initial_chart(int H, int W, VI R, VI C) {
n = H;
m = W;
rep(i, n*m) tex.pb({R[i], C[i]});
flx = fly = SEGTREE<(int)+2e9, less<int>>(n*m);
fgx = fgy = SEGTREE<(int)-2e9, greater<int>>(n*m);
rep(i, n*m) {
auto[x, y] = tex[i];
flx.upd(i, x);
fgx.upd(i, x);
fly.upd(i, y);
fgy.upd(i, y);
}
}
int swap_seats(int a, int b) {
swap(tex[a], tex[b]);
for (int i : {a, b}) {
auto[x, y] = tex[i];
flx.upd(i, x);
fgx.upd(i, x);
fly.upd(i, y);
fgy.upd(i, y);
}
RECTANGLE cur;
int curind = -1;
int ans = 1;
while (true) {
int nextind = 2e9;
setmin(nextind, flx.query(cur.mnx));
setmin(nextind, fgx.query(cur.mxx));
setmin(nextind, fly.query(cur.mny));
setmin(nextind, fgy.query(cur.mxy));
if (nextind == 2e9) break;
int area = cur.area();
ans += (curind <= area-1 && area-1 < nextind);
cur.addcell(tex[nextind].ff, tex[nextind].ss);
curind = nextind;
}
return ans;
}
};
bool test3;
void give_initial_chart(int H, int W, VI R, VI C) {
if (H <= 1000 && W <= 1000) test3 = true;
if (test3) TEST3::give_initial_chart(H, W, R, C);
else TEST4::give_initial_chart(H, W, R, C);
}
int swap_seats(int a, int b) {
if (test3) return TEST3::swap_seats(a, b);
else return TEST4::swap_seats(a, b);
}
