#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef pair<int, int> pi;
#define pb push_back
#define f first
#define s second
namespace debug {
template<class T1, class T2>
void pr(const pair<T1, T2> &x);
template<class T, size_t SZ>
void pr(const array<T, SZ> &x);
template<class T>
void pr(const vector<T> &x);
template<class T>
void pr(const set<T> &x);
template<class T1, class T2>
void pr(const map<T1, T2> &x);
template<class T>
void pr(const T &x) { cout << x; }
template<class T, class... Ts>
void pr(const T &first, const Ts &... rest) { pr(first), pr(rest...); }
template<class T1, class T2>
void pr(const pair<T1, T2> &x) { pr("{", x.f, ", ", x.s, "}"); }
template<class T>
void prIn(const T &x) {
pr("{");
bool fst = 1;
for (auto &a : x) {
pr(fst ? "" : ", ", a), fst = 0;
}
pr("}");
}
template<class T, size_t SZ>
void pr(const array<T, SZ> &x) { prIn(x); }
template<class T>
void pr(const vector<T> &x) { prIn(x); }
template<class T>
void pr(const set<T> &x) { prIn(x); }
template<class T1, class T2>
void pr(const map<T1, T2> &x) { prIn(x); }
void ps() { pr("\n"); }
template<class Arg, class... Args>
void ps(const Arg &first, const Args &... rest) {
pr(first, " ");
ps(rest...);
}
}
using namespace debug;
const int MAXN = 3100000;
const int INF = 1e9;
inline pi operator+(pi a, pi b) {
if (a.f != b.f) {
if (a.f < b.f) {
return a;
} else {
return b;
}
}
return {a.f, a.s + b.s};
}
int buf[MAXN];
struct LSegTr {
pi tr[4 * MAXN];
int lz[4 * MAXN];
void ps(int i, int l, int r) {
tr[i].f += lz[i];
if (l != r) {
lz[i * 2] += lz[i];
lz[i * 2 + 1] += lz[i];
}
lz[i] = 0;
}
void b(int i, int l, int r) {
if (l == r) {
tr[i] = {buf[l], 1};
return;
}
int mid = (l + r) / 2;
b(i * 2, l, mid);
b(i * 2 + 1, mid + 1, r);
tr[i] = tr[i * 2] + tr[i * 2 + 1];
// debug::ps(tr[i]);
}
pi q(int i, int l, int r, int s, int e) {
ps(i, l, r);
if (e < l || r < s) {
return {INF, 0};
}
if (s <= l && r <= e) {
return tr[i];
}
int mid = (l + r) / 2;
return q(i * 2, l, mid, s, e) + q(i * 2 + 1, mid + 1, r, s, e);
}
void u(int i, int l, int r, int s, int e, int d) {
ps(i, l, r);
if (e < l || r < s) {
return;
}
if (s <= l && r <= e) {
lz[i] += d;
ps(i, l, r);
return;
}
int mid = (l + r) / 2;
u(i * 2, l, mid, s, e, d);
u(i * 2 + 1, mid + 1, r, s, e, d);
tr[i] = tr[i * 2] + tr[i * 2 + 1];
}
} hist;
int nR, nC;
inline int l(int i, int j) {
return (nC + 2) * i + j;
}
int tim[MAXN];
int loc[MAXN];
int dLoc[4]; // u,l,d,r
int sqr[4];
vi times(4);
void mod(int a, int d) { // takes top left of 2x2
for (int i = 0; i < 4; i++) {
times[i] = tim[a + sqr[i]];
}
// ps(times);
sort(times.begin(), times.end());
// ps("upd:", times[0], times[1] - 1, d);
if (times[0] != times[1]) {
hist.u(1, 1, nR * nC, times[0], times[1] - 1, d);
}
if (times[2] != times[3]) {
hist.u(1, 1, nR * nC, times[2], times[3] - 1, d);
}
}
void modB(int a, int d) { // takes top left of 2x2
for (int i = 0; i < 4; i++) {
times[i] = tim[a + sqr[i]];
}
// ps(times);
sort(times.begin(), times.end());
// ps("upd:", times[0], times[1] - 1, d);
if (times[0] != times[1]) {
buf[times[0]] += d;
if (times[1] <= nR * nC) {
buf[times[1]] -= d;
}
}
if (times[2] != times[3]) {
buf[times[2]] += d;
if (times[3] <= nR * nC) {
buf[times[3]] -= d;
}
}
}
void modSur(int ct, int d) {
for (int i = 0; i < 4; i++) {
mod(ct, d);
ct += dLoc[i];
}
}
void give_initial_chart(int H, int W, vi R, vi C) {
// ps("in initial");
nR = H, nC = W;
fill_n(tim, MAXN, INF);
for (int i = 1; i <= nR * nC; i++) {
loc[i] = l(R[i - 1] + 1, C[i - 1] + 1);
// ps(R[i - 1], C[i - 1], l(R[i - 1], C[i - 1]));
tim[loc[i]] = i;
}
dLoc[0] = -(nC + 2);
dLoc[1] = -1;
dLoc[2] = (nC + 2);
dLoc[3] = 1;
// ps(dLoc[0], dLoc[1], dLoc[2], dLoc[3]);
sqr[0] = 0;
sqr[1] = dLoc[3]; // r
sqr[2] = dLoc[3] + dLoc[2]; // r, d
sqr[3] = dLoc[2]; // d
// ps(nR * nC);
/*ps("pre");
for (int i = 1; i <= 6; i++) {
ps(hist.q(1, 1, nR * nC, i, i));
}*/
memset(buf, 0, sizeof(buf));
for (int i = 0; i <= nR; i++) {
for (int j = 0; j <= nC; j++) {
modB(l(i, j), 1);
}
}
for (int i = 1; i <= nR * nC; i++) {
buf[i] += buf[i - 1];
}
hist.b(1, 1, nR * nC);
// ps("fin initial", hist.tr[1].s);
/*
for (int i = 1; i <= 6; i++) {
ps(hist.q(1, 1, nR * nC, i, i));
}*/
}
int swap_seats(int a, int b) {
a++, b++;
modSur(loc[a], -1);
modSur(loc[b], -1);
swap(loc[a], loc[b]);
tim[loc[a]] = a;
tim[loc[b]] = b;
modSur(loc[a], 1);
modSur(loc[b], 1);
// ps("printing", hist.tr[1].s);
return hist.tr[1].s; // min amt hist will always be 4, find # of times where it is 4
}
/*
int main() {
// ps("start");
vi R = {0, 1, 1, 0, 0, 1};
vi C = {0, 0, 1, 1, 2, 2};
give_initial_chart(2, 3, R, C);
ps(swap_seats(0, 5));
ps(swap_seats(0, 5));
}*/
