#include<bits/stdc++.h> //:3
using namespace std;
typedef long long ll;
#define all(a) (a).begin(), (a).end()
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define pi pair<int, int>
#define sz(x) (int)((x).size())
#include "seats.h"
const int dx[] = {0, 1, 0, -1};
const int dy[] = {1, 0, -1, 0};
const int N = 4000000 + 11;
pi t[4*N];
int lazy[4*N];
pi pos[4*N];
int tot, n, m;
vector<vector<int>>a;
int ln(int n){
return 2*n;
}
int rn(int n){
return 2*n + 1;
}
pi tcombine(pi a, pi b){
if(a.first < b.first){
return a;
} else if(a.first > b.first) {
return b;
} else {
return {a.first, a.second + b.second};
}
}
void push(int n){
if(lazy[n]){
t[n].first += lazy[n];
lazy[ln(n)] += lazy[n];
lazy[rn(n)] += lazy[n];
lazy[n] = 0;
}
}
void build(int n, int l, int r){
if(l == r){
t[n] = {0, 1};
return;
}
int pivot = (l+r)>>1;
build(ln(n), l, pivot);
build(rn(n), pivot + 1, r);
t[n] = tcombine(t[ln(n)], t[rn(n)]);
}
void update(int n, int l, int r, int ql, int qr, int add){
push(n);
if(ql <= l && r <= qr){
lazy[n] += add;
push(n);
return;
}
int pivot = (l+r)>>1;
if(ql <= pivot)
update(ln(n), l, pivot, ql, qr, add);
if(qr > pivot)
update(rn(n), pivot+1, r, ql, qr, add);
push(ln(n));
push(rn(n));
t[n] = tcombine(t[ln(n)], t[rn(n)]);
}
bool ok(pi x){
if(x.ff > 0 && x.ff <= n){
if(x.ss > 0 && x.ss <= m){
return 1;
}
}
return 0;
}
pi getB(pi x){
int l = a[x.ff][x.ss];
int r = tot + 1;
for(int i = 0; i < 4; i++){
pi A = x;
A.ff += dx[i];
A.ss += dy[i];
if(ok(A)){
if(i < 2)r = min(r, a[x.ff][x.ss]);
}
}
return {l, r};
}
int secondSmallestNeighbour(pi x){
vector<int>s;
for(int i = 0; i < 4; i++){
pi A = x;
A.ff += dx[i];
A.ss += dy[i];
if(ok(A)){
s.push_back(a[A.ff][A.ss]);
}
}
sort(all(s));
if(sz(s) > 1)return s[1];
return tot + 1;
}
void deleteA(pi x){
int l = secondSmallestNeighbour(x);
int r = a[x.ff][x.ss];
if(r > l){
update(1, 1, tot, l, r - 1, -1);
}
}
void updateA(pi x){
int l = secondSmallestNeighbour(x);
int r = a[x.ff][x.ss];
if(r > l){
update(1, 1, tot, l, r - 1, +1);
}
}
void deleteB(pi x){
pi p = getB(x);
if(p.ss > p.ff){
update(1, 1, tot, p.ff, p.ss - 1, -1);
}
}
void updateB(pi x){
pi p = getB(x);
if(p.ss > p.ff){
update(1, 1, tot, p.ff, p.ss - 1, +1);
}
}
void rewrite(pi x, int val){
deleteA(x);
for(int i = 0; i < 4; i++){
pi A = x;
A.ff += dx[i];
A.ss += dy[i];
if(ok(A)){
deleteA(A);
}
}
deleteB(x);
for(int i = 2; i < 4; i++){
pi A = x;
A.ff += dx[i];
A.ss += dy[i];
if(ok(A)){
deleteB(A);
}
}
a[x.ff][x.ss] = val;
updateA(x);
for(int i = 0; i < 4; i++){
pi A = x;
A.ff += dx[i];
A.ss += dy[i];
if(ok(A)){
updateA(A);
}
}
updateB(x);
for(int i = 2; i < 4; i++){
pi A = x;
x.ff += dx[i];
x.ss += dy[i];
if(ok(A)){
updateB(A);
}
}
}
void give_initial_chart(int H, int W, vector<int> R, vector<int> C){
m = W;
n = H;
tot = n*m;
build(1, 1, tot);
a = vector<vector<int>>(n + 5, vector<int>(m + 5, 0));
for(int i = 0 ; i < n*m; i++){
a[R[i] + 1][C[i] + 1] = i + 1;
pos[i] = {R[i] + 1, C[i] + 1};
}
for(int i = 1; i <= n; i++){
for(int j = 1; j <= m; j++){
updateA({i, j}); //first condition
updateB({i, j}); //second condition
}
}
}
int swap_seats(int A, int B) {
rewrite(pos[A], B + 1);
rewrite(pos[B], A + 1);
swap(pos[A], pos[B]);
return (t[1].ff == 1 ? t[1].ss : 0);
}
