#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
edi
http://www.algonotes.com/en/solutions-ioi2018/
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "seats.h"
template<typename T>
struct lazysegtree {
/*=======================================================*/
struct data {
int mn,mn_cnt;
};
struct lazy {
int a;
};
data d_neutral = {inf1,0};
lazy l_neutral = {0};
void merge(data &curr, data &left, data &right) {
if(left.mn <= right.mn) curr = left;
else curr = right;
if(left.mn == right.mn) curr.mn_cnt += right.mn_cnt;
}
void create(int x, int lx, int rx, T v) {
tr[x].mn = 0;
tr[x].mn_cnt = 1;
}
void modify(int x, int lx, int rx, T v) {
lz[x].a = v;
}
void propagate(int x, int lx, int rx) {
int v = lz[x].a;
if(!v) return;
tr[x].mn += v;
if(rx-lx > 1){
lz[2*x+1].a += v;
lz[2*x+2].a += v;
}
lz[x] = l_neutral;
}
/*=======================================================*/
int siz = 1;
vector<data> tr;
vector<lazy> lz;
lazysegtree() {
}
lazysegtree(int n) {
while (siz < n) siz *= 2;
tr.assign(2 * siz, d_neutral);
lz.assign(2 * siz, l_neutral);
}
void build(int n, int x, int lx, int rx) {
if (rx - lx == 1) {
if (lx < n) {
create(x, lx, rx, 0);
}
return;
}
int mid = (lx + rx) / 2;
build(n, 2 * x + 1, lx, mid);
build(n, 2 * x + 2, mid, rx);
merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
}
void build(int n) {
build(n, 0, 0, siz);
}
void rupd(int l, int r, T v, int x, int lx, int rx) {
propagate(x, lx, rx);
if (lx >= r or rx <= l) return;
if (lx >= l and rx <= r) {
modify(x, lx, rx, v);
propagate(x, lx, rx);
return;
}
int mid = (lx + rx) / 2;
rupd(l, r, v, 2 * x + 1, lx, mid);
rupd(l, r, v, 2 * x + 2, mid, rx);
merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
}
void rupd(int l, int r, T v) {
rupd(l, r + 1, v, 0, 0, siz);
}
data query(int l, int r, int x, int lx, int rx) {
propagate(x, lx, rx);
if (lx >= r or rx <= l) return d_neutral;
if (lx >= l and rx <= r) return tr[x];
int mid = (lx + rx) / 2;
data curr;
data left = query(l, r, 2 * x + 1, lx, mid);
data right = query(l, r, 2 * x + 2, mid, rx);
merge(curr, left, right);
return curr;
}
data query(int l, int r) {
return query(l, r + 1, 0, 0, siz);
}
};
vector<vector<int>> a;
vector<pii> pos;
lazysegtree<int> st;
int n,m;
void upd(int i, int j, int add){
// update the subsquare with corners (i,j),(i+1,j+1)
vector<int> vals;
for(int r = i; r <= i+1; ++r){
for(int c = j; c <= j+1; ++c){
vals.pb(a[r][c]);
}
}
sort(all(vals));
{
int l = vals[0], r = vals[1]-1;
st.rupd(l,r,add);
}
{
int l = vals[2], r = vals[3]-1;
if(l != inf1){
st.rupd(l,r,add);
}
}
}
void give_initial_chart(int n_, int m_, std::vector<int> R, std::vector<int> C) {
n = n_, m = m_;
a = vector<vector<int>>(n+5,vector<int>(m+5,inf1));
rep(i,n*m){
int r = R[i]+1, c = C[i]+1;
a[r][c] = i;
}
rep(i,n*m) pos.pb({R[i]+1,C[i]+1});
st = lazysegtree<int>(n*m);
st.build(n*m);
rep(i,n+1){
rep(j,m+1){
upd(i,j,1);
}
}
}
int swap_seats(int x, int y) {
auto [r1,c1] = pos[x];
auto [r2,c2] = pos[y];
set<pii> sqs;
for(int i = r1-1; i <= r1; ++i){
for(int j = c1-1; j <= c1; ++j){
sqs.insert({i,j});
}
}
for(int i = r2-1; i <= r2; ++i){
for(int j = c2-1; j <= c2; ++j){
sqs.insert({i,j});
}
}
for(auto [i,j] : sqs){
upd(i,j,-1);
}
swap(pos[x],pos[y]);
swap(a[r1][c1],a[r2][c2]);
for(auto [i,j] : sqs){
upd(i,j,1);
}
auto [mn,mn_cnt] = st.query(0,n*m-1);
assert(mn == 4);
int ans = mn_cnt;
return ans;
}
