#include "seats.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<int, int>
#define all(c) ((c).begin()), ((c).end())
#define sz(x) ((int)(x).size())
#ifdef LOCAL
#include <print.h>
#else
#define trace(...)
#define endl '\n'
#endif
// min, min_count segtree
struct Data{
int mn, mncnt;
Data() : mn(0), mncnt(1){}
Data(int mn, int mncnt) : mn(mn), mncnt(mncnt){}
};
Data merge(const Data & A, const Data & B){
Data ret;
ret.mn = min(A.mn, B.mn);
ret.mncnt = (A.mn == ret.mn ? A.mncnt : 0) + (B.mn == ret.mn ? B.mncnt : 0);
return ret;
}
struct segtree{
vector<Data> tree;
vector<int> lazy;
int n;
segtree(){}
segtree(vector<int> vals) : n(vals.size()){
tree.resize(4 * n);
lazy.resize(4 * n);
function<void(int, int, int)> make = [&](int s, int e, int ind){
if(s == e){
tree[ind] = Data(vals[s], 1);
return;
}
int mid = (s + e) >> 1;
make(s, mid, 2 * ind);
make(mid + 1, e, 2 * ind + 1);
tree[ind] = merge(tree[2 * ind], tree[2 * ind + 1]);
};
make(0, n - 1, 1);
}
void push(int s, int e, int ind){
int l = lazy[ind];
if(l == 0) return;
tree[ind].mn += l;
if(s != e){
lazy[2 * ind] += l;
lazy[2 * ind + 1] += l;
}
lazy[ind] = 0;
}
void add(int L, int R, int v, int s, int e, int ind){
push(s, e, ind);
if(L > e || s > R) return;
if(s >= L && e <= R){
lazy[ind] += v;
push(s, e, ind);
return;
}
int mid = (s + e) >> 1;
add(L, R, v, s, mid, 2 * ind);
add(L, R, v, mid + 1, e, 2 * ind + 1);
tree[ind] = merge(tree[2 * ind], tree[2 * ind + 1]);
}
void add(int L, int R, int v){
R = min(R, n - 1);
if(L > R) return;
add(L, R, v, 0, n - 1, 1);
}
};
int H, W;
vector<int> R, C;
vector<vector<int>> when;
segtree st;
vector<int> init;
void add_contribution(int i, int j, int k, bool flag = 0){
vector<int> times;
for(int _i : {i, i + 1}) for(int _j : {j, j + 1}){
times.push_back(when[_i][_j]);
}
sort(all(times));
for(int i : {0, 2}){
if(!flag) st.add(times[i], times[i + 1] - 1, k);
else if(times[i] < times[i + 1]){
init[times[i]]++;
if(times[i + 1] < H * W) init[times[i + 1]]--;
}
}
}
void give_initial_chart(int h, int w, vector<int> r, vector<int> c){
H = h; W = w;
R = r; C = c;
when.assign(H + 2, vector<int>(W + 2, H * W));
init.resize(H * W);
for(int i = 0; i < H * W; i++){
R[i]++; C[i]++;
when[R[i]][C[i]] = i;
}
for(int i = 0; i <= H; i++){
for(int j = 0; j <= W; j++){
add_contribution(i, j, 1, true);
}
}
for(int i = 1; i < H * W; i++) init[i] += init[i - 1];
st = segtree(init);
}
int swap_seats(int a, int b) {
set<pair<int, int>> changes;
int u = R[a], v = C[a];
for(int i : {u - 1, u})
for(int j : {v - 1, v})
changes.insert({i, j});
u = R[b], v = C[b];
for(int i : {u - 1, u})
for(int j : {v - 1, v})
changes.insert({i, j});
for(auto it : changes) add_contribution(it.first, it.second, -1);
when[R[b]][C[b]] = a;
when[R[a]][C[a]] = b;
swap(R[a], R[b]);
swap(C[a], C[b]);
for(auto it : changes) add_contribution(it.first, it.second, 1);
Data D = st.tree[1];
assert(D.mn == 4);
return D.mncnt;
}
