#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx,popcnt,sse4,abm")
#include <bits/stdc++.h>
#include "seats.h"
using namespace std;
#define ll long long
#define Waimai ios::sync_with_stdio(false), cin.tie(0)
#define FOR(x,a,b) for (int x = a, I = b; x <= I; x++)
#define pb emplace_back
#define F first
#define S second
#define lpos pos*2
#define rpos pos*2+1
const int SIZE = 1e6 + 5;
int n, m;
int x[SIZE], y[SIZE];
vector<int> a[SIZE];
pair<int, int> d[SIZE];
pair<int, int> operator + (const pair<int, int> &l, const pair<int, int> &r) {
return pair<int, int>(l.F + r.F, l.S + r.S);
}
pair<int, int>& operator += (pair<int, int> &l, const pair<int, int> &r) {
return l = l + r;
}
struct Node {
pair<int, int> mn, lazy;
int cnt;
Node() = default;
Node operator + (const Node &r) const {
Node re = Node();
re.mn = min(mn, r.mn);
re.cnt = (mn == re.mn ? cnt : 0) + (r.mn == re.mn ? r.cnt : 0);
return re;
}
} node[SIZE * 4];
void push(int pos, int l, int r) {
node[pos].mn += node[pos].lazy;
if (l < r) {
node[lpos].lazy += node[pos].lazy;
node[rpos].lazy += node[pos].lazy;
}
node[pos].lazy = {0, 0};
}
void pull(int pos, int l, int r) {
int mid = (l + r) / 2;
push(lpos, l, mid);
push(rpos, mid + 1, r);
node[pos] = node[lpos] + node[rpos];
}
void build(int pos, int l, int r) {
if (l == r) {
node[pos].mn = d[l];
node[pos].cnt = 1;
return;
}
int mid = (l + r) / 2;
build(lpos, l, mid);
build(rpos, mid + 1, r);
node[pos] = node[lpos] + node[rpos];
}
void upd(int pos, int l, int r, int L, int R, pair<int, int> x) {
if (l == L && r == R) {
node[pos].lazy += x;
return;
}
push(pos, L, R);
int mid = (L + R) / 2;
if (r <= mid) upd(lpos, l, r, L, mid, x);
else if (l > mid) upd(rpos, l, r, mid + 1, R, x);
else {
upd(lpos, l, mid, L, mid, x);
upd(rpos, mid + 1, r, mid + 1, R, x);
}
pull(pos, L, R);
}
void upd(int l, int r, pair<int, int> x) {
if (l > r) return;
upd(1, l, r, 0, n * m - 1, x);
}
int que() {
push(1, 0, n * m - 1);
if (node[1].mn == make_pair(4, 0)) return node[1].cnt;
return 0;
}
void add(int i, int j, int delta, bool pre = 0) {
vector<int> t;
FOR (di, 0, 1) FOR (dj, 0, 1) {
if (min(i + di, j + dj) < 0 || i + di >= n || j + dj >= m) t.pb(n * m);
else t.pb(a[i + di][j + dj]);
}
sort(t.begin(), t.end());
if (pre) {
d[t[0]] += {delta, 0};
d[t[1]] += {-delta, 0};
d[t[2]] += {0, delta};
d[t[3]] += {0, -delta};
return;
}
upd(t[0], t[1] - 1, {delta, 0});
upd(t[2], t[3] - 1, {0, delta});
}
void give_initial_chart(int H, int W, vector<int> R, vector<int> C) {
n = H, m = W;
FOR (i, 0, n - 1) a[i].resize(m);
FOR (i, 0, n * m - 1) {
tie(x[i], y[i]) = make_pair(R[i], C[i]);
a[x[i]][y[i]] = i;
}
FOR (i, -1, n - 1) FOR (j, -1, m - 1) add(i, j, 1, 1);
FOR (i, 1, n * m - 1) d[i] += d[i - 1];
build(1, 0, n * m - 1);
}
int swap_seats(int l, int r) {
FOR (dx, -1, 0) FOR (dy, -1, 0) {
add(x[l] + dx, y[l] + dy, -1);
add(x[r] + dx, y[r] + dy, -1);
}
swap(a[x[l]][y[l]], a[x[r]][y[r]]);
swap(x[l], x[r]), swap(y[l], y[r]);
FOR (dx, -1, 0) FOR (dy, -1, 0) {
add(x[l] + dx, y[l] + dy, 1);
add(x[r] + dx, y[r] + dy, 1);
}
return que();
}
