#include <bits/stdc++.h>
#include "seats.h"
using namespace std;
class segtree_t {
private:
struct node_t {
int tag, value, answer;
};
vector<node_t> tree;
int n;
void apply(int x, int value) {
tree[x].tag += value;
tree[x].value += value;
}
void push_up(int x, int z) {
tree[x].value = min(tree[x + 1].value, tree[z].value);
tree[x].answer = 0;
if (tree[x].value == tree[x + 1].value) {
tree[x].answer += tree[x + 1].answer;
}
if (tree[x].value == tree[z].value) {
tree[x].answer += tree[z].answer;
}
}
void push_down(int x, int z) {
if (tree[x].tag) {
apply(x + 1, tree[x].tag);
apply(z, tree[x].tag);
tree[x].tag = 0;
}
}
void build(int x, int l, int r, vector<int> &a) {
if (l == r) {
tree[x].value = a[l];
tree[x].answer = 1;
} else {
int y = l + r >> 1, z = x + (y - l + 1 << 1);
build(x + 1, l, y, a);
build(z, y + 1, r, a);
push_up(x, z);
}
}
void modify(int x, int l, int r, int ql, int qr, int value) {
if (l == ql && r == qr) {
apply(x, value);
} else {
int y = l + r >> 1, z = x + (y - l + 1 << 1);
push_down(x, z);
if (qr <= y) {
modify(x + 1, l, y, ql, qr, value);
} else if (ql > y) {
modify(z, y + 1, r, ql, qr, value);
} else {
modify(x + 1, l, y, ql, y, value);
modify(z, y + 1, r, y + 1, qr, value);
}
push_up(x, z);
}
}
public:
void init(vector<int> a) {
n = a.size();
tree.resize((n << 1) - 1);
build(0, 0, n - 1, a);
}
void modify(int l, int r, int value) {
if (l <= r) {
modify(0, 0, n - 1, l, r, value);
}
}
int query() {
return tree[0].answer;
}
};
const vector<int> dx = {1, -1, 0, 0};
const vector<int> dy = {0, 0, 1, -1};
vector<vector<int>> board;
segtree_t segtree;
vector<int> r, c;
int n, m;
bool in(int x, int y) {
return x >= 0 && x < n && y >= 0 && y < m;
}
void give_initial_chart(int _n, int _m, vector<int> _r, vector<int> _c) {
n = _n;
m = _m;
r = _r;
c = _c;
board = vector<vector<int>> (n, vector<int> (m));
for (int i = 0; i < n * m; ++i) {
board[r[i]][c[i]] = i;
}
vector<int> answer(n * m);
int current = 0;
for (int i = 0; i < n * m; ++i) {
int x = r[i], y = c[i], degree = 0;
for (int j = 0; j < 4; ++j) {
int nx = x + dx[j], ny = y + dy[j];
if (in(nx, ny)) {
if (board[nx][ny] > i) {
int degree = 0;
for (int k = 0; k < 4; ++k) {
int tx = nx + dx[k], ty = ny + dy[k];
if (in(tx, ty) && board[tx][ty] <= i) {
++degree;
}
}
if (degree == 2) {
++current;
}
} else {
++degree;
}
}
}
if (degree >= 2) {
--current;
}
if (in(x, y + 1) && board[x][y + 1] <= i && (!in(x - 1, y + 1) || board[x - 1][y + 1] > i)) {
--current;
}
if (in(x + 1, y) && board[x + 1][y] <= i && (!in(x + 1, y - 1) || board[x + 1][y - 1] > i)) {
--current;
}
if ((!in(x - 1, y) || board[x - 1][y] > i) && (!in(x, y - 1) || board[x][y - 1] > i)) {
++current;
}
answer[i] = current;
}
segtree.init(answer);
}
void modify(int x, int y, int value) {
vector<int> neighbor;
{
neighbor.clear();
for (int i = 0; i < 4; ++i) {
int nx = x + dx[i], ny = y + dy[i];
if (in(nx, ny)) {
neighbor.push_back(board[nx][ny]);
}
}
sort(neighbor.begin(), neighbor.end());
if (neighbor.size() >= 2) {
segtree.modify(neighbor[1], board[x][y] - 1, -1);
segtree.modify(neighbor[1], value - 1, 1);
}
}
for (int i = 0; i < 4; ++i) {
int nx = x + dx[i], ny = y + dy[i];
if (in(nx, ny)) {
neighbor.clear();
for (int j = 0; j < 4; ++j) {
int tx = nx + dx[j], ty = ny + dy[j];
if (in(tx, ty)) {
neighbor.push_back(board[tx][ty]);
}
}
sort(neighbor.begin(), neighbor.end());
if (neighbor.size() >= 2) {
segtree.modify(neighbor[1], board[nx][ny] - 1, -1);
}
for (int j = 0; j < neighbor.size(); ++j) {
if (neighbor[j] == board[x][y]) {
neighbor[j] = value;
break;
}
}
sort(neighbor.begin(), neighbor.end());
if (neighbor.size() >= 2) {
segtree.modify(neighbor[1], board[nx][ny] - 1, 1);
}
}
}
{
int bound = n * m;
if (in(x - 1, y)) {
bound = min(bound, board[x - 1][y]);
}
if (in(x, y - 1)) {
bound = min(bound, board[x][y - 1]);
}
segtree.modify(board[x][y], bound - 1, -1);
segtree.modify(value, bound - 1, 1);
}
if (in(x + 1, y)) {
int bound = n * m;
if (in(x + 1, y - 1)) {
bound = min(bound, board[x + 1][y - 1]);
}
segtree.modify(board[x + 1][y], min(bound, board[x][y]) - 1, -1);
segtree.modify(board[x + 1][y], min(bound, value) - 1, 1);
}
if (in(x, y + 1)) {
int bound = n * m;
if (in(x - 1, y + 1)) {
bound = min(bound, board[x - 1][y + 1]);
}
segtree.modify(board[x][y + 1], min(bound, board[x][y]) - 1, -1);
segtree.modify(board[x][y + 1], min(bound, value) - 1, 1);
}
board[x][y] = value;
}
int swap_seats(int a, int b) {
modify(r[a], c[a], b);
modify(r[b], c[b], a);
swap(r[a], r[b]);
swap(c[a], c[b]);
return segtree.query();
}
