1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
#include<bits/stdc++.h>
using namespace std;
using LL=long long;
#define FOR(i,l,r)for(int i=(l);i<=(r);++i)
#define REP(i,n)FOR(i,0,(n)-1)
#define ssize(x)int(x.size())
#ifdef DEBUG
auto operator<<(auto&o,auto x)->decltype(x.end(),o);
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<", "<<get<3>(t)<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

const int INF = 1e9;

using T = pair<int, int>; // {min, cnt_min}
const T neutral = {INF, 0};
T merge(T a, T b) {
	auto [a_min, a_cnt] = a;
	auto [b_min, b_cnt] = b;
	if (a_min < b_min)
		return a;
	if (b_min < a_min)
		return b;
	return {a_min, a_cnt + b_cnt};
}
int sz = 1;
struct Node {
	T value = {0, sz};
	int lazy = 0;
	int l = -1, r = -1;
};
vector<Node> nodes;
int get_Node() {
	int ret = ssize(nodes);
	nodes.emplace_back(Node{});
	return ret;
}
struct Tree {
	int root;
	Tree() : root(get_Node()) {}
	Tree(const Tree&) = delete;
	Tree(Tree&&) = default;
	void add_children(int w, int child_size) {
		if (nodes[w].l == -1) {
			auto left = get_Node();
			auto right = get_Node();
			nodes[w].l = left;
			nodes[w].r = right;
			nodes[left].value.second = child_size;
			nodes[right].value.second = child_size;
		}
	}
	void push(int w, int child_size) {
		add_children(w, child_size);
		const int lazy = nodes[w].lazy;
		if (lazy) {
			nodes[w].lazy = 0;
			for (int x : {nodes[w].l, nodes[w].r}) {
				nodes[x].value.first += lazy;
				nodes[x].lazy += lazy;
			}
		}
	}
	T que(int w, int a, int b, int l, int r) {
		if (a > r or b < l)
			return neutral;
		if (a >= l and b <= r)
			return nodes[w].value;
		const int middle = (a + b) / 2;
		push(w, b - middle);
		return merge(
				que(nodes[w].l, a, middle, l, r),
				que(nodes[w].r, middle + 1, b, l, r)
				);
	}
	void upd(int w, int a, int b, int l, int r, int value) {
		if (a > r or b < l)
			return;
		if (a >= l and b <= r) {
			nodes[w].value.first += value;
			nodes[w].lazy += value;
			return;
		}
		const int middle = (a + b) / 2;
		push(w, b - middle);
		upd(nodes[w].l, a, middle, l, r, value);
		upd(nodes[w].r, middle + 1, b, l, r, value);
		nodes[w].value = merge(nodes[nodes[w].l].value, nodes[nodes[w].r].value);
	}
	T query(int l, int r) {
		return que(root, 0, sz - 1, l, r);
	}
	void update(int l, int r, int value) {
		upd(root, 0, sz - 1, l, r, value);
	}
};

using P = pair<int, int>;

struct pair_hash {
    inline std::size_t operator()(const std::pair<int,int> & v) const {
        return v.first * size_t(1e6) + v.second;
    }
};

void solve() {
	int n, m, k, q;
	cin >> n >> m >> k >> q;
	map<P, int> s;
	REP(i, k) {
		int x, y;
		cin >> x >> y;
		--x, --y;
		s[pair(x, y)] = 0;
	}
	sz = 1;
	while (sz < n)
		sz *= 2;
	int sz_dfs = 1;
	while (sz_dfs < q + 1) {
		sz_dfs *= 2;
	}
	using Event = tuple<int, int, P>; // {l, r, value}
	vector<Event> events;
	REP(i, q) {
		int x, y;
		cin >> x >> y;
		--x, --y;
		P p = pair(x, y);
		if (s.contains(p)) {
			events.emplace_back(s[p], i, p);
			s.erase(p);
		}
		else {
			s[p] = i + 1;
		}
	}
	for (auto [p, l] : s) {
		events.emplace_back(l, sz_dfs - 1, p);
	}

	vector<vector<P>> dfs_tree(2 * sz_dfs);


	auto add_event = [&](auto&& self, int w, int a, int b, int l, int r, P p) {
		if (a > r or b < l)
			return;
		if (a >= l and b <= r) {
			dfs_tree[w].emplace_back(p);
			return;
		}
		const int middle = (a + b) / 2;
		self(self, 2 * w, a, middle, l, r, p);
		self(self, 2 * w + 1, middle + 1, b, l, r, p);
	};
	for (auto [l, r, p] : events) {
		add_event(add_event, 1, 0, sz_dfs - 1, l, r, p);
	}

	const auto rev = [&](P p) -> P {
		auto [x, y] = p;
		return {n - 1 - x, y};
	};
	const auto get_diag = [](P p) -> int {
		auto [x, y] = p;
		return x + y;
	};

	const int diags = n + m - 1;

	using I = pair<int, int>;

	int blocked_points = 0;
	vector points(2, unordered_set<P, pair_hash>{});
	const int initial_reserve = 3e6;
	REP(id, 2)
		points[id].reserve(initial_reserve);
	vector squares(2, vector (diags, set<int>{})); // has xs
	vector intervals(2, vector (diags, set<I>{}));
	vector<vector<Tree>> tree(2);
	REP(id, 2)
		tree[id].resize(diags);

	auto dfs = [&](auto&& self, int w, int a, int b) -> void {
		if (a > q)
			return;
		auto v = dfs_tree[w];
		vector<tuple<int, int, int>> revert_squares; // {id, diag, x}
		vector<tuple<int, int, I, bool>> revert_intervals; // {id, diag, x, true is add}
		vector<tuple<int, int, int, int>> revert_tree; // {id, diag, l, r}
		const auto add_square = [&](int id, P p) {
			auto [x, y] = p;
			const int diag = x + y;
			squares[id][diag].emplace(x);
			revert_squares.emplace_back(id, diag, x);
		};
		const auto add_interval = [&](int id, int diag, I i) {
			intervals[id][diag].emplace(i);
			revert_intervals.emplace_back(id, diag, i, false);
		};
		const auto remove_interval = [&](int id, int diag, I i) {
			intervals[id][diag].erase(i);
			revert_intervals.emplace_back(id, diag, i, true);
		};
		const auto add_point_to_intervals = [&](int id, P p) {
			auto [x, y] = p;
			const int diag = x + y;
			auto it = intervals[id][diag].lower_bound(I(x, y));
			if (it == intervals[id][diag].end() or it->first > x + 1) {
				if (it == intervals[id][diag].begin() or prev(it)->second < x - 1) {
					add_interval(id, diag, I(x, x));
				}
				else {
					const auto before = *prev(it);
					remove_interval(id, diag, before);
					add_interval(id, diag, I(before.first, x));
				}
			}
			else {
				if (it == intervals[id][diag].begin() or prev(it)->second < x - 1) {
					const auto after = *it;
					remove_interval(id, diag, after);
					add_interval(id, diag, I(x, after.second));
				}
				else {
					const auto before = *prev(it);
					const auto after = *it;
					remove_interval(id, diag, before);
					remove_interval(id, diag, after);
					add_interval(id, diag, I(before.first, after.second));
				}
			}
		};
		const auto get_my_interval = [&](int id, P p) -> I {
			const auto [x, y] = p;
			const int diag = x + y;
			auto it = intervals[id][diag].lower_bound(I(x + 1, -1));
			return *prev(it);
		};
		const auto is_part_of_square = [&](int id, P p) -> bool {
			const auto [x, y] = p;
			const int diag = x + y;
			return squares[id][diag].contains(x);
		};
		const auto ret_false = pair(false, I{-1, -1});
		// a good interval end with squares on both ends
		const auto get_good_interval = [&](int id, P p, bool to_right) -> pair<bool, I> { // {found, interval}
			auto [l, r] = get_my_interval(id, p);
			const auto [x, y] = p;
			const int diag = x + y;
			auto expand_left = [&](auto it) -> int {
				while (it != squares[id][diag].begin() and *it >= x and *prev(it) >= l)
					--it;
				return *it;
			};
			auto expand_right = [&](auto it) -> int {
				while (next(it) != squares[id][diag].end() and *it <= x and *next(it) <= r)
					++it;
				return *it;
			};
			auto it = squares[id][diag].lower_bound(x);
			if (it == squares[id][diag].end())
				return ret_false;
			int left = x, right = x;
			if (*it == x) {
				if (to_right)
					right = expand_right(it);
				else
					left = expand_left(it);
			}
			else {
				if (to_right) {
					right = expand_right(it);
					left = expand_left(it);
				}
				else {
					return ret_false;
				}
			}
			bool found = left <= x and right <= r;
			if (not found)
				return ret_false;
			const pair<bool, I> ret_true = {true, {left, right}};
			const P below = x == left ? P(x, y - 1) : P(x - 1, y);
			if (points[id].contains(below)) {
				auto [l2, r2] = get_my_interval(id, below);
				if (l2 <= left and r2 >= right - 1)
					return ret_true;
			}
			const P above = x == right ? P(x, y + 1) : P(x + 1, y);
			if (points[id].contains(above)) {
				auto [l2, r2] = get_my_interval(id, above);
				if (l2 <= left + 1 and r2 >= right)
					return ret_true;
			}
			return ret_false;
		};
		const auto update_interval = [&](int id, int diag, int l, int r, bool inc_blocked = true) {
			auto [minimum, cnt_min] = tree[id][diag].query(l, r);
			if (minimum > 0)
				return;
			if (inc_blocked) {
				blocked_points += cnt_min;
			}
			tree[id][diag].update(l, r, 1);
			revert_tree.emplace_back(id, diag, l, r);
		};
		const auto mark_as_square = [&](P p) {
			if (is_part_of_square(0, p))
				return;
			add_square(0, p);
			add_square(1, rev(p));
			const auto [x, y] = p;
			const int diag = x + y;
			const int min_0 = tree[0][diag].query(x, x).first;
			const auto [x_rev, y_rev] = rev(p);
			const int diag_rev = x_rev + y_rev;
			const int min_1 = tree[1][diag_rev].query(x_rev, x_rev).first;
			if (min_0 == 0 and min_1 == 0) {
				++blocked_points;
			}
			if (min_0 == 0) {
				update_interval(0, diag, x, x, false);
			}
			if (min_1 == 0) {
				update_interval(1, diag_rev, x_rev, x_rev, false);
			}
		};
		const auto work = [&](int id, P p, const vector<int>& vec) {
			if (not points[id].contains(p))
				return false;
			bool ret = false;
			for (bool to_right : vec) {
				auto [found, interval] = get_good_interval(id, p, to_right);
				if (found) {
					auto [l, r] = interval;
					update_interval(id, get_diag(p), l, r);
					ret = true;
				}
			}
			return ret;
		};

		const int previous_blocked_points = blocked_points;

		for (auto p : v) {
			REP(id, 2) {
				points[id].emplace(p);
				add_point_to_intervals(id, p);
				p = rev(p);
			}
			{
				const auto [x, y] = p;
				for (auto [dx, dy] : {pair<int, int>{1, 1}, {1, -1}, {-1, 1}, {-1, -1}}) {
					P p1 = {x + dx, y};
					P p2 = {x, y + dy};
					P p3 = {x + dx, y + dy};
					if (points[0].contains(p1) and points[0].contains(p2) and points[0].contains(p3)) {
						mark_as_square(p);
						mark_as_square(p1);
						mark_as_square(p2);
						mark_as_square(p3);
					}
				}
			}
			REP(id, 2) {
				const auto [x, y] = p;
				work(id, P(x + 1, y + 1), {true, false});

				{
					auto val = work(id, P(x, y + 1), {false});
					if (val)
						work(id, P(x + 1, y), {true});
					else
						work(id, P(x + 1, y), {true, false});
				}

				{
					auto val = work(id, P(x - 1, y + 1), {false});
					if (val)
						work(id, P(x, y), {true});
					else
						work(id, P(x, y), {true, false});
					work(id, P(x + 1, y - 1), {true});
				}

				{
					auto val = work(id, P(x - 1, y), {false});
					if (val)
						work(id, P(x, y - 1), {true});
					else
						work(id, P(x, y - 1), {true, false});
				}

				work(id, P(x - 1, y - 1), {true, false});

				p = rev(p);
			}
		}

		if (a == b) {
			const int answer = ssize(points[0]) - blocked_points;
			cout << answer << '\n';
		}
		else {
			const int middle = (a + b) / 2;
			self(self, w * 2, a, middle);
			self(self, w * 2 + 1, middle + 1, b);
		}

		blocked_points = previous_blocked_points;
		reverse(revert_intervals.begin(), revert_intervals.end());
		for (auto p : v) {
			REP(id, 2) {
				points[id].erase(p);
				p = rev(p);
			}
		}
		for (auto [id, diag, x] : revert_squares) {
			squares[id][diag].erase(x);
		}
		for (auto [id, diag, i, add] : revert_intervals) {
			if (add) {
				intervals[id][diag].emplace(i);
			}
			else {
				intervals[id][diag].erase(i);
			}
		}
		for (auto [id, diag, l, r] : revert_tree) {
			tree[id][diag].update(l, r, -1);
		}
	};
	dfs(dfs, 1, 0, sz_dfs - 1);
}

int main() {
	cin.tie(0)->sync_with_stdio(0);

	const int limit_nodes = 1e7;
	nodes.reserve(limit_nodes);

	solve();
}