union_of_rectangles.cpp

//
// 長方形の和集合
//
// verified:
//   Yosupo Library Checker - Area of Union of Rectangles
//     https://judge.yosupo.jp/problem/area_of_union_of_rectangles
//
//   AtCoder ABC 449 F - Grid Clipping
//     https://atcoder.jp/contests/abc449/tasks/abc449_f
//


#include <bits/stdc++.h>
using namespace std;


// Lazy Segment Tree
template<class Monoid, class Action> struct LazySegmentTree {
    // various function types
    using FuncMonoid = function<Monoid(Monoid, Monoid)>;
    using FuncAction = function<Monoid(Action, Monoid)>;
    using FuncComposition = function<Action(Action, Action)>;

    // core member
    int N;
    FuncMonoid OP;
    FuncAction ACT;
    FuncComposition COMP;
    Monoid IDENTITY_MONOID;
    Action IDENTITY_ACTION;
    
    // inner data
    int log, offset;
    vector<Monoid> dat;
    vector<Action> lazy;
    
    // constructor
    LazySegmentTree() {}
    LazySegmentTree(const FuncMonoid op, const FuncAction act, const FuncComposition comp,
                    const Monoid &identity_monoid, const Action &identity_action) 
                    : OP(op), ACT(act), COMP(comp), 
                    IDENTITY_MONOID(identity_monoid), IDENTITY_ACTION(identity_action) {}
    LazySegmentTree(int n, const FuncMonoid op, const FuncAction act, const FuncComposition comp,
                    const Monoid &identity_monoid, const Action &identity_action) {
        init(n, op, act, comp, identity_monoid, identity_action);
    }
    LazySegmentTree(const vector<Monoid> &v,
                    const FuncMonoid op, const FuncAction act, const FuncComposition comp,
                    const Monoid &identity_monoid, const Action &identity_action) {
        init(v, op, act, comp, identity_monoid, identity_action);
    }
    void init(const FuncMonoid op, const FuncAction act, const FuncComposition comp,
              const Monoid &identity_monoid, const Action &identity_action) {
        OP = op, ACT = act, COMP = comp;
        IDENTITY_MONOID = identity_monoid, IDENTITY_ACTION = identity_action;      
    }
    void init(int n) {
        N = n, 
        log = 0, offset = 1;
        while (offset < N) ++log, offset <<= 1;
        dat.assign(offset * 2, IDENTITY_MONOID);
        lazy.assign(offset * 2, IDENTITY_ACTION);
    }
    void init(const vector<Monoid> &v) {
        init((int)v.size());
        build(v);
    }
    void init(int n, const FuncMonoid op, const FuncAction act, const FuncComposition comp,
              const Monoid &identity_monoid, const Action &identity_action) {
        init(op, act, comp, identity_monoid, identity_action);
        init(n);
    }
    void init(const vector<Monoid> &v,
              const FuncMonoid op, const FuncAction act, const FuncComposition comp,
              const Monoid &identity_monoid, const Action &identity_action) {
        init((int)v.size(), op, act, comp, identity_monoid, identity_action);
        build(v);
    }
    void build(const vector<Monoid> &v) {
        assert(N == (int)v.size());
        for (int i = 0; i < N; ++i) dat[i + offset] = v[i];
        for (int k = offset - 1; k > 0; --k) pull_dat(k);
    }
    int size() const {
        return N;
    }
    
    // basic functions for lazy segment tree
    void pull_dat(int k) {
        dat[k] = OP(dat[k * 2], dat[k * 2 + 1]);
    }
    void apply_lazy(int k, const Action &f) {
        dat[k] = ACT(f, dat[k]);
        if (k < offset) lazy[k] = COMP(f, lazy[k]);
    }
    void push_lazy(int k) {
        apply_lazy(k * 2, lazy[k]);
        apply_lazy(k * 2 + 1, lazy[k]);
        lazy[k] = IDENTITY_ACTION;
    }
    void pull_dat_deep(int k) {
        for (int h = 1; h <= log; ++h) pull_dat(k >> h);
    }
    void push_lazy_deep(int k) {
        for (int h = log; h >= 1; --h) push_lazy(k >> h);
    }
    
    // setter and getter, update A[i], i is 0-indexed, O(log N)
    void set(int i, const Monoid &v) {
        assert(0 <= i && i < N);
        int k = i + offset;
        push_lazy_deep(k);
        dat[k] = v;
        pull_dat_deep(k);
    }
    Monoid get(int i) {
        assert(0 <= i && i < N);
        int k = i + offset;
        push_lazy_deep(k);
        return dat[k];
    }
    Monoid operator [] (int i) {
        return get(i);
    }
    
    // apply f for index i
    void apply(int i, const Action &f) {
        assert(0 <= i && i < N);
        int k = i + offset;
        push_lazy_deep(k);
        dat[k] = ACT(f, dat[k]);
        pull_dat_deep(k);
    }
    // apply f for interval [l, r)
    void apply(int l, int r, const Action &f) {
        assert(0 <= l && l <= r && r <= N);
        if (l == r) return;
        l += offset, r += offset;
        for (int h = log; h >= 1; --h) {
            if (((l >> h) << h) != l) push_lazy(l >> h);
            if (((r >> h) << h) != r) push_lazy((r - 1) >> h);
        }
        int original_l = l, original_r = r;
        for (; l < r; l >>= 1, r >>= 1) {
            if (l & 1) apply_lazy(l++, f);
            if (r & 1) apply_lazy(--r, f);
        }
        l = original_l, r = original_r;
        for (int h = 1; h <= log; ++h) {
            if (((l >> h) << h) != l) pull_dat(l >> h);
            if (((r >> h) << h) != r) pull_dat((r - 1) >> h);
        }
    }
    
    // get prod of interval [l, r)
    Monoid prod(int l, int r) {
        assert(0 <= l && l <= r && r <= N);
        if (l == r) return IDENTITY_MONOID;
        l += offset, r += offset;
        for (int h = log; h >= 1; --h) {
            if (((l >> h) << h) != l) push_lazy(l >> h);
            if (((r >> h) << h) != r) push_lazy(r >> h);
        }
        Monoid val_left = IDENTITY_MONOID, val_right = IDENTITY_MONOID;
        for (; l < r; l >>= 1, r >>= 1) {
            if (l & 1) val_left = OP(val_left, dat[l++]);
            if (r & 1) val_right = OP(dat[--r], val_right);
        }
        return OP(val_left, val_right);
    }
    Monoid all_prod() {
        return dat[1];
    }
    
    // get max r that f(get(l, r)) = True (0-indexed), O(log N)
    // f(IDENTITY) need to be True
    int max_right(const function<bool(Monoid)> f, int l = 0) {
        if (l == N) return N;
        l += offset;
        push_lazy_deep(l);
        Monoid sum = IDENTITY_MONOID;
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(OP(sum, dat[l]))) {
                while (l < offset) {
                    push_lazy(l);
                    l = l * 2;
                    if (f(OP(sum, dat[l]))) {
                        sum = OP(sum, dat[l]);
                        ++l;
                    }
                }
                return l - offset;
            }
            sum = OP(sum, dat[l]);
            ++l;
        } while ((l & -l) != l);  // stop if l = 2^e
        return N;
    }

    // get min l that f(get(l, r)) = True (0-indexed), O(log N)
    // f(IDENTITY) need to be True
    int min_left(const function<bool(Monoid)> f, int r = -1) {
        if (r == 0) return 0;
        if (r == -1) r = N;
        r += offset;
        push_lazy_deep(r - 1);
        Monoid sum = IDENTITY_MONOID;
        do {
            --r;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(OP(dat[r], sum))) {
                while (r < offset) {
                    push_lazy(r);
                    r = r * 2 + 1;
                    if (f(OP(dat[r], sum))) {
                        sum = OP(dat[r], sum);
                        --r;
                    }
                }
                return r + 1 - offset;
            }
            sum = OP(dat[r], sum);
        } while ((r & -r) != r);
        return 0;
    }
    
    // debug stream
    friend ostream& operator << (ostream &s, LazySegmentTree seg) {
        for (int i = 0; i < (int)seg.size(); ++i) {
            s << seg[i];
            if (i != (int)seg.size() - 1) s << " ";
        }
        return s;
    }
    
    // dump
    void dump() {
        for (int i = 0; i <= log; ++i) {
            for (int j = (1 << i); j < (1 << (i + 1)); ++j) {
                cout << "{" << dat[j] << "," << lazy[j] << "} ";
            }
            cout << endl;
        }
    }
};

// Area of Union of Rectangles
template<class VAL> struct RectangleUnion {
    using FVAL = array<VAL, 4>;
    vector<FVAL> rects;
    vector<VAL> ys;

    // constructor
    RectangleUnion() {}
    RectangleUnion(const vector<FVAL> &r) {
        for (auto [lx, rx, ly, ry] : r) add_rect(lx, rx, ly, ry);
    }
    void add_rect(VAL lx, VAL rx, VAL ly, VAL ry) {
        assert(lx <= rx && ly <= ry);
        rects.emplace_back(FVAL{lx, rx, ly, ry});
        ys.emplace_back(ly), ys.emplace_back(ry);
    }

    // calc
    VAL solve() {
        if (rects.empty()) return VAL(0);
        sort(ys.begin(), ys.end());
        ys.erase(unique(ys.begin(), ys.end()), ys.end());
        int Y = (int)ys.size();
        vector<FVAL> events;
        const VAL IN = 1, OUT = -1, INF = numeric_limits<VAL>::max() / 2;
        for (auto [lx, rx, ly, ry] : rects) {
            int lyi = lower_bound(ys.begin(), ys.end(), ly) - ys.begin();
            int ryi = lower_bound(ys.begin(), ys.end(), ry) - ys.begin();
            events.emplace_back(FVAL{lx, lyi, ryi, IN});
            events.emplace_back(FVAL{rx, lyi, ryi, OUT});
        }
        sort(events.begin(), events.end());

        using Monoid = pair<VAL, VAL>;  // (min, num)
        auto op = [&](Monoid a, Monoid b) -> Monoid {
            if (a.first == b.first) return make_pair(a.first, a.second + b.second);
            else return min(a, b);
        };
        auto mapping = [&](VAL f, Monoid a) -> Monoid {
            return make_pair(a.first + f, a.second);
        };
        auto composition = [&](VAL g, VAL f) -> VAL { 
            return g + f;
        };
        VAL res = 0, width = ys.back() - ys[0];
        vector<Monoid> ini(Y - 1);
        for (int i = 0; i < Y - 1; i++) ini[i] = Monoid(0, ys[i + 1] - ys[i]);
        LazySegmentTree<Monoid, VAL> seg(ini, op, mapping, composition, Monoid(INF, 0), 0);
        for (int i = 0; i + 1 < events.size(); i++) {
            auto [x, ly, ry, inout] = events[i];
            seg.apply(ly, ry, inout);
            auto [mi, num] = seg.all_prod();
            res += (width - (mi == 0 ? num : 0)) * (events[i + 1][0] - x);
        }
        return res;
    }
};


//------------------------------//
// Examples
//------------------------------//

// Yosupo Library Checker - Area of Union of Rectangles
void Yosupo_Area_of_Union_of_Rectangles() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    int N;
    cin >> N;
    RectangleUnion<long long> ru;
    for (int i = 0; i < N; i++) {
        long long l, d, r, u;
        cin >> l >> d >> r >> u;
        ru.add_rect(l, r, d, u);
    }
    long long res = ru.solve();
    cout << res << endl;
}

// AtCoder ABC 449 F - Grid Clipping
void ABC_449_F() {
    long long H, W, h, w, N;
    cin >> H >> W >> h >> w >> N;
    RectangleUnion<long long> ru;
    for (int i = 0; i < N; i++) {
        long long R, C;
        cin >> R >> C;
        R--, C--;
        ru.add_rect(max(0LL, R-h+1), min(H-h+1, R+1), max(0LL, C-w+1), min(W-w+1, C+1));
    }
    long long black = ru.solve();
    long long res = (H - h + 1) * (W - w + 1) - black;
    cout << res << endl;
}


int main() {
    //Yosupo_Area_of_Union_of_Rectangles();
    ABC_449_F();
}