#include <bits/stdc++.h>
#include "rainbow.h"
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define ALL(v) (v).begin(), (v).end()
#define MASK(i) (1LL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
// mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng(1);
ll rngesus(ll l, ll r){return ((ull) rng()) % (r - l + 1) + l;}
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll LASTBIT(ll mask){return mask & (-mask);}
ll pop_cnt(ll mask){return __builtin_popcountll(mask);}
ll ctz(ll mask){return __builtin_ctzll(mask);}
ll clz(ll mask){return __builtin_clzll(mask);}
ll logOf(ll mask){return 63 - clz(mask);}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b){a = b; return true;}
return false;
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b){a = b; return true;}
return false;
}
template <class T>
void printArr(T& a, string separator = " ", string finish = "\n", ostream& out = cout){
for(auto i: a) out << i << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
struct PST{
struct Node{
int child[2];
int sum;
Node(){memset(child, -1, sizeof child); sum = 0;}
};
int L, R;
vector<Node> a;
vector<int> version;
void add_child(int &x){
x = a.size();
a.push_back(Node());
}
PST(int _l, int _r){
L = _l, R = _r;
a.push_back(Node());
version.push_back(0);
build_tree(L, R, 0);
}
void build_tree(int l, int r, int id){
if (l == r) return;
int mid = (l + r) >> 1;
add_child(a[id].child[0]); add_child(a[id].child[1]);
build_tree(l, mid, a[id].child[0]);
build_tree(mid + 1, r, a[id].child[1]);
}
void update(int i, int v, int l, int r, int id, int prev_id){
a[id] = a[prev_id];
a[id].sum += v;
if (l == r) return;
int mid = (l + r) >> 1;
if (i <= mid){
add_child(a[id].child[0]);
update(i, v, l, mid, a[id].child[0], a[prev_id].child[0]);
}
else{
add_child(a[id].child[1]);
update(i, v, mid + 1, r, a[id].child[1], a[prev_id].child[1]);
}
}
void update(int i, int v){
int prev = version.back();
version.push_back(0);
add_child(version.back());
update(i, v, L, R, version.back(), prev);
}
int get(int u, int v, int l, int r, int id){
if (u <= l && r <= v) return a[id].sum;
int mid = (l + r) >> 1;
int ans = 0;
if (u <= mid) ans += get(u, v, l, mid, a[id].child[0]);
if (v > mid) ans += get(u, v, mid + 1, r, a[id].child[1]);
return ans;
}
int get(int l, int r, int ver){
int id = version[ver];
return get(l, r, L, R, id);
}
int get_version(){return version.size();}
};
const int INF = 1e9 + 69;
const int N = 2e5 + 69;
int dx[] = {-1, 1, 0, 0};
int dy[] = {0, 0, -1, 1};
#define Point pair<int, int>
vector<Point> dragon, verti_edge, hori_edge, vertices;
int xL, xR, yL, yR;
int cur_face;
PST dragon_cnt(1, N);
vector<int> dragon_row;
void init(int n, int m, int sr, int sc, int k, char *S) {
Point coord = {sr, sc};
dragon.push_back(coord);
for(int i = 0; i<k; ++i){
if (S[i] == 'N') coord.first--;
else if (S[i] == 'S') coord.first++;
else if (S[i] == 'W') coord.second--;
else coord.second++;
dragon.push_back(coord);
}
remove_dup(dragon);
for(pair<int, int> i: dragon){
for(int d = 0; d < 4; ++d){
if (d <= 1) hori_edge.push_back({i.first - (d == 0), i.second});
else verti_edge.push_back({i.first, i.second - (d == 2)});
}
}
remove_dup(hori_edge); remove_dup(verti_edge);
for(pair<int, int> i: hori_edge) {
vertices.push_back({i.first, i.second-1});
vertices.push_back({i.first, i.second});
}
for(pair<int, int> i: verti_edge){
vertices.push_back({i.first-1, i.second});
vertices.push_back({i.first, i.second});
}
remove_dup(vertices);
dragon_row.push_back(0);
vector<vector<int>> sigma(N);
for(pair<int, int> i: dragon) sigma[i.first].push_back(i.second);
for(int i = 1; i<N; ++i){
for(int j: sigma[i]) dragon_cnt.update(j, 1);
dragon_row.push_back(dragon_cnt.get_version() - 1);
}
// cout << "Dragon: \n";
// for(pair<int, int> i: dragon) cout << i.first << " " << i.second << "\n";
// cout << "Horizontal Edge: \n";
// for(pair<int, int> i: hori_edge) cout << i.first << " " << i.second << "\n";
// cout << "Vertical Edge: \n";
// for(pair<int, int> i: verti_edge) cout << i.first << " " << i.second << "\n";
// cout << "Vertices: \n";
// for(pair<int, int> i: vertices) cout << i.first << " " << i.second << "\n";
cur_face = 2 + hori_edge.size() + verti_edge.size() - vertices.size() - dragon.size();
xL = yL = INF;
xR = yR = 0;
for(pair<int, int> i: dragon){
maximize(xR, i.first); maximize(yR, i.second);
minimize(xL, i.first); minimize(yL, i.second);
}
}
int colour(int ar, int ac, int br, int bc) {
if (ar < xL && ac < yL && br > xR && bc > yR) return cur_face;
int cnt = 0;
int v_cnt = ((br - ar) + (bc - ac)) * 2, e_cnt = v_cnt;
int block_cnt = dragon_cnt.get(ac, bc, dragon_row[br]) - dragon_cnt.get(ac, bc, dragon_row[ar - 1]);
// cout << "Block_cnt: " << block_cnt << "\n";
for(pair<int, int> i: vertices){
if (ar <= i.first && i.first < br && ac <= i.second && i.second < bc)
v_cnt++;
}
for(pair<int, int> i: hori_edge){
if (ac <= i.second && i.second <= bc && ar <= i.first && i.first < br)
e_cnt++;
}
for(pair<int, int> i: verti_edge){
if (ar <= i.first && i.first <= br && ac <= i.second && i.second < bc)
e_cnt++;
}
return 1 + e_cnt - v_cnt - block_cnt;
}
// int main(void){
// ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// freopen("input.inp", "r", stdin);
// int n, m, k; cin >> n >> m;
// int sr, sc; cin >> sr >> sc;
// cin >> k;
// string s; cin >> s;
// init(n, m, sr, sc, k, (char*) s.c_str());
// int q; cin >> q;
// while(q--) {
// int a, b, c, d; cin >> a >> b >> c >> d;
// cout << colour(a, b, c, d) << "\n";
// }
// return 0;
// }
