#include "rainbow.h"
#include <bits/stdc++.h>
using namespace std;
using ii = pair<int, int>;
#define pb push_back
#define eb emplace_back
vector<int> row[200005], col[200005];
vector<ii> nodes, cells, horiz, vert;
int ptr;
struct node {
node *left, *right;
int S, E;
vector<int> val;
node(int _s, int _e, vector<ii> &vec) : S(_s), E(_e) {
if (S == E) {
while (ptr < (int)vec.size() && vec[ptr].first == S) {
val.pb(vec[ptr].second);
ptr++;
}
return;
}
int M = (S + E) / 2;
left = new node(S, M, vec);
right = new node(M + 1, E, vec);
merge(left->val.begin(), left->val.end(), right->val.begin(), right->val.end(), back_inserter(val));
}
int qry(int l, int r, int x, int y) {
if (l > E || r < S) {
return 0;
}
if (l <= S && E <= r) {
return upper_bound(val.begin(), val.end(), y) - lower_bound(val.begin(), val.end(), x);
}
return left->qry(l, r, x, y) + right->qry(l, r, x, y);
}
} *root_nodes, *root_cells, *root_horiz, *root_vert;
void init(int R, int C, int sr, int sc, int M, char *S) {
cells.eb(sr, sc);
for (int i = 0; i < M; i++) {
if (S[i] == 'N') {
sr--;
} else if (S[i] == 'S') {
sr++;
} else if (S[i] == 'E') {
sc++;
} else {
sc--;
}
cells.eb(sr, sc);
}
sort(cells.begin(), cells.end());
cells.erase(unique(cells.begin(), cells.end()), cells.end());
for (const auto &[r, c] : cells) {
//~ cout << "! " << r << ' ' << c << '\n';
nodes.eb(r, c);
nodes.eb(r + 1, c);
nodes.eb(r, c + 1);
nodes.eb(r + 1, c + 1);
horiz.eb(r, c);
horiz.eb(r + 1, c);
vert.eb(r, c);
vert.eb(r, c + 1);
}
for (auto *vec : {&nodes, &horiz, &vert}) {
sort(vec->begin(), vec->end());
vec->erase(unique(vec->begin(), vec->end()), vec->end());
}
//~ cout << "HERE" << endl;
for (const auto &[r, c] : nodes) {
//~ cout << r << ' ' << c << '\n';
row[r].pb(c);
col[c].pb(r);
}
for (int i = 1; i <= R; i++) {
sort(row[i].begin(), row[i].end());
}
for (int i = 1; i <= C; i++) {
sort(col[i].begin(), col[i].end());
}
root_nodes = new node(1, R, nodes);
ptr = 0;
root_cells = new node(1, R, cells);
ptr = 0;
root_horiz = new node(1, R, horiz);
ptr = 0;
root_vert = new node(1, R, vert);
//~ cout << "HERE" << endl;
}
int colour(int ar, int ac, int br, int bc) {
int V = (br - ar + 1) * 2 + (bc - ac + 1) * 2 - 4, E = V;
bool border = 0;
for (int tmp_r : {ar, br + 1}) {
auto it = lower_bound(row[tmp_r].begin(), row[tmp_r].end(), ac);
if (it != row[tmp_r].end() && *it <= bc + 1) {
border = 1;
}
}
for (int tmp_c : {ac, bc + 1}) {
auto it = lower_bound(col[tmp_c].begin(), col[tmp_c].end(), ar);
if (it != col[tmp_c].end() && *it <= br + 1) {
border = 1;
}
}
V += root_nodes->qry(ar + 1, br, ac + 1, bc);
//~ for (const auto &[r, c] : nodes) {
//~ if (ar + 1 <= r && r <= br && ac + 1 <= c && c <= bc) {
//~ V++;
//~ }
//~ }
if (!border) {
bool wraps = root_cells->qry(ar, br, ac, bc);
//~ for (const auto &[r, c] : cells) {
//~ if (ar <= r && r <= br && ac <= c && c <= bc) {
//~ wraps = 1;
//~ }
//~ }
if (!wraps) {
return 1;
}
V = nodes.size();
E = horiz.size() + vert.size();
int F = 2 - (V - E), water_F = cells.size();
return F - water_F;
}
E += root_horiz->qry(ar + 1, br, ac, bc);
//~ for (const auto &[r, c] : horiz) {
//~ if (ar + 1 <= r && r <= br && ac <= c && c <= bc) {
//~ E++;
//~ }
//~ }
E += root_vert->qry(ar, br, ac + 1, bc);
//~ for (const auto &[r, c] : vert) {
//~ if (ar <= r && r <= br && ac + 1 <= c && c <= bc) {
//~ E++;
//~ }
//~ }
int F = 2 - (V - E), water_F = root_cells->qry(ar, br, ac, bc);
//~ for (const auto &[r, c] : cells) {
//~ if (ar <= r && r <= br && ac <= c && c <= bc) {
//~ water_F++;
//~ }
//~ }
return F - water_F - 1;
}
