#include "rainbow.h"
#include <iostream>
#include <vector>
#include <cassert>
#include <algorithm>
#include <set>
namespace {
std::set<std::pair<int, int>> cells;
int minX, maxX, minY, maxY;
};
void init(int R, int C, int sr, int sc, int M, char *S) {
int x = sr, y = sc;
auto add = [&](int x, int y) {
cells.insert({x, y});
minX = std::min(minX, x);
maxX = std::max(maxX, x);
minY = std::min(minY, y);
maxY = std::max(maxY, y);
};
add(x, y);
for (int i = 0; i < M; i++) {
if (S[i] == 'N') {
x--;
} else if (S[i] == 'S') {
x++;
} else if (S[i] == 'W') {
y--;
} else {
y++;
}
add(x, y);
}
}
int colour(int x1, int y1, int x2, int y2) {
int V = 0;
for (int i = x1; i <= x2; i++) {
for (int j = y1; j <= y2; j++) {
if (!cells.count({i, j})) {
V++;
}
}
}
int E = 0;
for (int i = x1; i <= x2; i++) {
for (int j = y1; j < y2; j++) {
if (!cells.count({i, j}) && !cells.count({i, j + 1})) {
E++;
}
}
}
for (int i = x1; i < x2; i++) {
for (int j = y1; j <= y2; j++) {
if (!cells.count({i, j}) && !cells.count({i + 1, j})) {
E++;
}
}
}
int F = 0;
for (int i = x1; i < x2; i++) {
for (int j = y1; j < y2; j++) {
if (!cells.count({i, j}) && !cells.count({i, j + 1}) && !cells.count({i + 1, j}) && !cells.count({i + 1, j + 1})) {
F++;
}
}
}
F++;
if (x1 < minX && maxX < x2 && y1 < minY && maxY < y2) {
F++;
}
// std::cout << V << ' ' << E << ' ' << F << '\n';
// V + F = E + C + 1 (cred)
return V + F - E - 1;
}
