#include "rainbow.h"
#include <algorithm>
#include <set>
#include <utility>
#include <vector>
const int N = 200005;
const int T = N * 400;
int size = N << 1, val[T], left[T];
std::vector<int> edge_h[N], edge_v[N], pt_h[N], pt_v[N];
void update_y(int ind, int i, int d, int tl = 0, int tr = N)
{
if (tr - tl != 1) {
if (!left[ind]) {
left[ind] = size;
size += 2;
}
int m = tl + tr >> 1;
if (i < m) update_y(left[ind], i, d, tl, m);
else update_y(left[ind] | 1, i, d, m, tr);
}
val[ind] += d;
}
void update_x(int x, int y, int d)
{
for (x += N; x > 0; x >>= 1) update_y(x, y, d);
}
int query_y(int ind, int l, int r, int tl = 0, int tr = N)
{
if (tl >= r || tr <= l) return 0;
if (tl >= l && tr <= r) return val[ind];
if (!left[ind]) return 0;
int m = tl + tr >> 1;
return query_y(left[ind], l, r, tl, m) + query_y(left[ind] | 1, l, r, m, tr);
}
int query_x(int x1, int x2, int y1, int y2)
{
int ans = 0;
for (x1 += N, x2 += N; x1 < x2; x1 >>= 1, x2 >>= 1) {
if (x1 & 1) ans += query_y(x1++, y1, y2);
if (x2 & 1) ans += query_y(--x2, y1, y2);
}
return ans;
}
void add(int x, int y, bool type)
{
if (type) edge_h[x].push_back(y);
else edge_v[y].push_back(x);
update_x(x, y, 1);
}
void add_point(int x, int y)
{
pt_h[x].push_back(y);
pt_v[y].push_back(x);
update_x(x, y, -1);
}
int start_x, start_y;
void init(int r, int c, int sr, int sc, int m, char *s)
{
--sr;
--sc;
start_x = sr;
start_y = sc;
std::set<std::pair<int, int> > u;
for (int i = 0; i <= m; ++i) {
if (!u.count(std::make_pair(sr, sc))) {
u.insert(std::make_pair(sr, sc));
update_x(sr, sc, -1);
bool u_left = u.count(std::make_pair(sr, sc - 1)), u_up = u.count(std::make_pair(sr - 1, sc)), u_right = u.count(std::make_pair(sr, sc + 1)), u_down = u.count(std::make_pair(sr + 1, sc));
if (!u_left) {
add(sr, sc, 0);
if (!u_up && !u.count(std::make_pair(sr - 1, sc - 1))) add_point(sr, sc);
}
if (!u_up) {
add(sr, sc, 1);
if (!u_right && !u.count(std::make_pair(sr - 1, sc + 1))) add_point(sr, sc + 1);
}
if (!u_right) {
add(sr, sc + 1, 0);
if (!u_down && !u.count(std::make_pair(sr + 1, sc + 1))) add_point(sr + 1, sc + 1);
}
if (!u_down) {
add(sr + 1, sc, 1);
if (!u_left && !u.count(std::make_pair(sr + 1, sc - 1))) add_point(sr + 1, sc);
}
}
if (i < m) {
if (s[i] == 'N') --sr;
else if (s[i] == 'S') ++sr;
else if (s[i] == 'W') --sc;
else ++sc;
}
}
for (int i = 0; i < N; ++i) {
std::sort(edge_h[i].begin(), edge_h[i].end());
std::sort(edge_v[i].begin(), edge_v[i].end());
std::sort(pt_h[i].begin(), pt_h[i].end());
std::sort(pt_v[i].begin(), pt_v[i].end());
}
}
inline int count(std::vector<int> &v, int l, int r)
{
return std::lower_bound(v.begin(), v.end(), r) - std::lower_bound(v.begin(), v.end(), l);
}
int colour(int ar, int ac, int br, int bc)
{
--ar;
--ac;
return query_x(ar, br, ac, bc) - count(edge_h[ar], ac, bc) - count(edge_v[ac], ar, br) + count(pt_h[ar], ac, bc) + count(pt_v[ac], ar + 1, br) + 1 + (pt_h[ar].empty() && pt_h[br].empty() && pt_v[ac].empty() && pt_v[bc].empty() && start_x >= ar && start_x < br && start_y >= ac && start_y < bc);
}
