#include "rainbow.h"
#include <iostream>
#include <vector>
#include <algorithm>
#include <cassert>
#include <set>
using namespace std;
template <typename T>
void normalize(vector<T> &vec)
{
sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end());
}
struct SegmentTree2D
{
int nx;
vector<int> valx;
vector<vector<int>> valy, it;
int pos(vector<int> &vec, int x) { return int(upper_bound(vec.begin(), vec.end(), x) - vec.begin() - 1); }
void build(vector<pair<int, int>> vals)
{
valx.clear();
for (auto p : vals) valx.push_back(p.first);
normalize(valx);
nx = (int) valx.size();
valy.assign(nx * 2, vector<int>(0));
it.resize(nx * 2);
for (auto p : vals) {
for (int i = pos(valx, p.first) + nx; i >= 1; i >>= 1) valy[i].push_back(p.second);
}
for (int i = nx * 2 - 1; i >= 1; --i) {
normalize(valy[i]);
int ny = (int) valy[i].size();
it[i].assign(ny * 2, 0);
}
for (auto p : vals) {
for (int x = pos(valx, p.first) + nx; x >= 1; x >>= 1) {
int ny = (int) valy[x].size();
for (int y = pos(valy[x], p.second) + ny; y >= 1; y >>= 1) {
++it[x][y];
}
}
}
}
int get1d(int x, int ly, int ry)
{
int ans = 0, ny = (int) valy[x].size();
for (ly = pos(valy[x], ly - 1) + ny + 1, ry = pos(valy[x], ry) + ny + 1; ly < ry; ly >>= 1, ry >>= 1) {
if (ly & 1) ans += it[x][ly++];
if (ry & 1) ans += it[x][--ry];
}
return ans;
}
int get(int lx, int rx, int ly, int ry)
{
int ans = 0;
for (lx = pos(valx, lx - 1) + nx + 1, rx = pos(valx, rx) + nx + 1; lx < rx; lx >>= 1, rx >>= 1) {
if (lx & 1) ans += get1d(lx++, ly, ry);
if (rx & 1) ans += get1d(--rx, ly, ry);
}
return ans;
}
} hr, vt, sq, vx;
int minr, maxr, minc, maxc, fullans;
void init(int R, int C, int sr, int sc, int M, char *S)
{
vector<pair<int, int>> vxvec(M + 1);
vxvec[0] = make_pair(sr, sc);
minr = maxr = sr, minc = maxc = sc;
for (int i = 0; i < M; ++i) {
// cerr << S[i];
if (S[i] == 'N') --sr;
else if (S[i] == 'S') ++sr;
else if (S[i] == 'W') --sc;
else ++sc;
minr = min(minr, sr), maxr = max(maxr, sr);
minc = min(minc, sc), maxc = max(maxc, sc);
vxvec[i + 1] = make_pair(sr, sc);
}
// cerr << endl;
normalize(vxvec);
auto hrvec = vxvec, vtvec = vxvec, sqvec = vxvec;
for (auto p : vxvec) {
hrvec.emplace_back(p.first, p.second - 1);
vtvec.emplace_back(p.first - 1, p.second);
sqvec.emplace_back(p.first, p.second - 1);
sqvec.emplace_back(p.first - 1, p.second);
sqvec.emplace_back(p.first - 1, p.second - 1);
}
normalize(hrvec), normalize(vtvec), normalize(sqvec);
hr.build(hrvec), vt.build(vtvec), sq.build(sqvec), vx.build(vxvec);
set<pair<int, int>> vxset(vxvec.begin(), vxvec.end());
// for (auto p : vxvec) cerr << p.first << ' ' << p.second << endl; cout << " - " << endl;
fullans = 0;
for (auto p : sqvec) {
int cur = 0;
if (vxset.find(make_pair(p.first, p.second)) != vxset.end()) ++cur;
if (vxset.find(make_pair(p.first + 1, p.second)) != vxset.end()) ++cur;
if (vxset.find(make_pair(p.first, p.second + 1)) != vxset.end()) ++cur;
if (vxset.find(make_pair(p.first + 1, p.second + 1)) != vxset.end()) ++cur;
if (cur == 1) ++fullans;
if (cur == 3) --fullans;
// cerr << p.first << ' ' << p.second << ": " << cur << endl;
}
assert(fullans % 4 == 0);
assert(fullans <= 4);
fullans = 2 - fullans / 4;
// cerr << fullans << endl;
}
int colour(int ar, int ac, int br, int bc)
{
if (ar < minr && maxr < br && ac < minc && maxc < bc) return fullans;
int64_t hrcnt = 1ll * (br - ar + 1) * (bc - ac) - hr.get(ar, br, ac, bc - 1);
int64_t vtcnt = 1ll * (br - ar) * (bc - ac + 1) - vt.get(ar, br - 1, ac, bc);
int64_t sqcnt = 1ll * (br - ar) * (bc - ac) - sq.get(ar, br - 1, ac, bc - 1);
int64_t vxcnt = 1ll * (br - ar + 1) * (bc - ac + 1) - vx.get(ar, br, ac, bc);
// cerr << hrcnt << ' ' << vtcnt << ' ' << sqcnt << ' ' << vxcnt << endl;
return (int) (vxcnt + sqcnt - hrcnt - vtcnt);
}
