#include "rainbow.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef vector<int> vi;
typedef vector<pi> vpi;
#define mp make_pair
#define f first
#define s second
#define ins insert
#define pb push_back
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
void ckmin(int& a, int b){
a = min(a, b);
}
void ckmax(int& a, int b){
a = max(a, b);
}
vector<char> dchar = vector<char>{'S', 'E', 'N', 'W'};
vi dx = vi{1, 0, -1, 0};
vi dy = vi{0, 1, 0, -1};
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
struct hashFunc{
size_t operator()(pi a) const {
ll res = ll(a.f)*200005+ll(a.s);
ll BIG_RAND = 102923014203249LL;
return __builtin_bswap64((unsigned long long)(res)*BIG_RAND);
}
};
const int mx = 200005;
struct node{
ll val;
node* c[2];
node(){
val = 0;
c[0] = c[1] = NULL;
}
void pull(){
val = 0;
for(int i = 0; i < 2; i++){
if(c[i]){
val+=c[i]->val;
}
}
}
};
const int SZ = 262144;
node* build(int L = 0, int R = SZ-1){
node* a = new node();
if(L == R){
return a;
}
int M = (L+R)/2;
a->c[0] = build(L, M);
a->c[1] = build(M+1, R);
return a;
}
node* upd(node* cur, int pos, int L = 0, int R = SZ-1){
assert(cur);
node* res = new node();
*res = *cur;
if(L == R){
res->val++;
return res;
}
assert(cur->c[0]);
assert(cur->c[1]);
int M = (L+R)/2;
if(pos <= M){
res->c[0] = upd(cur->c[0], pos, L, M);
}
else{
res->c[1] = upd(cur->c[1], pos, M+1, R);
}
res->pull();
return res;
}
ll query(node* cur, int l, int r, int L = 0, int R = SZ-1){
if(r < L || R < l) return 0;
if(l <= L && R <= r){
return cur->val;
}
int M = (L+R)/2;
return query(cur->c[0], l, r, L, M)+query(cur->c[1], l, r, M+1, R);
}
struct Off2DBIT{
node* seg[mx];
vpi all_updates;
void update(int X, int Y){
all_updates.pb(mp(X, Y));
}
void initBT(){
// cout << "all_updates: " << "\n";
// for(const auto& u: all_updates){
// cout << u.f << " " << u.s << "\n";
// }
seg[0] = build();
for(auto &u: all_updates){
swap(u.s, u.f);
}
sort(all(all_updates));
int cur_ind = 0;
for(int i = 1; i < mx; i++){
seg[i] = seg[i-1];
while(cur_ind < sz(all_updates)){
assert(all_updates[cur_ind].f >= i);
if(all_updates[cur_ind].f > i) break;
seg[i] = upd(seg[i], all_updates[cur_ind].s);
cur_ind++;
}
}
}
ll query(int xl, int yl, int xr, int yr){
return ::query(seg[yr], xl, xr)-::query(seg[yl-1], xl, xr);
}
// ll query(int xl, int yl, int xr, int yr){
// ll res = 0;
// for(auto& u: all_updates){
// if(xl <= u.f && u.f <= xr && yl <= u.s && u.s <= yr){
// res++;
// }
// }
// return res;
// }
};
Off2DBIT bits[2][2];
gp_hash_table<pi, null_type, hashFunc> rects[4];
int min_sr, max_sr, min_sc, max_sc;
void init(int R, int C, int sr, int sc, int M, char *S) {
min_sr = sr;
min_sc = sc;
max_sr = sr;
max_sc = sc;
for(int i = 0; i <= M; i++){
for(int i = 0; i <= 1; i++){
for(int j = 0; j <= 1; j++){
for(int xl = sr-i; xl <= sr; xl++){
for(int yl = sc-j; yl <= sc; yl++){
if(1 <= xl && 1 <= yl){
rects[2*i+j][mp(xl, yl)];
}
}
}
}
}
if(i < M){
for(int d = 0; d < 4; d++){
if(S[i] == dchar[d]){
sr+=dx[d];
sc+=dy[d];
break;
}
}
}
ckmin(min_sr, sr);
ckmin(min_sc, sc);
ckmax(max_sr, sr);
ckmax(max_sc, sc);
}
for(int i = 0; i <= 1; i++){
for(int j = 0; j <= 1; j++){
// cout << "i, j = " << i << ", " << j << "\n";
for(auto u: rects[2*i+j]){
// cout << "RECT " << i << " " << j << " " << u.f << " " << u.s << "\n";
bits[i][j].update(u.f, u.s);
}
}
}
for(int i = 0; i <= 1; i++){
for(int j = 0; j <= 1; j++){
bits[i][j].initBT();
}
}
}
int colour(int ar, int ac, int br, int bc) {
ll ans = 0;
if(ar+1 <= min_sr && max_sr+1 <= br && ac+1 <= min_sc && max_sc+1 <= bc){
ans++;
}
for(int i = 0; i <= 1; i++){
for(int j = 0; j <= 1; j++){
ll val = ll(br-i-ar+1)*ll(bc-j-ac+1);
// cout << "val: " << val << "\n";
// cout << "querying " << i << " " << j << "\n";
val-=bits[i][j].query(ar, ac, br-i, bc-j);
if((i+j) % 2 == 0){
ans+=val;
}
else{
ans-=val;
}
// cout << i << " " << j << " " << val << "\n";
}
}
return (int)(ans);
}
