#include "rainbow.h"
#include <bits/stdc++.h>
using namespace std;
// macros
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef pair<ll, ll> lll;
typedef tuple<int, int, int> iii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<ll> vll;
typedef vector<lll> vlll;
#define REP(a,b,c) for(int a=int(b); a<int(c); a++)
#define RE(a,c) REP(a,0,c)
#define RE1(a,c) REP(a,1,c+1)
#define REI(a,b,c) REP(a,b,c+1)
#define REV(a,b,c) for(int a=int(c-1); a>=int(b); a--)
#define FOR(a,b) for(auto& a : b)
#define all(a) a.begin(), a.end()
#define INF 1e9
#define EPS 1e-9
#define pb push_back
#define popb pop_back
#define fi first
#define se second
#define sz size()
const int MX = (1<<22);
const int N = (1<<19);
int R, C, sr, sc, m;
set<ii> blue;
set<ii> points;
set<ii> edges;
int minR, maxR, minC, maxC;
struct QuadTree {
int pointX[MX][5];
int pointY[MX][5];
int tot[MX];
int child[MX][4];
int nxt=1;
QuadTree() {
RE(i,N) tot[i]=0;
RE(i,N) RE(j,4) child[i][j] = -1;
}
void add(int x, int y, int l=0, int r=N-1, int u=0, int d=N-1, int p=0) {
tot[p]++;
if(tot[p] <= 5) {
pointX[p][tot[p]-1] = x;
pointY[p][tot[p]-1] = y;
return;
}
if(l == r)
return;
int mh = (l+r)/2;
int mv = (u+d)/2;
int cd = 0;
if(x <= mh) cd += 1, r=mh;
else l=mh+1;
if(y <= mv) cd += 2, d=mv;
else u=mv+1;
if(child[p][cd] == -1) child[p][cd] = nxt++;
add(x,y,l,r,u,d,child[p][cd]);
}
int get(int a, int b, int x, int y, int l=0, int r=N-1, int u=0, int d=N-1, int p=0) {
if(p == -1) return 0;
if(b < l || a > r || y < u || x > d) return 0;
if(a <= l && b >= r && x <= u && y >= d) return tot[p];
int res = 0;
RE(i,min(5,tot[p]))
if(a <= pointX[p][i] && pointX[p][i] <= b && x <= pointY[p][i] && pointY[p][i] <= y)
res++;
if(tot[p] <= 5)
return res;
int mh = (l+r)/2;
int mv = (u+d)/2;
res += get(a,b,x,y, mh+1, r , mv+1, d , child[p][0]);
res += get(a,b,x,y, l , mh, mv+1, d , child[p][1]);
res += get(a,b,x,y, mh+1, r , u , mv, child[p][2]);
res += get(a,b,x,y, l , mh, u , mv, child[p][3]);
return res;
}
} blueCells, bluePoints, blueLandEdgesH, blueLandEdgesV;
void init(int _R, int _C, int _sr, int _sc, int M, char *S) {
R=_R; C=_C; sr=_sr; sc=_sc;
minR=maxR=sr;
minC=maxC=sc;
RE(i,M) {
blue.insert({sc,sr});
if(S[i] == 'N') sr--;
if(S[i] == 'S') sr++;
if(S[i] == 'E') sc++;
if(S[i] == 'W') sc--;
}
blue.insert({sc,sr});
FOR(p,blue) {
minR = min(minR, p.se);
minC = min(minC, p.fi);
maxR = max(maxR, p.se);
maxC = max(maxC, p.fi);
blueCells.add(p.fi,p.se);
points.insert({p.fi ,p.se });
points.insert({p.fi ,p.se+1});
points.insert({p.fi+1,p.se });
points.insert({p.fi+1,p.se+1});
if(!blue.count({p.fi-1,p.se })) blueLandEdgesV.add(p.fi , p.se );
blueLandEdgesV.add(p.fi+1, p.se );
if(!blue.count({p.fi ,p.se-1})) blueLandEdgesH.add(p.fi , p.se );
blueLandEdgesH.add(p.fi , p.se+1);
}
FOR(p,points)
bluePoints.add(p.fi,p.se);
}
int colour(int ar, int ac, int br, int bc) {
int blueCellsCnt = blueCells .get(ac ,bc,ar ,br);
int bluePointsCnt = bluePoints.get(ac+1,bc,ar+1,br);
int blueLandEdges = blueLandEdgesH.get(ac,bc,ar+1,br) + blueLandEdgesV.get(ac+1,bc,ar,br);
int W = bc - ac + 1;
int H = br - ar + 1;
int V = W*H - blueCellsCnt;
int F = (W-1)*(H-1) - bluePointsCnt + 1;
int E = (W-1)*H + (H-1)*W - blueLandEdges;
if(ar < minR && maxR < br && ac < minC && maxC < bc)
F++;
return V - E + F - 1;
}
