#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;
int root=0;
struct QuadTree {
int seg1[MX];
int point1[MX];
int child1[MX][2];
int nxt1=0;
int seg2[MX];
int child2[MX][2];
int nxt2=1;
QuadTree() {
RE(i,MX) seg1[i]=0;
RE(i,MX) seg2[i]=-1;
RE(i,MX) RE(j,2) child1[i][j] = child2[i][j] = -1;
}
void add1(int x, int l, int r, int& p) {
if(p == -1) p = nxt1++;
seg1[p]++;
if(l == r) return;
int m = (l+r)/2;
if(seg1[p] == 1) {
point1[p] = x;
return;
}
if(point1[p] != -1) {
int y = point1[p];
if(y <= m) add1(y, l , m, child1[p][0]);
else add1(y, m+1, r, child1[p][1]);
point1[p] = -1;
}
if(x <= m) add1(x, l , m, child1[p][0]);
else add1(x, m+1, r, child1[p][1]);
}
void add(int x, int y, int l=0, int r=N-1, int& p=root) {
if(p == -1) p = nxt2++;
add1(y, 0, N-1, seg2[p]);
if(l == r) return;
int m = (l+r)/2;
if(x <= m) add(x, y, l , m, child2[p][0]);
else add(x, y, m+1, r, child2[p][1]);
}
int get1(int i, int j, int l, int r, int p) {
if(j < l || i > r) return 0;
if(p == -1) return 0;
if(i <= l && j >= r) return seg1[p];
if(point1[p] != -1) return i <= point1[p] && point1[p] <= j;
int m = (l+r)/2;
int a = get1(i, j, l , m, child1[p][0]);
int b = get1(i, j, m+1, r, child1[p][1]);
return a+b;
}
int get(int i, int j, int x, int y, int l=0, int r=N-1, int p=root) {
if(j < l || i > r) return 0;
if(p == -1) return 0;
if(i <= l && j >= r) return get1(x,y,0,N-1,seg2[p]);
int m = (l+r)/2;
int a = get(i, j, x, y, l , m, child2[p][0]);
int b = get(i, j, x, y, m+1, r, child2[p][1]);
return a+b;
}
} 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;
}
