#include "rainbow.h"
#include <bits/stdc++.h>
using namespace std;
#define debug(x) cerr << #x << " = " << x << '\n';
#define BP() cerr << "OK!\n";
#define PR(A, n) {cerr << #A << " = "; for (int _=1; _<=n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define PR0(A, n) {cerr << #A << " = "; for (int _=0; _<n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define FILE_NAME "data"
const int X[] = {1, 0, -1, 0};
const int Y[] = {0, 1, 0, -1};
const int INF = 1e9;
struct fenwick_tree_2D {
int m, n;
vector<vector<int> > bit;
void init(int _m, int _n) {
m = _m;
n = _n;
bit.resize(m+1);
for (int i=0; i<=m; ++i)
bit[i].resize(n+1);
}
void add(int x, int y) {
if (!bit[x][y])
++bit[x][y];
}
void process() {
for (int i=1; i<=m; ++i) {
for (int j=1; j<=n; ++j)
bit[i][j] += bit[i-1][j] + bit[i][j-1] - bit[i-1][j-1];
}
}
int get(int x1, int y1, int x2, int y2) {
if (x1>x2 || y1>y2)
return 0;
return bit[x2][y2] - bit[x2][y1-1] - bit[x1-1][y2] + bit[x1-1][y1-1];
}
};
int m, n, min_x, max_x, min_y, max_y;
vector<pair<int, int> > snake;
bool visited[52][52];
fenwick_tree_2D T1, T2, R, C;
void add(pair<int, int> p) {
T1.add(p.first, p.second);
for (int i=0; i<4; ++i) {
T2.add(p.first, p.second);
p.first += X[i];
p.second += Y[i];
}
C.add(p.first, p.second);
C.add(p.first, p.second+1);
R.add(p.first, p.second);
R.add(p.first+1, p.second);
}
void init(int _R, int _C, int sr, int sc, int M, char *S) {
m = _R;
n = _C;
max_x = max_y = -INF;
min_x = min_y = INF;
snake.resize(M+1);
snake[0] = {sr, sc};
for (int i=1; i<=M; ++i) {
snake[i] = snake[i-1];
if (S[i-1]=='N')
--snake[i].first;
else if (S[i-1]=='S')
++snake[i].first;
else if (S[i-1]=='W')
--snake[i].second;
else
++snake[i].second;
}
sort(snake.begin(), snake.end());
snake.resize(unique(snake.begin(), snake.end()) - snake.begin());
if (1LL*m*n<=1000000) {
T1.init(m+1, n+1);
T2.init(m+1, n+1);
R.init(m+1, n+1);
C.init(m+1, n+1);
}
for (auto p : snake) {
min_x = min(min_x, p.first);
max_x = max(max_x, p.first);
min_y = min(min_y, p.second);
max_y = max(max_y, p.second);
if (1LL*m*n<=1000000)
add(p);
}
if (1LL*m*n<=1000000) {
T1.process();
T2.process();
R.process();
C.process();
}
}
int subtask3(int x1, int y1, int x2, int y2) {
set<pair<int, int> > v;
set<pair<pair<int, int>, pair<int, int> > > e;
int res = 0;
for (int i=x1; i<=x2+1; ++i) {
v.insert({i, y1});
v.insert({i, y2+1});
if (i<=x2) {
pair<int, int> tmp1(i, y1), tmp2(i+1, y1);
e.insert({min(tmp1, tmp2), max(tmp1, tmp2)});
pair<int, int> tmp3(i, y2+1), tmp4(i+1, y2+1);
e.insert({min(tmp3, tmp4), max(tmp3, tmp4)});
}
}
for (int i=y1; i<=y2+1; ++i) {
v.insert({x1, i});
v.insert({x2+1, i});
if (i<=y2) {
pair<int, int> tmp1(x1, i), tmp2(x1, i+1);
e.insert({min(tmp1, tmp2), max(tmp1, tmp2)});
pair<int, int> tmp3(x2+1, i), tmp4(x2+1, i+1);
e.insert({min(tmp3, tmp4), max(tmp3, tmp4)});
}
}
for (auto p : snake) {
if (x1<=p.first && p.first<=x2 && y1<=p.second && p.second<=y2) {
--res;
for (int i=0; i<4; ++i) {
v.insert(p);
pair<int, int> tmp = p;
p.first += X[i];
p.second += Y[i];
e.insert({min(p, tmp), max(p, tmp)});
}
}
}
// debug(v.size());
// debug(e.size());
res += (int)e.size() - (int)v.size() + 1;
if (x1<min_x && max_x<x2 && y1<min_y && max_y<y2)
++res;
return res;
}
int colour(int x1, int y1, int x2, int y2) {
if (1LL*m*n>1000000)
return subtask3(x1, y1, x2, y2);
int v = T2.get(x1+1, y1+1, x2, y2);
int e = R.get(x1+1, y1, x2, y2) + C.get(x1, y1+1, x2, y2);
// debug(R.get(x1+1, y1+1, x2, y2-1));
int res = e - v + 1;
if (x1<min_x && max_x<x2 && y1<min_y && max_y<y2)
++res;
res -= T1.get(x1, y1, x2, y2);
return res;
}
