/* be name khoda */
// #define long_enable
#include <iostream>
#include <algorithm>
#include <cstring>
#include <numeric>
#include <vector>
#include <fstream>
#include <set>
#include <map>
using namespace std;
#ifdef long_enable
typedef long long int ll;
#else
typedef int ll;
#endif
typedef pair<ll, ll> pii;
typedef pair<pii, ll> ppi;
typedef pair<ll, pii> pip;
typedef vector<ll> vi;
typedef vector<pii> vpii;
#define forifrom(i, s, n) for (ll i = s; i < n; ++i)
#define forirto(i, n, e) for (ll i = (n) - 1; i >= e; --i)
#define fori(i, n) forifrom (i, 0, n)
#define forir(i, n) forirto (i, n, 0)
#define F first
#define S second
#define pb push_back
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define smin(a, b) a = min(a, (b))
#define smax(a, b) a = max(a, (b))
#define debug(x) cout << #x << " -> " << (x) << endl
#define debug2(x, y) cout << #x << ' ' << #y << " -> " << (x) << ' ' << (y) << endl
#define debug3(x, y, z) cout << #x << ' ' << #y << ' ' << #z << " -> " << (x) << ' ' << (y) << ' ' << (z) << endl
#define debug4(x, y, z, t) cout << #x << ' ' << #y << ' ' << #z << ' ' << #t << " -> " << (x) << ' ' << (y) << ' ' << (z) << ' ' << (t) << endl
#define debuga(x, n) cout << #x << " -> "; fori (i1_da, n) { cout << (x)[i1_da] << ' '; } cout << endl
#define debugaa(x, n, m) cout << #x << " ->\n"; fori (i1_daa, n) { fori (i2_daa, m) { cout << (x)[i1_daa][i2_daa] << ' '; } cout << '\n'; } cout << endl
const ll MOD = 1000000007;
const ll INF = 2000000000;
const long long BIG = 1446803456761533460LL;
#define XL (x << 1)
#define XR (XL | 1)
#define MD ((l + r) >> 1)
#define Add(a, b) a = ((a) + (b)) % MOD
#define Mul(a, b) a = (1LL * (a) * (b)) % MOD
// -----------------------------------------------------------------------
const ll maxn = 400000 + 10;
ll n, m, rmn = maxn, rmx = 0, cmn = maxn, cmx = 0;
pii d[256];
struct Segment {
vi seg[maxn * 2];
void add(ll r, ll c) {
seg[r + n].eb(c);
}
void build() {
fori (i, n) {
sort(all(seg[i + n]));
seg[i + n].resize(unique(all(seg[i + n])) - seg[i + n].begin());
}
forirto (i, n, 1) {
ll lsz = seg[i << 1].size(), rsz = seg[i << 1 ^ 1].size();
seg[i].resize(lsz + rsz);
merge(all(seg[i << 1]), all(seg[i << 1 ^ 1]), seg[i].begin());
}
}
inline ll count(vi &ar, ll l, ll r) {
return lower_bound(all(ar), r) - lower_bound(all(ar), l);
}
ll get(ll l1, ll r1, ll l2, ll r2) {
ll s = 0;
for (l1 += n, r1 += n; l1 < r1; l1 >>= 1, r1 >>= 1) {
if (l1 & 1) s += count(seg[l1], l2, r2), ++l1;
if (r1 & 1) --r1, s += count(seg[r1], l2, r2);
}
return s;
}
} verts, edgesV, edgesH, faces;
void move(ll r, ll c) {
smin(rmn, r), smax(rmx, r);
smin(cmn, c), smax(cmx, c);
faces.add(r, c);
fori (i, 4) verts.add(r + (i & 1), c + (i >> 1));
fori (i, 2) edgesV.add(r, c + i), edgesH.add(r + i, c);
}
void init(ll Ri, ll Ci, ll sr, ll sc, ll M, char *P) {
d['N'] = {-1, 0};
d['S'] = {1, 0};
d['W'] = {0, -1};
d['E'] = {0, 1};
n = Ri, m = Ci;
--sr, --sc;
move(sr, sc);
fori (i, M) {
sr += d[(ll) P[i]].F, sc += d[(ll) P[i]].S;
move(sr, sc);
}
verts.build();
edgesV.build();
edgesH.build();
faces.build();
}
ll colour(ll ar, ll ac, ll br, ll bc) {
--ar, --ac;
ll v = verts.get(ar + 1, br, ac + 1, bc);
ll e = edgesV.get(ar, br, ac + 1, bc) + edgesH.get(ar + 1, br, ac, bc);
ll river = faces.get(ar, br, ac, bc);
bool inside = (ar < rmn && rmx < br - 1 && ac < cmn && cmx < bc - 1);
ll c = 1 + inside;
ll f = c - v + e + 1 - 1; // c = v - e + (f - 1) (-1 was for big face)
ll ans = f - river;
return ans;
}
