#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <cassert>
//#include <utility>
//#include <memory>
//#include <functional>
//#include <deque>
//#include <cctype>
//#include <ctime>
//#include <numeric>
//#include <list>
//#include <iomanip>

//#if __cplusplus >= 201103L
//#include <array>
//#include <tuple>
//#include <initializer_list>
//#include <forward_list>
//
//#define cauto const auto&
//#else

//#endif

using namespace std;


typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()){
    v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t){
    stringstream ss;
    ss << f;
    ss >> t;
}

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define reep(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) reep((i),0,(n))
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define F first
#define S second
#define mkp make_pair
#define RALL(v) (v).rbegin(),(v).rend()
#define DEBUG
#ifdef DEBUG
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#else
#define dump(x) 
#define debug(x) 
#endif

#define MOD 1000000007LL
#define EPS 1e-8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
#define maxs(x,y) x=max(x,y)
#define mins(x,y) x=min(x,y)

void mainmain(){
	int n,h,w;
	cin>>n>>w>>h;
	vector<pii> a(n),b(n);
	int mod=2*(h+w);
	rep(i,n){
		int x,y;
		cin>>x>>y;
		char c;
		cin>>c;
		if(c=='N'){
			a[i]=pii(w-x,h-y);
			b[i]=pii(h+w+h+x,h-y);
		}
		if(c=='W'){
			a[i]=pii(w+h-y,x);
			b[i]=pii(h+w+y,x);
		}
		if(c=='S'){
			a[i]=pii(w+h+x,y);
			b[i]=pii(h+w-x,y);
		}
		if(c=='E'){
			a[i]=pii(w+h+w+y,w-x);
			b[i]=pii(h-y,w-x);
		}
		a[i]=pii(a[i].F-a[i].S,a[i].F+a[i].S);
		b[i]=pii(b[i].F-b[i].S,b[i].F+b[i].S);
		a[i]=pii((a[i].F+mod)%mod,(a[i].S+mod)%mod);
		b[i]=pii((b[i].F+mod)%mod,(b[i].S+mod)%mod);
	}
	int ans=INF;
	rep(o,2){
		rep(i,n){
			vector<pii> tmp=(o?a:b);
			rep(j,n){
				int t=(i+j)%n;
				tmp[j]=pii(a[t].F-a[i].F,a[t].S-a[i].F);
				tmp[j]=pii((tmp[j].F+mod)%mod,(tmp[j].S+mod)%mod);
			}
			vector<bool> used(n);
			used[0]=true;
			reep(j,1,n){
				if(tmp[j].F>tmp[j].S) used[j]=true;
				if(tmp[j].F==0) used[j]=true;
			}
			vector<pii> v;
			rep(j,n){
				if(used[j]) continue;
				v.PB(pii(tmp[j].F,-j));
				v.PB(pii(tmp[j].S,j));
			}
			sort(ALL(v));
			queue<int> q;
			int tans=1;
			rep(i,v.size()){
				if(v[i].S<0){
					q.push(-v[i].S);
				}
				else{
					if(used[v[i].S]) continue;
					used[v[i].S]=true;
					tans++;
					while(q.size()){
						used[q.front()]=true;
						q.pop();
					}
				}
			}
			mins(ans,tans);
		}
	}
	cout<<ans<<endl;
}


signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout<<fixed<<setprecision(20);
    mainmain();
}
### Prompt

Please provide a CPP coded solution to the problem described below:

Example

Input

2 10 6
4 4 E
6 4 W


Output

2

### Response

```cpp
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <cassert>
//#include <utility>
//#include <memory>
//#include <functional>
//#include <deque>
//#include <cctype>
//#include <ctime>
//#include <numeric>
//#include <list>
//#include <iomanip>

//#if __cplusplus >= 201103L
//#include <array>
//#include <tuple>
//#include <initializer_list>
//#include <forward_list>
//
//#define cauto const auto&
//#else

//#endif

using namespace std;


typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()){
    v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t){
    stringstream ss;
    ss << f;
    ss >> t;
}

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define reep(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) reep((i),0,(n))
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define F first
#define S second
#define mkp make_pair
#define RALL(v) (v).rbegin(),(v).rend()
#define DEBUG
#ifdef DEBUG
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#else
#define dump(x) 
#define debug(x) 
#endif

#define MOD 1000000007LL
#define EPS 1e-8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
#define maxs(x,y) x=max(x,y)
#define mins(x,y) x=min(x,y)

void mainmain(){
	int n,h,w;
	cin>>n>>w>>h;
	vector<pii> a(n),b(n);
	int mod=2*(h+w);
	rep(i,n){
		int x,y;
		cin>>x>>y;
		char c;
		cin>>c;
		if(c=='N'){
			a[i]=pii(w-x,h-y);
			b[i]=pii(h+w+h+x,h-y);
		}
		if(c=='W'){
			a[i]=pii(w+h-y,x);
			b[i]=pii(h+w+y,x);
		}
		if(c=='S'){
			a[i]=pii(w+h+x,y);
			b[i]=pii(h+w-x,y);
		}
		if(c=='E'){
			a[i]=pii(w+h+w+y,w-x);
			b[i]=pii(h-y,w-x);
		}
		a[i]=pii(a[i].F-a[i].S,a[i].F+a[i].S);
		b[i]=pii(b[i].F-b[i].S,b[i].F+b[i].S);
		a[i]=pii((a[i].F+mod)%mod,(a[i].S+mod)%mod);
		b[i]=pii((b[i].F+mod)%mod,(b[i].S+mod)%mod);
	}
	int ans=INF;
	rep(o,2){
		rep(i,n){
			vector<pii> tmp=(o?a:b);
			rep(j,n){
				int t=(i+j)%n;
				tmp[j]=pii(a[t].F-a[i].F,a[t].S-a[i].F);
				tmp[j]=pii((tmp[j].F+mod)%mod,(tmp[j].S+mod)%mod);
			}
			vector<bool> used(n);
			used[0]=true;
			reep(j,1,n){
				if(tmp[j].F>tmp[j].S) used[j]=true;
				if(tmp[j].F==0) used[j]=true;
			}
			vector<pii> v;
			rep(j,n){
				if(used[j]) continue;
				v.PB(pii(tmp[j].F,-j));
				v.PB(pii(tmp[j].S,j));
			}
			sort(ALL(v));
			queue<int> q;
			int tans=1;
			rep(i,v.size()){
				if(v[i].S<0){
					q.push(-v[i].S);
				}
				else{
					if(used[v[i].S]) continue;
					used[v[i].S]=true;
					tans++;
					while(q.size()){
						used[q.front()]=true;
						q.pop();
					}
				}
			}
			mins(ans,tans);
		}
	}
	cout<<ans<<endl;
}


signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout<<fixed<<setprecision(20);
    mainmain();
}
```