Problem: Example

Input

2 10 6
4 4 E
6 4 W


Output

2

Solution (in CPP):

Solution:
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <cfloat>
#include <ctime>
#include <cassert>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <numeric>
#include <list>
#include <iomanip>
#include <fstream>
#include <bitset>

using namespace std;

#define foreach(it, c) for (__typeof__((c).begin()) it=(c).begin(); it != (c).end(); ++it)
template <typename T> void print_container(ostream& os, const T& c) { const char* _s = " "; if (!c.empty()) { __typeof__(c.begin()) last = --c.end(); foreach (it, c) { os << *it; if (it != last) os << _s; } } }
template <typename T> ostream& operator<<(ostream& os, const vector<T>& c) { print_container(os, c); return os; }
template <typename T> ostream& operator<<(ostream& os, const set<T>& c) { print_container(os, c); return os; }
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& c) { print_container(os, c); return os; }
template <typename T> ostream& operator<<(ostream& os, const deque<T>& c) { print_container(os, c); return os; }
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& c) { print_container(os, c); return os; }
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) { os << "(" << p.first << ", " << p.second << ")"; return os; }

template <typename T> void print(T a, int n, const string& split = " ") { for (int i = 0; i < n; i++) { cout << a[i]; if (i + 1 != n) cout << split; } cout << endl; }
template <typename T> void print2d(T a, int w, int h, int width = -1, int br = 0) { for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) { if (width != -1) cout.width(width); cout << a[i][j] << ' '; } cout << endl; } while (br--) cout << endl; }
template <typename T> void input(T& a, int n) { for (int i = 0; i < n; ++i) cin >> a[i]; }
#define dump(v) (cout << #v << ": " << v << endl)

#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define erep(i, n) for (int i = 0; i <= (int)(n); ++i)
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define clr(a, x) memset(a, x, sizeof(a))
#define sz(a) ((int)(a).size())
#define mp(a, b) make_pair(a, b)
#define ten(n) ((long long)(1e##n))

template <typename T, typename U> void upmin(T& a, const U& b) { a = min<T>(a, b); }
template <typename T, typename U> void upmax(T& a, const U& b) { a = max<T>(a, b); }
template <typename T> void uniq(T& a) { sort(a.begin(), a.end()); a.erase(unique(a.begin(), a.end()), a.end()); }
template <class T> string to_s(const T& a) { ostringstream os; os << a; return os.str(); }
template <class T> T to_T(const string& s) { istringstream is(s); T res; is >> res; return res; }
void fast_io() { cin.tie(0); ios::sync_with_stdio(false); }
bool in_rect(int x, int y, int w, int h) { return 0 <= x && x < w && 0 <= y && y < h; }

typedef long long ll;
typedef pair<int, int> pint;

const int dx[] = { 0, 1, 0, -1 };
const int dy[] = { 1, 0, -1, 0 };


int main()
{
    int n, w, h;
    cin >> n >> w >> h;
    const int peri = 2 * (w + h);

    auto index = [&](int x, int y, int dx, int dy)
    {
        if (dx < 0)
        {
            int ty = y + x * dy;
            if (0 <= ty && ty <= h)
                return (w + h + w + (h - ty)) % peri;
        }
        else
        {
            int ty = y + (w - x) * dy;
            if (0 <= ty && ty <= h)
                return (w + ty) % peri;
        }

        if (dy < 0)
        {
            int tx = x + y * dx;
            if (0 <= tx && tx <= w)
                return tx % peri;
        }
        else
        {
            int tx = x + (h - y) * dx;
            if (0 <= tx && tx <= w)
                return (w + h + (w - tx)) % peri;
        }
        assert(false);
    };

    vector<pint> seg;
    rep(i, n)
    {
        int x, y;
        char d;
        cin >> x >> y >> d;

        switch (d)
        {
            case 'E':
                seg.push_back(pint(index(x, y, +1, -1), index(x, y, +1, +1)));
                break;
            case 'N':
                seg.push_back(pint(index(x, y, +1, +1), index(x, y, -1, +1)));
                break;
            case 'W':
                seg.push_back(pint(index(x, y, -1, +1), index(x, y, -1, -1)));
                break;
            case 'S':
                seg.push_back(pint(index(x, y, -1, -1), index(x, y, +1, -1)));
                break;
            default:
                assert(false);
        }
    }

    vector<int> split;
    for (auto& it : seg)
    {
        split.push_back(it.first % peri);
        split.push_back(it.second % peri);
    }
    uniq(split);

//     dump(peri);
//     dump(seg);

    int res = 1919810;
    for (int x : split)
    {
//         dump(x);
        vector<pint> nseg;
        for (auto& it : seg)
        {
            auto s = it;

            if (s.first > s.second)
                s.second += peri;

            if (s.second < x)
            {
                s.first += peri;
                s.second += peri;
            }

            if (s.first <= x && x <= s.second || s.first <= x + peri && x + peri <= s.second)
                continue;

            assert(s.first <= s.second);
//             printf("(%3d, %3d) -> (%3d, %3d)\n", it.first, it.second, s.first, s.second);
            nseg.push_back(s);
        }
        sort(all(nseg), [](const pint& a, const pint& b){ return a.second < b.second; });

//         if (x == 22)
//             dump(nseg);

//         dump(x);
//         dump(nseg);
//         cout << endl;

        int clocks = 1;
        for (int i = 0; i < nseg.size(); )
        {
            ++clocks;

            int r = nseg[i].second;
            while (i < nseg.size() && nseg[i].first <= r)
                ++i;
        }
        upmin(res, clocks);
    }
    cout << res << endl;
}