Problem:
Problem D: Futon

The sales department of Japanese Ancient Giant Corp. is visiting a hot spring resort for their
recreational trip. For deepening their friendships, they are staying in one large room of a
Japanese-style hotel called a ryokan.

In the ryokan, people sleep in Japanese-style beds called futons. They all have put their futons
on the floor just as they like. Now they are ready for sleeping but they have one concern: they
don’t like to go into their futons with their legs toward heads — this is regarded as a bad custom
in Japanese tradition. However, it is not obvious whether they can follow a good custom. You
are requested to write a program answering their question, as a talented programmer.

Here let's model the situation. The room is considered to be a grid on an xy-plane. As usual,
x-axis points toward right and y-axis points toward up. Each futon occupies two adjacent cells.
People put their pillows on either of the two cells. Their heads come to the pillows; their foots
come to the other cells. If the cell of some person's foot becomes adjacent to the cell of another
person's head, regardless their directions, then it is considered as a bad case. Otherwise people
are all right.

Input

The input is a sequence of datasets. Each dataset is given in the following format:

n

x1 y1 dir1

...

xn yn dirn

n is the number of futons (1 ≤ n ≤ 20,000); (xi, yi) denotes the coordinates of the left-bottom
corner of the i-th futon; diri is either 'x' or 'y' and denotes the direction of the i-th futon,
where 'x' means the futon is put horizontally and 'y' means vertically. All coordinate values are
non-negative integers not greater than 109 .

It is guaranteed that no two futons in the input overlap each other.

The input is terminated by a line with a single zero. This is not part of any dataset and thus
should not be processed.

Output

For each dataset, print "Yes" in a line if it is possible to avoid a bad case, or "No" otherwise.

Sample Input

4
0 0 x
2 0 x
0 1 x
2 1 x
4
1 0 x
0 1 x
2 1 x
1 2 x
4
0 0 x
2 0 y
0 1 y
1 2 x
0

Output for the Sample Input

Yes
No
Yes

Solution in C++ (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <numeric>
#include <vector>
#include <cassert>
#include <string>
#include <memory.h>
#include <queue>
#include <cstdio>
#include <cstdlib>
#include <set>
#include <map>
#include <cctype>
#include <iomanip>
#include <sstream>
#include <cctype>
#include <fstream>
#include <cmath>
using namespace std;

#define REP2(i, m, n) for(int i = (int)(m); i < (int)(n); i++)
#define REP(i, n) REP2(i, 0, n)
#define ALL(c) (c).begin(), (c).end()
#define ITER(c) __typeof((c).begin())
#define PB(e) push_back(e)
#define FOREACH(i, c) for(ITER(c) i = (c).begin(); i != (c).end(); ++i)
#define MP(a, b) make_pair(a, b)
#define PARITY(n) ((n) & 1)

typedef long long ll;
typedef pair<ll, ll> P;
const int INF = 1000 * 1000 * 1000 + 7;
const double EPS = 1e-10;

const int sz = 100010;
vector<int> G[sz];
vector<int> rG[sz];
int cmp[sz];
bool visit[sz];

void dfs(int v, vector<int> &vs){
  visit[v] = true;
  REP(i, G[v].size()) if(!visit[G[v][i]]) dfs(G[v][i], vs);
  vs.push_back(v);
}

void rdfs(int v, int k){
  visit[v] = true;
  cmp[v] = k;
  REP(i, rG[v].size()) if(!visit[rG[v][i]]) rdfs(rG[v][i], k);
}

int scc(int V){
  int k = 0;
  vector<int> vs;
  
  memset(visit, false, sizeof(visit));  
  REP(i, V) if(!visit[i]) dfs(i, vs);
  memset(visit, false, sizeof(visit));
  reverse(ALL(vs));
  REP(i, vs.size())if(!visit[vs[i]]) rdfs(vs[i], k++);
  return k;
}

void clear(){
  REP(i, sz){
    G[i].clear();
    rG[i].clear();
  }
}

void add_edge(int from, int to){
  G[from].push_back(to);
  rG[to].push_back(from);
}

int main(){
  int n;
  while(cin >> n && n){
    clear();
    char dir;
    vector<int> x(n * 2);
    vector<int> y(n * 2);
    vector<int> d(n * 2);
    
    REP(i, n){
      cin >> x[i] >> y[i] >> dir;
      x[i+n] = x[i];
      y[i+n] = y[i];
      
      if(dir == 'x'){
        x[i+n]++;
        d[i] = 0;
        d[i+n] = 2;
      }
      
      if(dir == 'y'){
        y[i+n]++;
        d[i] = 1;
        d[i+n] = 3;
      }
    }
    
    n *= 2;
    map<P, int> futon;    
    REP(i, n) futon[P(x[i], y[i])] = i;
    
    REP(i, n){
      int dx[4] = {1, 0, -1, 0};
      int dy[4] = {0, 1, 0, -1};     
      REP(j, 4){
        int xa = x[i] + dx[j];
        int ya = y[i] + dy[j];

        if(futon.find(P(xa, ya)) != futon.end()){
          int f = futon[P(xa, ya)];
          if(j == d[i]){
            add_edge(i, f + n);
            add_edge(i + n, f);
          }else{
            add_edge(i + n, f + n);
          }
        }
      }
    }

    bool possible = true;
    scc(2 * n);
    REP(i, n){
      possible &= cmp[i] != cmp[n + i];
    }
    cout << (possible ? "Yes" : "No") << endl;
  }
  return 0;
}