Problem: 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.

Example

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

Yes
No
Yes

Solution (in CPP):

Solution:
#include <stdio.h>
#include <cmath>
#include <algorithm>
#include <cfloat>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <iostream>
#include <set>
#include <map>
#include <time.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;

#define NUM 20000
#define HEAD MOD
#define FOOT MOD+1

typedef pair<int,int> Point;

enum Type{
	TATE,
	YOKO,
};

struct Info{
	int row,col;
	Type dir;
};

struct Data{
	Data(int arg_row,int arg_col,int arg_index,int arg_which){
		row = arg_row;
		col = arg_col;
		index = arg_index;
		which = arg_which;
	}

	int row,col,index,which;
};


map<Point,int> MAP; //<座標、布団インデックス>
Info info[NUM];
vector<int> Group[NUM]; //隣接している布団のグループ

int near_row[4] = {1,0,0,-1},near_col[4] = {0,-1,1,0};
int diff_row[2][6] = {{2,1,1,0,0,-1},{-1,-1,0,0,1,1}},diff_col[2][6] = {{0,-1,1,-1,1,0},{0,1,-1,2,0,1}};

int N;
int boss[NUM],height[NUM];

//自分のボスのindexを取得しつつ、経路圧縮を行う関数
int get_boss(int id){
	if(boss[id] == id)return id; //自分が代表なら、自分の値を返す
	else{
		return boss[id] = get_boss(boss[id]); //代表でないなら、自分が所属する組織の代表を返しつつ、経路圧縮
	}
}

void unite(int x,int y){
	int boss_x = get_boss(x);
	int boss_y = get_boss(y);

	//既に同じグループなら何もしない
	if(boss_x == boss_y)return;

	//高さが高い方に吸収する
	if(height[x] > height[y]){

		boss[boss_y] = boss_x;

	}else if(height[x] < height[y]){

		boss[boss_x] = boss_y;

	}else{ //height[x] == height[y]

		boss[boss_y] = boss_x;
		height[x]++;
	}
}

void init(){
	for(int i = 0; i < N; i++){
		boss[i] = i;
		height[i] = 0;
	}
}

bool check(int group_id){

	map<Point,int> ROOM;
	queue<Data> Q;

	//ボスの、左下側を頭にする(ボスのid == group_id)
	ROOM[Point(info[group_id].row,info[group_id].col)] = HEAD;
	//printf("(%d,%d)に%dの頭を配置\n",info[group_id].row,info[group_id].col,group_id);
	Q.push(Data(info[group_id].row,info[group_id].col,group_id,HEAD));

	bool FLG = true;

	int adj_row,adj_col,adj_index;

	while(!Q.empty()){

		//printf("index:%d row:%d col:%d type:%d\n",Q.front().index,Q.front().row,Q.front().col,Q.front().which);

		//隣接4近傍を検索
		for(int i = 0; i < 4; i++){
			adj_row = Q.front().row+near_row[i];
			adj_col = Q.front().col+near_col[i];

			auto at = MAP.find(Point(adj_row,adj_col));
			if(at == MAP.end())continue; //隣接する布団がなければSKIP

			adj_index = MAP[Point(adj_row,adj_col)];
			//printf("adj_row:%d,adj_col:%d adj_index:%d\n",adj_row,adj_col,adj_index);

			if(adj_index != Q.front().index){ //自分以外の布団が隣接

				at = ROOM.find(Point(adj_row,adj_col));

				if(at == ROOM.end()){ //まだ割り当てがされていない
					if(Q.front().which == HEAD){
						ROOM[Point(adj_row,adj_col)] = HEAD; //頭と足は隣接してはいけない
						Q.push(Data(adj_row,adj_col,adj_index,HEAD));
						//printf("(%d,%d)に%dの頭を配置\n",adj_row,adj_col,adj_index);
					}else{
						ROOM[Point(adj_row,adj_col)] = FOOT;
						Q.push(Data(adj_row,adj_col,adj_index,FOOT));
						//printf("(%d,%d)に%dの足を配置\n",adj_row,adj_col,adj_index);
					}
				}else{ //割り当て済
					if((ROOM[Point(adj_row,adj_col)] == FOOT && Q.front().which == HEAD) ||
							(ROOM[Point(adj_row,adj_col)] == HEAD && Q.front().which == FOOT)){ //矛盾発生
						//printf("異種隣接\n");
						FLG = false;
						break;
					}
				}

			}else{ //自分の布団が隣接
				//自分のもう一方に、不適な割り当てがされていないか調べる
				at = ROOM.find(Point(adj_row,adj_col));

				if(at == ROOM.end()){ //まだ割り当てがされていない
					if(Q.front().which == HEAD){
						ROOM[Point(adj_row,adj_col)] = FOOT;
						Q.push(Data(adj_row,adj_col,Q.front().index,FOOT));
						//printf("(%d,%d)に%dの頭を配置\n",adj_row,adj_col,Q.front().index);
					}else{
						ROOM[Point(adj_row,adj_col)] = HEAD;
						Q.push(Data(adj_row,adj_col,Q.front().index,HEAD));
						//printf("(%d,%d)に%dの足を配置\n",adj_row,adj_col,Q.front().index);
					}
				}else{ //割り当て済
					if(ROOM[Point(adj_row,adj_col)] == Q.front().which){ //矛盾発生
						//printf("同じパーツが重複\n");
						FLG = false;
						break;
					}
				}
			}
		}

		if(!FLG)break;

		Q.pop();
	}

	if(FLG)return true;


	FLG = true;
	ROOM.clear();

	//ボスの、左下側を足にする
	ROOM[Point(info[group_id].row,info[group_id].col)] = FOOT;
	Q.push(Data(info[group_id].row,info[group_id].col,group_id,FOOT));
	//printf("(%d,%d)に%dの足を配置\n",info[group_id].row,info[group_id].col,group_id);

	while(!Q.empty()){

		//printf("index:%d row:%d col:%d type:%d\n",Q.front().index,Q.front().row,Q.front().col,Q.front().which);

		//隣接4近傍を検索
		for(int i = 0; i < 4; i++){
			adj_row = Q.front().row+near_row[i];
			adj_col = Q.front().col+near_col[i];

			auto at = MAP.find(Point(adj_row,adj_col));
			if(at == MAP.end())continue; //隣接する布団がなければSKIP

			adj_index = MAP[Point(adj_row,adj_col)];
			//printf("adj_row:%d,adj_col:%d adj_index:%d\n",adj_row,adj_col,adj_index);

			if(adj_index != Q.front().index){ //自分以外の布団が隣接

				at = ROOM.find(Point(adj_row,adj_col));

				if(at == ROOM.end()){ //まだ割り当てがされていない
					if(Q.front().which == HEAD){
						ROOM[Point(adj_row,adj_col)] = HEAD; //頭と足は隣接してはいけない
						Q.push(Data(adj_row,adj_col,adj_index,HEAD));
						//printf("(%d,%d)に%dの頭を配置\n",adj_row,adj_col,adj_index);
					}else{
						ROOM[Point(adj_row,adj_col)] = FOOT;
						Q.push(Data(adj_row,adj_col,adj_index,FOOT));
						//printf("(%d,%d)に%dの足を配置\n",adj_row,adj_col,adj_index);
					}
				}else{ //割り当て済
					if((ROOM[Point(adj_row,adj_col)] == FOOT && Q.front().which == HEAD) ||
							(ROOM[Point(adj_row,adj_col)] == HEAD && Q.front().which == FOOT)){ //矛盾発生
						//printf("異種隣接\n");
						FLG = false;
						break;
					}
				}

			}else{ //自分の布団が隣接
				//自分のもう一方に、不適な割り当てがされていないか調べる
				at = ROOM.find(Point(adj_row,adj_col));

				if(at == ROOM.end()){ //まだ割り当てがされていない
					if(Q.front().which == HEAD){
						ROOM[Point(adj_row,adj_col)] = FOOT;
						Q.push(Data(adj_row,adj_col,Q.front().index,FOOT));
						//printf("(%d,%d)に%dの頭を配置\n",adj_row,adj_col,Q.front().index);
					}else{
						ROOM[Point(adj_row,adj_col)] = HEAD;
						Q.push(Data(adj_row,adj_col,Q.front().index,HEAD));
						//printf("(%d,%d)に%dの足を配置\n",adj_row,adj_col,Q.front().index);
					}
				}else{ //割り当て済
					if(ROOM[Point(adj_row,adj_col)] == Q.front().which){ //矛盾発生
						//printf("同じパーツが重複\n");
						FLG = false;
						break;
					}
				}
			}
		}

		if(!FLG)break;

		Q.pop();
	}


	return FLG;
}

void func(){

	MAP.clear();
	for(int i = 0; i < N; i++)Group[i].clear();

	init();

	char buf[2];

	for(int i = 0; i < N; i++){
		scanf("%d %d %s",&info[i].col,&info[i].row,buf);
		if(buf[0] == 'x'){
			info[i].dir = YOKO;
		}else{
			info[i].dir = TATE;
		}
		MAP[Point(info[i].row,info[i].col)] = i; //マップに登録(2マス分)
		if(info[i].dir == YOKO){
			MAP[Point(info[i].row,info[i].col+1)] = i;
		}else{
			MAP[Point(info[i].row+1,info[i].col)] = i;
		}
	}

	//隣接している布団のグループを作る
	int adj_row,adj_col;
	for(int i = 0; i < N; i++){
		for(int k = 0; k < 6; k++){
			adj_row = info[i].row+diff_row[info[i].dir][k];
			adj_col = info[i].col+diff_col[info[i].dir][k];

			auto at = MAP.find(Point(adj_row,adj_col));
			if(at == MAP.end())continue;

			unite(i,MAP[Point(adj_row,adj_col)]); //隣接している布団を同じグループにする
		}
	}

	vector<int> BOSS;
	for(int i = 0; i < N; i++){ //布団をグループに振り分ける
		Group[get_boss(i)].push_back(i);
		if(boss[i] == i){
			BOSS.push_back(i); //ボスを収集する
		}
	}

	for(int i = 0; i < BOSS.size(); i++){
		if(check(BOSS[i]) == false){
			printf("No\n");
			return;
		}
	}

	printf("Yes\n");
}

int main(){

	while(true){
		scanf("%d",&N);
		if(N == 0)break;

		func();
	}

	return 0;
}