问题 A: Katu Puzzle

内存限制:128 MB 时间限制:1.000 S
评测方式:文本比较 命题人:
提交:1 解决:1

题目描述

Katu Puzzle is presented as a directed graph G(V, E) with each edge e(a, b) labeled by a boolean operator op (one of AND, OR, XOR) and an integer c(0≤c≤1). One Katu is solvable if one can find each vertex Vi a value Xi(0≤Xi≤1) such that for each edge e(a, b) labeled by op and c, the following formula holds:
Xa op Xb=c
The calculating rules are:


AND 0 1
0 0 0
1 0 1
OR 0 1
0 0 1
1 1 1
XOR 0 1
0 0 1
1 1 0
Given a Katu Puzzle, your task is to determine whether it is solvable.

输入

The first line contains two integers N(1≤N≤1000) and M(0≤M≤1,000,000) indicating the number of vertices and edges.
The following M lines contain three integers a(0≤a<N), b(0≤b<N), c and an operator op each, describing the edges.

输出

Output a line containing "YES" or "NO".

样例输入 复制

4 4
0 1 1 AND
1 2 1 OR
3 2 0 AND
3 0 0 XOR

样例输出 复制

YES

提示

X0=1,X1=1,X2=0,X3=1.