Katu Puzzle(2-sat)

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:

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

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

样例输出

YES

提示

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

 

裸的2-sat。