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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.
The first line contains two integers N (1 ≤ N ≤ 1000) and M,(0 ≤ M ≤ 1,000,000) indicating the number of vertices and edges.
Output a line containing "YES" or "NO".
4 4 0 1 1 AND 1 2 1 OR 3 2 0 AND 3 0 0 XOR
X0 = 1, X1 = 1, X2 = 0, X3 = 1.
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