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Time limit per test: 0.25 second(s)

Memory limit: 262144 kilobytes

Memory limit: 262144 kilobytes

input: standard

output: standard

output: standard

This is the moment you've been waiting for all your life: you've invented a way to quickly solve the Maximal Clique problem: given an undirected graph find the size of the maximal subset of its vertices that form a clique (are pairwise connected). This problem is NP-hard, meaning you've got a proof that P=NP!

Unfortunately, the scientific community is not so eager to listen to you. Your papers on the subject are being rejected because of "solving an obviously unsolvable problem". Your phone number is already on the ignore list of all Computer Science professors you know. The world seems to hate you.

So you've decided to create a solver for the Maximal Clique problem and put it online, so that everyone can check for himself that you're right. You've already implemented the solver and almost launched the website, but then you've realized that this is not a very good idea: if you make the solver available, everyone will be able to solve every problem from NP by reducing it to the Maximal Clique problem. What if people will just silently use it instead of bringing you fame and respect?

Luckily, the only proof of NP-hardness of the Maximal Clique problem you know works by reducing the 3-SAT problem to it in a very specific way. So you've decided to check if the input graph given to your solver could be obtained from this reduction, and if yes, refuse to solve the problem. That way, nobody will be able to get quick solutions for all problems from NP, but everyone will still be able to verify your solver by feeding other graphs to it.

3-SAT problem statement is: given a formula of form , where each term

The reduction works in the following manner. From the above formula, we create a graph with 3n vertices, one for each variable of each clause. Two vertices corresponding to terms

The following picture shows the resulting graph for the formula :

Now a clique of size

Given a graph, you need to check if it could be created by the above reduction. The vertices are permuted arbitrarily.

sample input | sample output |

9 22 1 3 1 6 7 1 8 9 9 1 2 3 2 4 2 5 2 6 2 8 3 4 3 5 3 7 4 8 4 9 5 6 5 7 5 8 5 9 6 7 6 9 7 8 | YES |

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