Petya is an unexperienced programming contestant. Recently he has come across the following problem:

You are given a non-directed graph which consists of *n* nodes and *m* edges. Your task is to determine whether the graph contains a Hamiltonian path.

Petya wrote a quick bug-free code which he believes solves this problem. After that Petya decided to give this problem for April Fools Day contest. Unfortunately, Petya might have made a mistake, and it's quite possible that his algorithm is wrong. But this isn't a good excuse to leave the contest without submitting this problem, is it?
The first line contains two integers *n*, *m* (1 ≤ *n* ≤ 20; 0 ≤ *m* ≤ 400). Next *m* lines contain pairs of integers *v*<sub class="lower-index">*i*</sub>, *u*<sub class="lower-index">*i*</sub> (1 ≤ *v*<sub class="lower-index">*i*</sub>, *u*<sub class="lower-index">*i*</sub> ≤ *n*).
print("_RANDOM_GUESS_1690503372.772103")# 1690503372.7721267