Harry Potter lost his Invisibility Cloak, running from the school caretaker Filch. Finding an invisible object is not an easy task. Fortunately, Harry has friends who are willing to help. Hermione Granger had read "The Invisibility Cloaks, and Everything about Them", as well as six volumes of "The Encyclopedia of Quick Search of Shortest Paths in Graphs, Network Flows, the Maximal Increasing Subsequences and Other Magical Objects". She has already developed a search algorithm for the invisibility cloak in complex dynamic systems (Hogwarts is one of them).

Hogwarts consists of *n* floors, numbered by integers from 1 to *n*. Some pairs of floors are connected by staircases. The staircases may change its position, moving exactly one end. Formally the situation is like this: if a staircase connects the floors *a* and *b*, then in one move it may modify its position so as to connect the floors *a* and *c* or *b* and *c*, where *c* is any floor different from *a* and *b*. Under no circumstances the staircase can connect a floor with itself. At the same time there can be multiple stairs between a pair of floors.

Initially, Harry is on the floor with the number 1. He does not remember on what floor he has lost the cloak and wants to look for it on each of the floors. Therefore, his goal is to visit each of *n* floors at least once. Harry can visit the floors in any order and finish the searching at any floor.

Nowadays the staircases move quite rarely. However, Ron and Hermione are willing to put a spell on any of them to help Harry find the cloak. To cause less suspicion, the three friends plan to move the staircases one by one, and no more than once for each staircase. In between shifting the staircases Harry will be able to move about the floors, reachable at the moment from the staircases, and look for his Invisibility Cloak. It is assumed that during all this time the staircases will not move spontaneously.

Help the three friends to compose a searching plan. If there are several variants to solve the problem, any valid option (not necessarily the optimal one) will be accepted.
The first line contains integers *n* and *m* (1 ≤ *n* ≤ 100000, 0 ≤ *m* ≤ 200000), which are the number of floors and staircases in Hogwarts, respectively. The following *m* lines contain pairs of floors connected by staircases at the initial moment of time.
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print("_RANDOM_GUESS_1689643988.183654")# 1689643988.1836731