playlist

Ion is an young artists, preparing to hold his first show. At the show he will sing n songs, numbered from 1 to n.
Now he wants to set the order of the songs (the playlist).
He knows that some songs would certainly not have the same effect on the audience if they we're played one after the other (they don't go well together) and he therefore has to watch out for this aspect when he decides the order in which the songs will be played.
For instance, if n=3, and the songs 1 and 2 don't go well togther, the only acceptable playlists are 1, 3, 2 or 2, 3, 1.

Task

Determine an acceptable playlist.

Input data

Input file playlist.in contains on the first line the positive integer n, representing the number of songs. The second line contains a positive integer m, representing the number of pairs of songs that don't match if sung one after the other. Each of the following m lines contains two integers between 1 and n, separated by one space character, representing the pairs of songs that don't go well if played one after the other.

Output data

Output file playlist.out will contain a single line with n integers separated by a single space character, representing the songs int the order from the playlist.

Constraints

• 1 < n <= 13
• 1 < m <= 30
• For all the test data there is a solution, not necessarily unique. If there is more than one solution, the first in lexicographical order will be displayed.

Time limit: 0.4 seconds

prof. Emanuela Cerchez
Liceul de Informatica "Grigore Moisil" Iasi
Contact:emanuela.cerchez@gmail.com