Permutation
Imagine a permutation of numbers from 1 to N is written on a board. In Petryk's notebook, there are several ordered pairs of numbers, where each number is between 1 and N, and the numbers in a pair are distinct. If two numbers on the board are adjacent and form one of the pairs in the notebook in the same order, Petryk can erase either of these two numbers. Petryk considers that the numbers separated by the erased number are now adjacent.
**Task**
Write a program called 'permutation' that, given a set of pairs of numbers from Petryk's notebook, constructs an example of an initial permutation of numbers that Petryk can reduce to a single (arbitrary) number through successive erasures, or determines that such a permutation does not exist.
**Input**
The first line of the input file contains the natural numbers N and M (2 ≤ N ≤ 10^{5}, 2 ≤ M ≤ 10^5), where M is the number of ordered pairs in Petryk's notebook. The next M lines each contain two numbers — the elements of the respective pairs. Each number is a natural number, does not exceed N, and is different from the other number in the pair. There are no duplicate ordered pairs among the given ones.
**Output**
The first line of the output file should display any example of a permutation of numbers from 1 to N that Petryk can reduce to one number, and the second line should display a sequence of N-1 numbers that Petryk will erase one by one. If such a permutation does not exist, the output file should contain the single number 0.
**Scoring**
The test set consists of 3 blocks, with the following additional conditions:
1. 20% of the points: 2 ≤ N ≤ 5. 2. 35% of the points: 5 < N ≤ 1000. 3. 45% of the points: 1000 < N ≤ 10^5.
**Explanation.** In the permutation 1 3 4 2, we can erase the three because we have the pair 3 4. The sequence of numbers on the board then becomes: 1 4 2. Now we can erase the four because we have the pair 1 4. The board is left with the pair of numbers 1 2. Since this pair is also in Petryk's notebook, we can erase, for example, the one, leaving a single number on the board (in this case — 2).