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<Submit a solution> [0/100]**Task statistics**

Number of users: 123

Number of users with 100 points: 82

Average result: 77.5691

# Multidrink

### Memory limit: 256 MB

## Input

## Output

## Example

Number of users: 123

Number of users with 100 points: 82

Average result: 77.5691

Byteasar lives in Byteburg, a city famous for its milk bars on every corner. One day Byteasar came up with an idea of a "milk multidrink": he wants to visit each milk bar for a drink exactly once. Ideally, Byteasar would like to come up with a route such that the next bar is always no further than two blocks (precisely: intersections) away from the previous one.

The intersections in Byteburg are numbered from to , and all the streets are bidirectional. Between each pair of intersections there is a unique direct route, ie, one that does not visit any intersection twice. Byteasar begins at the intersection no. and finishes at the intersection no. .

Your task is to find any route that satisfies Byteasar's requirements if such a route exists.

An exemplary route satisfying the requirements is:

There is no route that satisfies the requirements.

In the first line of the standard input there is a single integer (), denoting the number of intersections in Byteburg. Each of the following lines holds a pair of distinct integers and (), separated by a single space, that represent the street linking the intersections no. and .

In tests worth of all points the condition holds.

If there is no route satisfying Byteasar's requirements, your program
should print a single word "`BRAK`" (Polish for *none*),
without the quotation marks to the standard output. Otherwise, your program
should print lines to the standard output, the -th of which should
contain the number of the -th intersection on an arbitrary route
satisfying Byteasar's requirements. Obviously, in that case the first line
should hold the number , and the -th line - number .

For the input data:

12 1 7 7 8 7 11 7 2 2 4 4 10 2 5 5 9 2 6 3 6 3 12

the correct result is:

1 11 8 7 4 10 2 9 5 6 3 12

For the input data:

15 1 14 14 7 7 8 7 11 7 2 2 4 4 10 2 5 5 9 2 6 3 6 3 15 11 12 8 13

the correct result is:

BRAK

*Task authors: Jakub Radoszewski, Wojciech Rytter.*