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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.
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