Multidrink

Memory limit: 256 MB

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.

Input

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.

Output

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 .

Example

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.