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A gambling machine consists of n generators of integers: G1, ..., Gn, where 1 <= n <= 1000. The generator Gi can generate integers only from the certain set Si included in the interval {1,..., n}, or 0 which means that the game is over. The Si can be an empty set. Let ki be the number of elements of the set Si. The sum of all the integers ki, for i = 1,..., n, cannot exceed 12000.
While Gi is activated for the first time it generates an integer from the set Si. The next activating ends up in generating an integer from the set Si, which was not chosen before. If there is no such an integer, Gi generates zero.
The machine starts with activating G1. Then the generators are activated according to the following rule :
• In case when a generator generated a positive integer r, the next activated generator is Gr.
• If zero is generated the machine stops.
The machine looses if the generator Gn generates zero and the rest of the generators had exhausted their sets of integers.
The machine is well constructed if it may generate a sequence of integers ending with zero, but not leading to a defeat (i.e. a sequence shorter then 1 + ( the sum of integers ki for i = 1,...,n) ).
Write a program that:
• Reads from the text file HAZ.IN the description of the machine, i.e. the number of generators n, integers ki and sets Si,
• Verifies, whether the machine described in the input file is well constructed,
• if it is well constructed, writes a sequence of integers, which may be generated by the machine, is ended with zero, and does not lead to defeat,
• if not, writes one word NIE ("no" in Polish) in the text file HAZ.OUT. 


In the first line of the text file HAZ.IN there is written one positive integer n <= 1000. This is the number of generators. In the (i + 1)−st line (for i = 1,..., n) there is written an integer ki followed by all the elements of the set Si (written in arbitrary order). The integers in each line are separated by single spaces.


In the text file HAZ.OUT there should be written one word NIE (if the machine isn't well constructed) or one line containing an appropriate finite series of integers separated by single spaces.


For the input file HAZ1.IN:
2 1 2
1 2
For the input file HAZ2.IN:
1 2


the correct answer is the output file HAZ1.OUT:
2 2 0

the correct answer is the output file HAZ2.OUT: