A gambling machine consists of n generators of integers: G₁, ..., G_n, where 1 <= n <= 1000. The generator G_i can generate integers only from the certain set S_i included in the interval {1,..., n}, or 0 which means that the game is over. The S_i can be an empty set. Let k_i be the number of elements of the set S_i. The sum of all the integers k_i, for i = 1,..., n, cannot exceed 12000.

While G_i is activated for the first time it generates an integer from the set S_i. The next activating ends up in generating an integer from the set S_i, which was not chosen before. If there is no such an integer, G_i 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 G_r.
• If zero is generated the machine stops.

The machine looses if the generator G_n 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 k_i for i = 1,...,n) ).

Task

Write a program that:

• Reads from the text file HAZ.IN the description of the machine, i.e. the number of generators n, integers k_i and sets S_i,
• 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.

Input

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 k_i followed by all the elements of the set S_i (written in arbitrary order). The integers in each line are separated by single spaces.

Output

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.

Example

For the input file HAZ.IN:
2
2 1 2
1 2

the correct answer is the output file HAZ.OUT:

2 2 0

For the input file HAZ.IN:
2
1 2
0

the correct answer is the output file HAZ.OUT:
NIE

Your program should look for the file HAZ.IN in the current directory and produce the output file HAZ.OUT in the current directory too. The file containing the source code of your program should have a name HAZ.???, whereas you should put three-letter abbreviation of the used programming language name instead of ???. The same program in executable form should be written in file HAZ.EXE