8105번 - Gambling 다국어

A gambling machine consists of n generators of integers: G₁, ..., G_n, where 1 ≤ n ≤ 1,000. The generator G_i can generate integers only from the certain set Si ⊆ {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 12,000.

While G_i 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 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.

Write a program that:

• reads from the standard input 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 to the standard output 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 (which means “no” in Polish).

In the first line of the standard input there is written one positive integer n, n ≤ 1,000. 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.

In the standard output 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.