Alchemy

Without Knowledge, Skill cannot be focused, without Skill, Strength
cannot be brought to bear and without Strength, Knowledge may not be
applied.  - Alexandre the Great.

Alexander the Great, king of Macedonia, was a king of success leading
his army and conquering every piece of land he trod. But in every story
there is some hidden information. Alexander had in his troops a council
of alchemists that helped him to create medicines from basic elements
and transmute base metals into nobel metals like gold so they can
continuosly paying the army fees and repairing shields and weapons.

The old alchemy documents show the process to transmute some basic
elements into others, so your work as an historian is to recover this
information and report for different transmutations, the required basic
elements to finish the process.

Input

The input starts with the number of test cases T ≤ 100. For each test
case, there is an intenger N ≤ 1000 that represents the number of
elements in the document. The next N lines, show the requirements for
the nth transmutation, and they are described with the number of
required elements E ≤ 10, following E elements indexes. If an elements
has E =  = 0 it means it is a basic element. You may assume that there
are no cyclic dependencies between elements.

Output

For each test case, output N lines with the required basic elements for
the nth transmutation. Leave an empty line after each test case.

In the first example, 0 and 1 are basic elements so the only requirement
is themselves. But element 2 requires the elements 0 and 1 for the
transmutation.

In the second example, elements 0, 1, 3, 4, 5 and 7 are basic; element 2
only requires the two basic 0 and 1; element 6 requires the basic
elements 3, 4 and 5; element 8 only requires one basic that is 7; and
element 9 requires three complex elements 2, 6 and 8 that are composed
of the basic elements 0, 1, 3, 4, 5 and 7.

Problem information

Author: Javier Segovia

Generation: 2026-01-25T14:43:23.751Z

© Jutge.org, 2006–2026.
https://jutge.org
