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An Old Stone Game
There is an old stone game, played on an arbitrary general tree T. The goal is to put one stone on the root of T observing the following rules:
The player wins the game if by following the above rules, he succeeds to put one stone on the root of the tree.
You are to write a program to determine the least number of stones to be picked at the beginning of the game (K), so that the player can win the game on the given input tree.
The input describes several trees. The first line of this file is M, the number of trees (1 <= M <= 10). Description of these M trees comes next in the file. Each tree has N < 200 nodes, labeled 1, 2, ... N, and each node can have any possible number of children. Root has label 1. Description of each tree starts with N in a separate line. The following N lines describe the children of all nodes in order of their labels. Each line starts with a number p (1 <= p <= N, the label of one of the nodes), r the number of the immediate children of p, and then the labels of these r children.
One line for each input tree showing the minimum number of stones to be picked in step 1 above, in order to win the game on that input tree.
2 7 1 2 2 3 2 2 5 4 3 2 6 7 4 0 5 0 6 0 7 0 12 1 3 2 3 4 2 0 3 2 5 6 4 3 7 8 9 5 3 10 11 12 6 0 7 0 8 0 9 0 10 0 11 0 12 0
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