A family hierarchy is usually presented by a pedigree tree. Your job is to count those family members who have no child.
Each input file contains one test case. Each case starts with a line containing $0<N<100$, the number of nodes in a tree, and $M (<N)$, the number of non-leaf nodes. Then M lines follow, each in the format:
ID K ID ID ... ID[K]
IDis a two-digit number representing a given non-leaf node,
Kis the number of its children, followed by a sequence of two-digit
ID‘s of its children. For the sake of simplicity, let us fix the root ID to be
The input ends with N being 0. That case must NOT be processed.
For each test case, you are supposed to count those family members who have no child for every seniority levelstarting from the root. The numbers must be printed in a line, separated by a space, and there must be no extra space at the end of each line.
The sample case represents a tree with only 2 nodes, where
01is the root and
02is its only child. Hence on the root
01level, there is
0leaf node; and on the next level, there is
1leaf node. Then we should output
0 1in a line.