## Problem D: Marbles on a tree

*n* boxes are placed on the vertices of a rooted tree, which
are numbered from 1 to *n*,
1 ≤ *n* ≤ 10000. Each box is either
empty or contains a number of marbles; the total number of marbles is
*n*.
The task is to move the marbles such that each box contains exactly
one marble. This is to be accomplished be a sequence of moves; each
move consists of moving one marble to a box at an adjacent vertex.
What is the minimum number of moves required to achieve the goal?

The input contains a number of cases. Each case starts with the
number *n* followed by *n* lines. Each line contains at
least three numbers which are: *v* the number of a vertex,
followed by the number of marbles originally placed at vertex
*v* followed by a number *d* which is the number of
children of *v*, followed by *d* numbers giving the
identities of the children of *v*.

The input is terminated by a case where *n* = 0 and
this case should not be processed.

For each case in the input, output the smallest
number of moves of marbles resulting in one marble at each vertex
of the tree.

### Sample input

9
1 2 3 2 3 4
2 1 0
3 0 2 5 6
4 1 3 7 8 9
5 3 0
6 0 0
7 0 0
8 2 0
9 0 0
9
1 0 3 2 3 4
2 0 0
3 0 2 5 6
4 9 3 7 8 9
5 0 0
6 0 0
7 0 0
8 0 0
9 0 0
9
1 0 3 2 3 4
2 9 0
3 0 2 5 6
4 0 3 7 8 9
5 0 0
6 0 0
7 0 0
8 0 0
9 0 0
0

### Output for sample input

7
14
20

*P. Rudnicki*

Waterloo Local - June 12, 2004.