# Marbles on a tree

Time Limit: 1000 mSec

Memory Limit: 32768 KB

## Description

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?

## Input

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.

## Output

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


## Sample Output

7
14
20


Waterloo