Background

Special for beginners, ^_^

Description

Farmer John completed his new barn just last week, complete with all the latest milking technology. Unfortunately, due to engineering problems, all the stalls in the new barn are different. For the first week, Farmer John randomly assigned cows to stalls, but it quickly became clear that any given cow was only willing to produce milk in certain stalls. For the last week, Farmer John has been collecting data on which cows are willing to produce milk in which stalls. A stall may be only assigned to one cow, and, of course, a cow may be only assigned to one stall. Given the preferences of the cows, compute the maximum number of milk-producing assignments of cows to stalls that is possible.

农夫John的牛棚共有M个牛栏，其中一共养了N头奶牛。每头奶牛只愿意在它喜欢的那些牛栏中产奶。一个牛栏只能容纳一头奶牛，一头奶牛也只在一个牛栏中产奶。请你将奶牛分配到牛栏中，使得愿意产奶的奶牛数T最大。限制：N≤200，M≤200

Format

Input

The input includes several cases. For each case, the first line contains two integers, N (0 <= N <= 200) and M (0 <= M <= 200). N is the number of cows that Farmer John has and M is the number of stalls in the new barn. Each of the following N lines corresponds to a single cow. The first integer (Si) on the line is the number of stalls that the cow is willing to produce milk in (0 <= Si <= M). The subsequent Si integers on that line are the stalls in which that cow is willing to produce milk. The stall numbers will be integers in the range (1..M), and no stall will be listed twice for a given cow.

第一行n,m

下面n行，每行第一个数x表示后面接了x个喜欢的牛栏。后面接了x个数

Output

For each case, output a single line with a single integer, the maximum number of milk-producing stall assignments that can be made.

Samples

5 5
2 2 5
3 2 3 4
2 1 5
3 1 2 5
1 2

4

Limitation

1s, 1024KiB for each test case.