Boys and Girls

Time Limit: 1000 mSec

Memory Limit: 32768 KB

Description

the second year of the university somebody started a study on the romantic relations between the students. The relation “romantically involved” is defined between one girl and one boy. For the study reasons it is necessary to find out the maximum set satisfying the condition: there are no two students in the set who have been “romantically involved”. The result of the program is the number of students in such a set.

The input contains several data sets in text format. Each data set represents one set of subjects of the study, with the following description:

the number of students the description of each student, in the following format student_identifier: (number_of_romantic_relations) student_identifier1 student_identifier2 ... or student_identifier: (0)

Input

Output

Sample Input

7
0: (3) 4 5 6 1: (2) 4 6 2: (0) 3: (0) 4: (2) 0 1 5: (1) 0 6: (2) 0 1 3 0: (2) 1 2 1: (1) 0 2: (1) 0

Sample Output

5
2

Hint

Source

Southeastern European Regional Programming Co

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