Problem Statement

There are $N$ people numbered $1$ to $N$. Each of them is either an honest person whose testimonies are always correct or an unkind person whose testimonies may be correct or not.

Person $i$ gives $A_i$ testimonies. The $j$-th testimony by Person $i$ is represented by two integers $x_{ij}$ and $y_{ij}$. If $y_{ij} = 1$, the testimony says Person $x_{ij}$ is honest; if $y_{ij} = 0$, it says Person $x_{ij}$ is unkind.

How many honest persons can be among those $N$ people at most?

Constraints

• All values in input are integers.
• $1 \leq N \leq 15$
• $0 \leq A_i \leq N - 1$
• $1 \leq x_{ij} \leq N$
• $x_{ij} \neq i$
• $x_{ij_1} \neq x_{ij_2} (j_1 \neq j_2)$
• $y_{ij} = 0, 1$

Input

Input is given from Standard Input in the following format:

N
A_1
x_{11} y_{11}
x_{12} y_{12}
:
x_{1A_1} y_{1A_1}
A_2
x_{21} y_{21}
x_{22} y_{22}
:
x_{2A_2} y_{2A_2}
:
A_N
x_{N1} y_{N1}
x_{N2} y_{N2}
:
x_{NA_N} y_{NA_N}

Output

Print the maximum possible number of honest persons among the $N$ people.