Diamond Inheritance (Large)

You inspect class diagrams and decide whether they contain a diamond inheritance. The diagram below has four classes $A$, $B$, $C$ and $D$. An arrow from $X$ to $Y$ means that class $X$ inherits from class $Y$.

In this diagram $D$ inherits from both $B$ and $C$, $B$ inherits from $A$, and $C$ also inherits from $A$.

An inheritance path from class $X$ to class $Y$ is a sequence of classes $X, C_1, C_2, \dots, C_n, Y$ in which $X$ inherits from $C_1$, class $C_i$ inherits from $C_{i+1}$ for every $i$ with $1 \le i \le n - 1$, and $C_n$ inherits from $Y$. The case $n = 0$ counts too: if $X$ inherits from $Y$ directly, the sequence $X, Y$ is itself one inheritance path. The example above has two inheritance paths from $D$ to $A$, namely $D, B, A$ and $D, C, A$.

A class diagram contains a diamond inheritance if some pair of classes $X$, $Y$ has at least two different inheritance paths from $X$ to $Y$. The diagram above is the standard example. Decide whether a given class diagram contains a diamond inheritance.

The first line holds the number of test cases $T$. Then $T$ test cases follow, each describing one class diagram.

The first line of a test case holds the number of classes $N$ in that diagram. The classes are numbered from $1$ to $N$. Of the $N$ lines that follow, line $i$ starts with the number of classes that class $i$ inherits from, $M_i$, followed by $M_i$ distinct integers between $1$ and $N$. Those integers are the numbers of the classes that class $i$ inherits from.

The input satisfies the following.

• If there is an inheritance path from $X$ to $Y$, then there is no inheritance path from $Y$ to $X$.
• No class inherits from itself.

Limits

• $1 \le T \le 50$
• $1 \le N \le 1000$
• $0 \le M_i \le 10$

For each diagram print one line Case #x: y, where $x$ is the test case number starting from $1$, and $y$ is Yes if that diagram contains a diamond inheritance and No if it does not.