Sort the Fabrics

Each fabric has three properties:

• Color ($\mathbf{C}$): a string of lowercase English letters giving the color of the fabric.
• Durability ($\mathbf{D}$): an integer giving the durability of the fabric.
• Unique identifier ($\mathbf{U}$): an integer giving the ID of the fabric.

Ada and Charles work at the Kick Start fabric factory. Each day they receive $\mathbf{N}$ fabrics, and one of them sorts the batch using these rules:

• Ada sorts in lexicographically increasing order by color ($\mathbf{C}$).
• Charles sorts in ascending order by durability ($\mathbf{D}$).
• Ties are broken by ascending order of the unique identifier ($\mathbf{U}$).

Given $\mathbf{N}$ fabrics, count the fabrics that end up in the same position whether Ada or Charles sorts them.

The first line contains the number of test cases $\mathbf{T}$. Then $\mathbf{T}$ test cases follow.

Each test case begins with a line containing the integer $\mathbf{N}$, the number of fabrics. Then $\mathbf{N}$ lines follow, each with a string $\mathbf{C_i}$, an integer $\mathbf{D_i}$, and an integer $\mathbf{U_i}$: the color, durability, and unique identifier of the $i$-th fabric.

For each test case, output one line in the form Case #x: y. Here $x$ is the test case number starting from 1, and $y$ is the number of fabrics that end up in the same position whether they are sorted by color or by durability.

• $1 \le \mathbf{T} \le 100$
• $1 \le$ length of $\mathbf{C_i} \le 10$
• $\mathbf{C_i}$ consists only of lowercase English letters.
• No two fabrics have the same $\mathbf{U_i}$.