To write a test case generator for the "Four Tea" problem, we need to create random values for the number of players \(N\), the prices of the tea packages \(p_A, p_B, p_C, p_D\), and the respective number of tea cups \(t_A, t_B, t_C, t_D\) that each package can make. The constraints given in the problem will guide us in generating valid test cases. Here is a sample implementation of the test case generator in Python:

```python
import random

def tcgen():
    # Generate a random number of players (1 to 100)
    N = random.randint(1, 100)
    
    # Generate random prices for tea packages A, B, C, D (1 to 100)
    p_A = random.randint(1, 100)
    p_B = random.randint(1, 100)
    p_C = random.randint(1, 100)
    p_D = random.randint(1, 100)
    
    # Generate random number of cups for tea packages A, B, C, D (1 to 100)
    t_A = random.randint(1, 100)
    t_B = random.randint(1, 100)
    t_C = random.randint(1, 100)
    t_D = random.randint(1, 100)
    
    return N, (p_A, p_B, p_C, p_D), (t_A, t_B, t_C, t_D)

# Example of how to use the test case generator
if __name__ == "__main__":
    N, prices, tea_cups = tcgen()
    print("N:", N)
    print("Prices:", prices)
    print("Tea cups:", tea_cups)
```

This code will generate a test case with:

- A random number of players \(N\) between 1 and 100.
- Random prices for each type of tea package between 1 and 100.
- Random numbers of tea cups that each package can make, also between 1 and 100.

### Explanation of the Output Structure
- \(N\): Number of players.
- `prices`: A tuple containing the prices of tea packages A, B, C, and D.
- `tea_cups`: A tuple containing the number of tea cups that packages A, B, C, and D can make.

### Example Output
The output from running the generator might look like this:
```
N: 45
Prices: (56, 78, 12, 34)
Tea cups: (7, 14, 20, 45)
```

You can use this generator to create multiple test cases for the problem, ensuring that all inputs are within the specified constraints.