Certainly! To generate test cases for this problem, where you need to sort a permutation of integers using the specified operation, we will create a function that generates a random permutation of integers from 1 to \(N\) and outputs this permutation along with its length \(N\).

Here is the test case generator for this problem:

```python
import random

def tcgen():
    # Define the constraints
    N = random.randint(1, 2 * 10**5)  # N is a random integer between 1 and 200,000
    
    # Generate a random permutation of integers from 1 to N
    P = list(range(1, N + 1))
    random.shuffle(P)
    
    return N, P

# Example of how to use the test case generator
N, P = tcgen()
print(N)
for num in P:
    print(num)
```

**Explanation:**

1. **N generation:** We generate \(N\) as a random integer between 1 and 200,000, adhering to the constraints provided.
   
2. **Permutation generation:** We create a list `P` that contains integers from 1 to \(N\) in ascending order and then shuffle it to create a random permutation.

3. **Return values:** The function returns the length \(N\) and the permutation `P`.

This generator ensures that each generated test case is valid according to the problem constraints and simulates the complexity that may be encountered in actual competitive programming scenarios.