Sure! Here's a test case generator for the given problem statement:

```python
import random

def tcgen():
    # Number of operations, n
    n = random.randint(1, 1000)
    
    operations = []
    for _ in range(n):
        # Randomly choose between '(' and ')'
        p = random.choice(['(', ')'])
        
        # Randomly choose an integer x_i (1 ≤ x_i ≤ 10^6)
        x = random.randint(1, 10**6)
        
        operations.append((p, x))
    
    return n, operations

# Function to print the test case in the required format
def print_test_case(n, operations):
    print(n)
    for p, x in operations:
        print(p, x)

# Generate a test case and print it
if __name__ == "__main__":
    n, operations = tcgen()
    print_test_case(n, operations)
```

This generator will produce random test cases conforming to the constraints specified in the problem statement.

### Explanation of the Test Case Generator:

1. **Generate `n`**:
   - Randomly choose an integer `n` between 1 and 1000.

2. **Generate Operations**:
   - For each of the `n` operations:
     - Randomly choose a character `p` which is either '(' or ')'.
     - Randomly choose an integer `x` between 1 and \(10^6\).

3. **Print the Test Case**:
   - The `print_test_case` function prints the test case in the required format.
   - It first prints the number of operations `n`.
   - Then, for each operation, it prints the character `p` and the integer `x`.

### Example Output:

Running the generator might produce an output like this:

```
3
( 1000000
) 500000
( 750000
```

This represents a test case where `n` is 3, and the operations are to add:
1. `1000000` occurrences of '('
2. `500000` occurrences of ')'
3. `750000` occurrences of '('

You can use this generator to create multiple test cases for testing the solution to the problem.