Sure! Below is a test case generator for the problem statement you provided:

```python
import random

def tcgen():
    # Generate N, ensuring it's even and within the specified range
    N = random.randint(1, 250000) * 2  # Since N needs to be even and between 2 and 500,000
    
    # Generate the sequence S with elements within the specified range
    S = [random.randint(-100000000, 100000000) for _ in range(N)]
    
    # Generate Q, the number of queries
    Q = random.randint(1, 100000)
    
    queries = []
    
    for _ in range(Q):
        l = random.randint(1, N)
        r = random.randint(l, N)
        x = random.randint(-1000, 1000)
        queries.append((l, r, x))
    
    # Format the output as required by the problem statement
    input_data = f"{N}\n" + " ".join(map(str, S)) + f"\n{Q}\n"
    input_data += "\n".join(f"{l} {r} {x}" for l, r, x in queries)
    
    return input_data

# Example Usage:
print(tcgen())
```

This test case generator creates:
1. An even integer `N`, between 2 and 500,000.
2. A sequence `S` of length `N` with integers between -100,000,000 and 100,000,000.
3. A number of queries `Q`, between 1 and 100,000.
4. For each query, values of `l`, `r`, and `x` within the specified ranges.

The output is formatted as required by the input format of the problem statement. This generator can be used to produce robust and varied test cases for the problem.