Write a Python function `count_unique_tuples(lst)` that takes a list of tuples as input and returns the number of unique tuples in the list. Two tuples are considered the same if they contain the same elements, regardless of their order.
#### Example Usage
```python [main.nopy]
print(count_unique_tuples([(3, 4), (1, 2), (4, 3), (5, 6)])) # Output: 3
print(count_unique_tuples([(4, 15), (2, 3), (5, 4), (6, 7)])) # Output: 4
print(count_unique_tuples([(5, 16), (2, 3), (6, 5), (6, 9)])) # Output: 4
```