------
## 最终结论
```python
def count_bidirectional(tuples):
    seen = set()
    count = 0
    
    for a, b in tuples:
        if (b, a) in seen:
            count += 1
        seen.add((a, b))
    
    return str(count)

# Test cases
assert count_bidirectional([(5, 6), (1, 2), (6, 5), (9, 1), (6, 5), (2, 1)]) == '3'
assert count_bidirectional([(5, 6), (1, 3), (6, 5), (9, 1), (6, 5), (2, 1)]) == '2'
assert count_bidirectional([(5, 6), (1, 2), (6, 5), (9, 2), (6, 5), (2, 1)]) == '4'
```