------
## 最终结论
```python
def min_operations_to_zero(n):
    operations = 0
    while n > 0:
        if n & 1 == 0:  # If the rightmost bit is 0, move to the next bit
            n >>= 1
        else:
            if (n & 2) == 0:  # Check if the second bit is not set
                n >>= 1
            else:
                # Change the ith bit where conditions are met
                i = 1
                while (n >> i) & 1 == 1 and (n >> (i + 1)) & ((1 << i) - 1) == 0:
                    i += 1
                n ^= (1 << i)
        operations += 1
    return operations

# Example usage:
print(min_operations_to_zero(0))   # Output: 0
print(min_operations_to_zero(3))   # Output: 2
print(min_operations_to_zero(6))   # Output: 4
print(min_operations_to_zero(9))   # Output: 14
print(min_operations_to_zero(333)) # Output: 393
```