Given four integers `length`, `width`, `height`, and `mass`, representing the dimensions and mass of a box, respectively, return _a string representing the **category** of the box_.

*   The box is `"Bulky "` if:
    *   **Any** of the dimensions of the box is greater or equal to `104`.
    *   Or, the **volume** of the box is greater or equal to `109`.
*   If the mass of the box is greater or equal to `100`, it is `"Heavy ".`
*   If the box is both `"Bulky "` and `"Heavy "`, then its category is `"Both "`.
*   If the box is neither `"Bulky "` nor `"Heavy "`, then its category is `"Neither "`.
*   If the box is `"Bulky "` but not `"Heavy "`, then its category is `"Bulky "`.
*   If the box is `"Heavy "` but not `"Bulky "`, then its category is `"Heavy "`.

**Note** that the volume of the box is the product of its length, width and height.

**Example 1:**

**Input:** length = 1000, width = 35, height = 700, mass = 300
**Output:**  "Heavy "
**Explanation:** 
None of the dimensions of the box is greater or equal to 104. 
Its volume = 24500000 <= 109. So it cannot be categorized as  "Bulky ".
However mass >= 100, so the box is  "Heavy ".
Since the box is not  "Bulky " but  "Heavy ", we return  "Heavy ".

**Example 2:**

**Input:** length = 200, width = 50, height = 800, mass = 50
**Output:**  "Neither "
**Explanation:** 
None of the dimensions of the box is greater or equal to 104.
Its volume = 8 \* 106 <= 109. So it cannot be categorized as  "Bulky ".
Its mass is also less than 100, so it cannot be categorized as  "Heavy " either. 
Since its neither of the two above categories, we return  "Neither ".

**Constraints:**

*   `1 <= length, width, height <= 105`
*   `1 <= mass <= 103`


def boxCategory(length: int, width: int, height: int, mass: int) -> str:
    bulky = length >= 10000 or width >= 10000 or height >= 10000 or int(length) * width * height >= 1000000000
    heavy = mass >= 100

    if bulky and heavy:
        return "Both "
    if bulky:
        return "Bulky "
    if heavy:
        return "Heavy "
    return "Neither "
