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An industrial robot is tasked to fill up boxes with parts. All parts are of the same type. Boxes come in four different sizes: Small (S), medium (M), large (L), and extra large (XL). The maximum number of parts for each box type is different. The maximum number of parts in smaller boxes should always be lower than the maximum number of parts in bigger boxes. Here are some examples of valid and invalid number of parts for each box type. Max number of parts: 5 (S), 16 (M), 20 (L), 25 (XL): Valid. Max number of parts: 15 (S), 10 (M), 20 (L), 25 (XL): Invalid: S>M. The boxes can not be partially filled. They are either full or empty. Rules: 1. The robot must fill up bigger boxes before filling up smaller ones. In this case, the robot has to fill up XL boxes first, then L boxes, then M boxes, and finally S boxes. 2. Boxes can not be partially filled. They either have to be full or empty. If a box can contain 10 parts then you can only have 10 parts or 0 part in this box.