What is the liability when sequential injuries damage a tooth and its root?

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If a first assailant breaks the tooth, and a second assailant breaks the remainder, the second is liable for the remaining portion of the Arsh. If the second person extracts the remainder along with its root (snukh), the liability depends on the first injury. If the first injury broke the tooth transversely (without reaching the root), the second person owes nothing for the root, as the root is merely accessory to the visible part extracted. If the first person broke half the tooth lengthwise without damaging the root, and the second extracts the remainder along with the entire remaining root, the second is liable for the Diyya of the remaining half-tooth and a discretionary compensation for the portion of the root corresponding to the part broken by the first assailant.