A warehouse has three types of boxes: small, medium, and large. Each small box contains $\frac{1}{3}$ of a unit of material, each medium box contains $\frac{5}{6}$ of a unit of material, and each large box contains 2 units of material. If the warehouse has 15 small boxes, 10 medium boxes, and 7 large boxes, what is the maximum integer number of full units of material the warehouse can have, using the ceiling function? Let's think step by step and output the final answer within \boxed{}.
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