Suppose you draw an upside down staircase with boxes that create an x by x grid. The uncolored staircase attached photo shows heights 2, 3, and 4. Tiling a staircase of height, x, means to create nonoverlapping rectangles within the staircase. Prove that tiling with x rectangles is a Catalan object. Note: A Catalan object is proven by one of the following (i) a bijection of a known Catalan object (ii) show it satifies a Catalan recursion

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