The Alternating Gate Logic

Evaluate a boolean expression tree. Nodes are operations: 'A' (AND), 'O' (OR), 'X' (XOR). A node is formatted as 'Op(arg1,arg2,...)'. A leaf is just '0' or '1'. Crucially, at every ODD depth (root is depth 0), the gate's logic is inverted (AND becomes NAND, OR becomes NOR, XOR becomes XNOR). Example: 'A(1,0)' at Depth 0. - Root (Depth 0) is 'A' (AND). 1 AND 0 = 0. Example: 'A(1,0)' at Depth 1. - Root is Depth 1 (Odd), so 'A' is NAND. 1 NAND 0 = 1. Input: A string expression. Output: The final bit (0 or 1).