Design a circuit that has two inputs, clk and X, and produces one output O. X may change every clock cycle, and the change happens at the falling edge. The circuit samples the input at every rising edge of the clock. If the input is 1, consider as read a 1, else read a 0. O is 1 (for one clock cycle, from positive edge to positive edge) if the last three bits read are 001, with 1 as the most recent bit.

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