|q⟩ Bad Qubits

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Multiple choice
After running this circuit, what is the probability of measuring |000⟩?
⚛ The apparatus
const c = circuit(3);
c.h(0); c.h(1); c.h(2);

// Oracle: phase-flip |000>
c.x(0); c.x(1); c.x(2);
c.h(2); c.ccx(0, 1, 2); c.h(2);
c.x(0); c.x(1); c.x(2);

// Oracle: phase-flip |111>
c.h(2); c.ccx(0, 1, 2); c.h(2);

// Diffuser
c.h(0); c.h(1); c.h(2);
c.x(0); c.x(1); c.x(2);
c.h(2); c.ccx(0, 1, 2); c.h(2);
c.x(0); c.x(1); c.x(2);
c.h(0); c.h(1); c.h(2);

return c;

Commit your prediction for P(|000⟩) — then run it.