; (II) the State program funded under this part or any other State program funded with qualified State expenditures (as defined in section 409(a)(7)(B)(i)); and (III) any assistance provided to a household, landlord, or public housing agency (as defined in section 3(b)(6) of the United States Housing Act of 1937 ( 42 U.S.C. 1437a(b)(6) )) to subsidize the rental payment for a dwelling unit, including assistance provided for public housing dwelling units under section 3 of the United States Housing Act of 1937 ( 42 U.S.C. 1437a ) and assistance provided under section 8 of that Act ( 42 U.S.C. 1437f ). (ii) Value of benefits during sanction For purposes of clause (i), if the dollar value of one or more benefits received by a household in a month has been reduced under paragraph (8) or another sanction requirement, the calculated dollar value of the sanctioned benefits shall equal the dollar value of the benefit that would have been received if the benefit had not been reduced by the sanction. (C) Additional activities Nothing in this paragraph shall prevent a State from requiring an eligible participant to engage in activities not described in subparagraph (A) for additional hours during a month. (10) Calculation of work preparation participation rates (A) Definition of sanctioned recipient In this subsection, the term sanctioned recipient means any eligible participant who— (i) was required to participate in work preparation in a month; (ii) failed to perform the assigned work and work preparation activities so as to meet the relevant hourly requirements