; (iv) reconstruction, resurfacing, restoration, rehabilitation, or replacement of a toll highway, bridge, or tunnel or approach to the highway, bridge, or tunnel; (v) reconstruction or replacement of a toll-free bridge or tunnel and conversion of the bridge or tunnel to a toll facility; (vi) reconstruction of a toll-free Federal-aid highway (other than a highway on the Interstate System) and conversion of the highway to a toll facility; (vii) reconstruction, restoration, or rehabilitation of a highway on the Interstate System if the number of toll-free non-HOV lanes, excluding auxiliary lanes, after reconstruction, restoration, or rehabilitation is not less than the number of toll-free non-HOV lanes, excluding auxiliary lanes, before reconstruction, restoration, or rehabilitation; (viii) conversion of a high occupancy vehicle lane on a highway, bridge, or tunnel to a toll facility, subject to the requirements of section 166; and (iv) preliminary studies to determine the feasibility of a toll facility for which Federal participation is authorized under this paragraph. (B) Agreement to toll (i) In general Before the Secretary may authorize tolling as described in this paragraph, the public authority with jurisdiction over a highway, bridge, or tunnel shall enter into an agreement with the Secretary to ensure compliance with the requirements of this subsection. (ii) Applicability (I) In general The provisions of this paragraph shall apply to— (aa) Federal participation under subparagraph (A); (bb) any prior Federal participation in the facility proposed to be tolled