Granite Insurance Company entered into a treaty reinsurance agreement with Rock Solid Reinsurance $($RSR$).$ Granite's retention limit is $$400,000$ and RSR agreed to provide reinsurance for up to $$2\mathrm{.}0$ million. If Granite writes an $$800,000$ policy for a client and its client recently suffers from a $$500,000$ loss,$($a$)$ How much will Granite pay?$($b$)$ How much will RSR pay?