Jim has an annual income of $$250,000.$

Jim is looking to buy a house with monthly property taxes of $$100$ and monthly homeowner$$s insurance of $$125.$ He also has $$258$ in monthly student loan payments.

Mes Bank has a maximum front$-$end PTI limit of $28\%$ and a maximum back$-$end PTI limit of $36\%.$ Both limits must be satisfied.

Mes Bank is offering a fully amortizing $30-$year FRM at an annual rate of $8\mathrm{.}5\%,$ compounded monthly, and $80\%$ LTV $($loan$-$to$-$value ratio$).$

Assuming Jim has the savings to pay the down payment and various fees. The highest price Jim can bid for this house is $$\_\_\_\_\_\_\_.$