Pierre, a cash basis, unmarried taxpayer, had $$1,400$ of state income tax withheld during $2024.$ Also in $2024,$ Pierre paid $$455$ that was due when he filed his $2023$ state income tax return and made estimated payments of $$975$ toward his $2024$ state income tax liability. When Pierre files his $2024$ Federal income tax return in April $2025,$ he elects to itemize deductions, which amount to $$17,650,$ including the state income tax payments and withholdings, all of which reduce his taxable income.

a$.$ What is Pierre's $2024$ state income tax deduction?

b$.$ As a result of overpaying his $2024$ state income tax, Pierre receives a refund of $$630$ early in $2025.$ The standard deduction for single taxpayers for $2024$ was $$14,600.$ How much of the $$630$ will Pierre include in his $2025$ gross income?