Aubrey Beck is single, covered by an employer retirement plan, and she contributed $$4,000$ to a new Roth IRA on June $16,2023.$ On December $29,2023,$ she determines that her $2023$ modified AGI will allow a full traditional IRA deduction. On that same date, Aubrey recharacterizes the Roth IRA contribution as a traditional IRA contribution and has $$4,200,$ the balance in the Roth IRA account $($$$4,000$ contribution plus $$200$ related earnings$),$ transferred from her Roth IRA to a traditional IRA in a trustee$-$to$-$trustee transfer. Aubrey can deduct what amount as a traditional IRA contribution on her $2023$ Form $1040?$