$($c$1)$ Now assume that the bond in part $($b$)$ has an attached American put option as well as the American call option. In particular, the bond can be put to the issuer at a price of $$99$ at the end of times $1$ or $2.$ For this bond at each node in times $1$ and $2,$ what is the optional strategy, and what is the associated value of the position $?$