In April $2024,$ let$$s consider a $1-$year put option on IBM stock with an exercise price of $$650.$

The risk$-$free interest rate is $2\mathrm{.}2\%$ a year.

Suppose we are going to use $2-$step binomial method to value this put option, each step covers $6$ months

We assume the current stock price is $$650,$ and for each step, stock price will either increase by $30\%,$ or descrease by $23\mathrm{.}08\%$ over each step.

What should be the value of this put option based on two$-$step binomial method?