You are evaluating a put option on $F$ with a strike price of $$448.$

If $F$ is able to develop a new technology, the price per share will go up to $$644.$ Otherwise, the price will go down to $$381.$ Let's assume that these are the only two possible scenarios. F shares today are trading at $$536.$ You know that the risk$-$free rate is $5\%.$

What is the price of this put option?

Please round your answer to the nearest three decimals $($i$.$e$.5\mathrm{.}44).$ Please do not type the $ symbol.