A call option on GM is priced at $$12$ today, with a maturity $6$ months from today and a strike price of $$52.$ The stock price of GM is $$51\mathrm{.}50$ today, and the risk$-$less rate for $6$ months is $3\mathrm{.}7\%($this is the actual risk$-$less return for $6$ months at which both borrowing and lending is possible$).$

Assuming transactions costs are zero, according to put call parity what should be the price of a put option with $6$ months maturity and $$52$ strike price?