Suppose you hold LLL employee stock options representing options to buy $10,400$ shares of LLL stock. LLL accountants estimated the value of these options using the Black$-$Scholes$-$Merton formula and the following assumptions:

$S=$ current stock price $=$$$27\mathrm{.}07$

$K=$ option strike price $=$$$27\mathrm{.}5$

$r=$ risk$-$free interest rate $=0\mathrm{.}055$

$=$ stock volatility $=0\mathrm{.}20$

$T=$ time to expiration $=3\mathrm{.}5$ years

You wish to hedge your position by buying put options with three$-$month expirations and a $$30\mathrm{.}00$ strike price. How many put option contracts are required? $($Note that such a trade may not be permitted by the covenants of many ESO plans. Even if the trade were permitted, it could be considered unethical.$)$

Note: Do not round intermediate calculations. Round your answer to the nearest whole number.

Number of put option contracts