Suppose you want to hedge a $$410$ million bond portfolio with a duration of $5\mathrm{.}2$ years using $10-$year Treasury note futures with a duration of $6\mathrm{.}7$ years, a futures price of $105,$ and $6$ months to expiration. The multiplier on Treasury note futures is $$100,000.$ How many contracts do you buy or sell?

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