You manage an investment portfolio that currently has a delta of $20,$ a gamma of $9,$ and a vega of $5.$ You want to delta$-$gamma$-$vega hedge your portfolio by trading the following three assets:Asset $1$: delta$=-\mathrm{.}25,$ gamma$=\mathrm{.}15,$ vega$=\mathrm{.}05.$Asset $2$: delta$=\mathrm{.}10,$ gamma$=\mathrm{.}15,$ vega$=\mathrm{.}10.$Asset $3$: delta$=0\mathrm{.}37,$ gamma$=0,$ vega$=0.$If you decide to buy $40$ of Asset $2,$ then how many units of Asset $3$ should you trade? Write a positive number to buy Asset $3$ and a negative number to sell it$.$ Round to the nearest unit.

The correct answer is $57,$ can you show the steps to get to $57$