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A square tin sheet of side $12$ inches is converted into a box with open top in the following steps – The sheet is placed horizontally. Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If $x$ is an integer, then what value of $x$ maximizes the volume of the box?

1. $3$
2. $4$
3. $1$
4. $2$

1