When large forest fires are being controlled by fire management specialists, fire breaks are often cut into unburned areas in an attempt to create a space to stop the fire from spreading any further. While the break stops the fire from progressing, all of the area up to and including the break is sacrificed.

Consider a $50$ mile by $50$ mile square area that has an existing fire somewhere within the region. As the fire manager, you must determine how many fire breaks to place. Each fire break is equally spaced as a cut fully from one side of the region to the other in a straight line $\frac{1}{2}$ mile wide. The region between the breaks that is on fire is totally consumed but cannot spread outside that region. Examples of $1$ and $2$ breaks are shown below.

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Your job is to determine the number of breaks you should place to minimize the total area lost from the fire as well as the amount of area lost.