Your company is hired by the WA state highway agency to place warning signs along a dangerous road. On that road are n locations at which you may place a sign, at mile posts m1 < m2 < · · · < mn, where each mi is measured from the starting point m1 = 0. The only places you are allowed to place a sign are at one of the given mileposts. In addition, you must place one at locations m1 and mn. (If n = 1 then you just place one at m1.) The requirement is to place one every 50 miles, but this may not be possible (depending on the spacing of the mileposts). If you place two consecutive signs x miles apart, the penalty for that placement is (50−x) 2 which will be deducted from your payment. You want to arrange a placement so as to minimize the total penalty - that is, the sum, over all locations, of the penalties. Perform the two steps above to start the process of determining the minimum possible penalty.