during a recent campaign for office, a candidate made a tour of a country that we assume lies in a plane. on the first day of the tour she went east, on the second day she went north, on the third day west, on the fourth day south, on the fifth day east, and so on. if the candidate went $n^2/2$ miles on the $n^{\text{th}}$ day of her tour, how many miles was she from her starting point at the end of the 40th day?