BD-BDMO 2016 Problem 4

Consider the set of integers $\left \{ 1, 2, \dots , 100 \right \}$ . Let $\left \{ x_1, x_2, \dots , x_{100} \right \}$ be some arbitrary arrangement of the integers $\left \{ 1, 2, \dots , 100 \right \}$ , where all of the $x_i$ are different. Find the smallest possible value of the sum $$S = \left | x_2 - x_1 \right | + \left | x_3 - x_2 \right | + \cdots+ \left |x_{100} - x_{99} \right | + \left |x_1 - x_{100} \right | .$$