SMO 2014 Senior Round 1 Question 34

Let $x_1,x_2,\ldots,x_{100}$ be real numbers such that $$|x_1|=63,\quad\text{and}\quad |x_{n+1}|=|x_n+1|\quad\text{for }n=1,2,\ldots,99.$$ Find the largest possible value of $(-x_1-x_2-\cdots-x_{100})$.