2006 AIME I Problem 15

Given that a sequence satisfies x_0=0 and |x_k|=|x_{k-1}+3| for all integers k\ge 1, find the minimum possible value of |x_1+x_2+\cdots+x_{2006}|.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.