AUSTRIAN-POLISH 2001 Problem 10

The sequence $a_{1},a_{2},\cdots,a_{2010}$ has the following properties:

(1) each sum of the 20 successive values of the sequence is nonnegative,

(2) $|a_{i}a_{i+1}| \leq 1$ for $i=1,2,\cdots,2009$ .

Determine the maximal value of the expression $\sum_{i=1}^{2010}a_{i}$ .