AT-OEMO-FED1 2004 Problem 4

Each of the $2N = 2004$ real numbers $x_1, x_2, \ldots , x_{2004}$ equals either $\sqrt 2 -1$ or $\sqrt 2 +1$ . Can the sum $\sum_{k=1}^N x_{2k-1}x_2k$ take the value $2004$ ? Which integral values can this sum take?