PAMO 2001 Problem 4

Let $n$ be a positive integer, and let $a>0$ be a real number. Consider the equation: $$\sum_{i=1}^{n}(x_i^2+(a-x_i)^2)= na^2$$ How many solutions ( $x_1, x_2 \cdots , x_n$ ) does this equation have, such that: $$0 \leq x_i \leq a, i \in N^+$$