Positive integers a, b, c, and d satisfy a>b>c>d, a+b+c+d=2010, and a^{2}-b^{2}+c^{2}-d^{2}=2010. Find the number of possible values of a.
Positive integers a, b, c, and d satisfy a>b>c>d, a+b+c+d=2010, and a^{2}-b^{2}+c^{2}-d^{2}=2010. Find the number of possible values of a.