ISL 2001 N3

Let $a_1 = 11^{11}, a_2 = 12^{12}, a_3 = 13^{13}$ , and $a_n = |a_{n - 1} - a_{n - 2}| + |a_{n - 2} - a_{n - 3}|, n \geq 4.$ Determine $a_{14^{14}}$ .