Loog at this Familiar Recursive!

Consider the sequence a1,a2,a3,a_1, a_2, a_3, \ldots where

a1=1,a2=3,an=an1an2a_1= 1, a_2 = 3, a_n = a_{n - 1} a_{n - 2}

for n3n \geq 3. Calculate the remainder when a514a_{514} is divided by 1111.

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