MathDB

I start with a sequence of letters

A_1 A_2 \cdots A_{2021} A_1 A_2 \cdots A_{2021} A_1 A_2 \cdots A_{2021}

. I go through

i = 1, 2, 3, \cdots, 6062

in order, and for each

i

, I can choose to swap letters

i

and

i+1

. Let

N

be the number of distinct strings I can end up with. What is the remainder when

N

is divided by

2017

Problem Statement