Tower of Hanoi with a twist

Logic Level 5

I hope you are familiar with the Tower of Hanoi. In this modified version, you have to move all the disks from peg 1 to peg 3 with one constraint. You cannot transfer a disk directly from peg 1 to peg 3 or vice versa. In other words all moves must either begin or end in peg 2.

In this modified version it take 2 moves to move one disk from peg 1 to peg 3 and 8 moves for 2 disks.

What are the last three digits of the minimum number of moves required to solve this modified version of the Tower of Hanoi with 12 disks?

Image Credit: Wikimedia.

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