Rectangle Paths

A \(2 \times 13\) rectangle is divided into unit squares. You must write the numbers 1 through \(26\) into these unit squares, and satisfy the following criteria.

1) Each number is in a different square.

2) The number 1 must be in a corner.

3) The numbers \(i\) and \(i+1\) must share an edge (of a unit square), for \(1 \leq i \leq 25\).

How many different ways can you write the numbers into the squares?


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