Rectangle Paths

Probability Level 5

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?