Sqaure in square
The square $ EFGH $ is located inside another square $ ABCD $ as shown on the picture below. It is known that $ AH = 1 $, $ BE = 2 $, $ CF = 3 $. The length of the segment $ DG $ is representable as $ \sqrt {a} $ for some natural number $ a $. What is $ a (a-1) $ equal to?
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