Match Stick Squares

You are arranging match sticks to form a grid area for some rectangle. For example, a square unit has 4 match sticks; a rectangle of \(1\times 2\) \(unit^2\) has 7 match sticks; and a square of \(2 \times 2\) \(unit^2\) has 12 match sticks, as shown above.

Then a square of \(17\times 17\) \(unit^2\) is created with the same method before it is rearranged into a rectangle with the integer side lengths, by using the same amount of match sticks as the square.

What is the least possible area difference between the square and the new rectangle?

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