Regions

Is it possible to place every one of the following numbers 12, 22, 32, 42, 52, , 252, 262, 2721^2,\ 2^2,\ 3^2,\ 4^2,\ 5^2,\ \dots,\ 25^2,\ 26^2,\ 27^2 into either of the two regions AA and BB below such that the sums of the numbers in each region are equal?

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