-- 4 elements, rank 2
******
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-- 5 elements, rank 2
**********
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-- 6 elements, rank 2
***************
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-- 6 elements, rank 3
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-- 7 elements, rank 2
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-- 7 elements, rank 3
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-- 8 elements, rank 2
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-- 8 elements, rank 3
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-- 8 elements, rank 4
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