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StrandSort[ input_ ] := Module[ {results = {}, A = input},
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While[Length@A > 0,
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sublist = {A[[1]]}; A = A[[2;;All]];
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For[i = 1, i < Length@A, i++,
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If[ A[[i]] > Last@sublist, AppendTo[sublist, A[[i]]]; A = Delete[A, i];]
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];
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results = #[[Ordering@#]]&@Join[sublist, results];];
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results ]
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