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The special purpose sorting operation, context directed swap (CDS), is an example of the block interchange sorting operation studied in prior work on permutation sorting. CDShas been postulated to model certain molecular sorting events that occur in the genome maintenance program of some species of ciliates. We investigate the mathematical structure of permutations not sortable by the CDSsorting operation. In particular, we present substantial progress towards quantifying permutations with a given strategic pile size, which can be understood as a measure of CDSnon-sortability. Our main results include formulas for the number of permutations in [Formula: see text] with maximum size strategic pile. More generally, we derive a formula for the number of permutations in [Formula: see text] with strategic pile size [Formula: see text], in addition to an algorithm for computing certain coefficients of this formula, which we call merge numbers.