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pS€żị"¥pỤị⁵ 

Takes number of rows, number of columns and a flat list as separate command-line arguments.

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How it works

pS€żị"¥pỤị⁵ Main link. Argument: m (rows), n (columns), A (list, flat) p Compute the Cartesian product [1, ..., m] × [1, ..., n]. This yields the indices of the matrix M, i.e., [[1, 1], [1, 2], ..., [m, n]]. S€ Compute the sums of all index pairs. p Yield the Cartesian product. ¥ Dyadic chain. Arguments: Sums, Cartesian product. ị" For each index pair in the Cartesian product, retrieve the coordinate at the index of its sum, i.e., map [i, j] to i if i + j is odd and to j if i + j is even. ż Zip the sums with the retrieved indices. Ụ Sort [1, ..., mn] by the corresponding item in the resulting list. ị⁵ Retrieve the corresponding items from A.