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Define a crossword puzzle to be a 15 x 15 grid of squares, each of which is either black or white. In a crossword puzzle, define a word to be a sequence of one or more consecutive white squares in a row or column such that the squares immediately before and after the sequence both are either black or do not exist. (The latter case would occur if an end of a word coincides with an end of a row or column of the grid.) A crossword puzzle is tasty if every word consists of an even number of white squares.

Compute the sum of all nonnegative integers n such that there exists a tasty crossword puzzle with exactly n white squares.