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Parity Party XIII

Three primes, two cubes, six squares!

Normal Sudoku rules apply. No digit may repeat in a row, column, or box.

Special rules of Parity Party: A number at the edge of the grid indicates the sum of cells encountered when moving through the grid from that vantage point, UP TO AND INCLUDING the first odd or first even digit. For example, a 15 at the end of a diagonal could indicate something like 7-8, 8-7, 1-3-5-6 or 2-6-4-3 (among others) when reading from that vantage point... and because digits on a diagonal can repeat, 1-3-3-3-4 or 2-4-2-2-7 are also possible; but not 1-2-3-4-5 or 2-6-3-4 etc. That is, the parity of the farthest digit must deviate from that of all the others.

Please note: Unlike in 'little killer' puzzles, you're not necessarily seeing the sum of all digits in the diagonal.

Note: If the clue is less than 10, it might simply indicate the value of the first cell. That is to say, you could be adding up zero odd and one even number, or vice versa.