Normal sudoku rules apply. In addition, draw a one-cell-wide snake (ie a non looping or branching string of orthogonally connected cells with two ends - head and tail) that may not touch itself orthogonally such that: the snake divides the rest of the grid into orthogonally connected regions, each of which sums to the same total and contains no repeated digits; and, all given digits belong to the snake and may not decrease when read along the snake from head to tail.