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Snake Sandwich

This is my second attempt at a snake puzzle. The first Snub Snake was on an unusually shaped grid. I had some nice comments about it so I thought I would try something similar in a normal sudoku grid.

Snake Sandwich

Normal sudoku rules apply.
Cells separated by a white dot are consecutive – not all white dots are given.
The snake begins in one of the outside clues and immediately enters the grid at the nearest cell. It traces a continuous orthogonally connected one-cell wide path through the grid visiting each box at least once and finally leaves at one of the other outside clues. The snake does not touch itself even diagonally.
Outside clues give the sum of the digits between its nearest two snake cells in that row or column.