The Dead Marshes

'Yes, they are all round us,' he whispered. 'The tricksy lights. Candles of corpses, yes, yes. Don't you heed them! Don't look! Don't follow them!'

Frodo, Sam, and Gollum have arrived at the northern edge of the Dead Marshes and must find a path through, starting at r1c1 and ending at r9c9. Adjacent digits along the path must differ by at least 5. Draw the path such that:

• it is orthogonally connected
• it visits every box exactly once
• it does not touch itself orthogonally or diagonally
• it does not enter a cell with a tricksy light (flame)
• it does not enter a corpse location (cage)

Normal sudoku rules apply.

Digits in a cage must sum to the value shown.

A digit on a flame indicates how many flames contain that digit.