The Floor Is Lava

Twelve platforms (cages) are arranged around the playground (grid). You have twelve planks (each 3 cells in length) to link the platforms together into a single loop.

Place each plank (draw straight lines) such that one end is on one platform and the other end on another platform. Every cage cell contains the end of a plank. Six of the planks are GREEN and six are BLUE. The position and color of each plank (line) is to be determined by the solver.

Normal sudoku rules apply.

Digits in cages sum to the total shown.

Along GREEN lines, adjacent digits differ by at least 5.

Box borders divide the BLUE lines into segments with the same sum. Every blue line has at least two segments.