Normal sudoku rules apply. Placing a correct digit in the grid will clear any fog in the surrounding cells. Lines are Renbans, German Whispers, or Region Sum Lines. The identity of each line must be deduced. Lines never cross or branch in this puzzle. Therefore, if two line segments enter the same cell, those line segments must be connected. Renbans are a sequence of non-repeating digits in any order. Along German Whispers adjacent digits on the line have a difference of at least 5. Region Sum Lines have the same sum in every 3x3 box they visit. If a Region Sum Line visits a box multiple times, each visit is counted as a separate sum. A dot between two digits means that those digits are either consecutive or have a 1:2 ratio. Not all dots are given.