This is a Deformable Total Masyu puzzle, a variant of Masyu. In addition to the rules of Masyu, all possible circles have been given; i.e. it is not possible to add any more circles to the grid so that it is consistent with the solution. Further, any white circle may instead behave as a black circle.
Puz-PRE link. (Note: Puz-PRE has neither the "total" nor "deformable" constraints programmed in. The solver may incorrectly mark incorrect answers as correct, and may mark a valid answer as incorrect.)
This is truly the most evil puzzle on my blog so far. Expect to use every single constraint in the rules, along with a bunch of techniques you may have not encountered before. I honestly don't blame you if you stop trying after 10 seconds.
And remember, you have to prove uniqueness!
