How to play Bangle

Bangle is Bracelet but there need not be one loop (branching is permitted), meaning it turns into a kind of tree.
Shade paths that join the numbers, all in one piece. Paths only branch at a number, and loops are allowed.
Each path turns at most once (turning on a number is free), holds at least one cell (no number is 0), and passes over no other number.
Each number counts the cells between it and the number at the other end of one of its paths. A "?" is a number whose count isn't told.
Two paths can't touch orthogonally, though a path may run beside a number that isn't one of its ends.

Breaks rule 2: Shade paths that join the numbers, all in one piece. Paths only branch at a number, and loops are allowed.

Breaks rule 3: Each path turns at most once (turning on a number is free), holds at least one cell (no number is 0), and passes over no other number.

Breaks rule 4: Each number counts the cells between it and the number at the other end of one of its paths. A "?" is a number whose count isn't told.

Breaks rule 5: Two paths can't touch orthogonally, though a path may run beside a number that isn't one of its ends.