2. The numbers 1 through 15 are each colored blue or red. Determine all possible colorings that satisfy the following rules:

- The number 15 is red.
- If the numbers $x$ and $y$ have different colors and $x+y \leqslant 15$, then $x+y$ is blue.
- If the numbers $x$ and $y$ have different colors and $x \cdot y \leqslant 15$, then $x \cdot y$ is red.