$\mathrm{P}_{1}, \mathrm{P}_{2}, \ldots, \mathrm{P}_{\mathrm{n}}$ are points in the plane and $\mathrm{r}_{1}, \mathrm{r}_{2}, \ldots, \mathrm{r}_{\mathrm{n}}$ are real numbers such that the distance between $P_{i}$ and $P_{j}$ is $r_{i}+r_{j}$ (for $i$ not equal to $j$ ). Find the largest $n$ for which this is possible.