n models each have error variance v, and every pair of them is correlated rho. Return the variance of their average error.

$$\mathrm{Var}\left(\bar{e}\right) = \frac{v}{n}\bigl(1 + (n-1)\rho\bigr)$$

This is the central fact about ensembling. At $\rho = 0$ the variance falls like $1/n$; at $\rho = 1$ it does not fall at all. Averaging models that make the same mistakes buys you nothing.

Input

n = 10
v = 1.0
rho = 0.0

Output

0.1