Kuti-Pi has a circular farm of radius 1 unit. He loves to irrigate his farm. For the next N days, he chooses a random point on his farm and irrigates a circular area concentric with the farm, passing through the chosen point. Let S be the total sum of the areas he has to irrigate in N days. The probability of S being less than x (0 < x < $\pi$) is P(x,N).

Calculate $\mathbf{Ans}$ = $\sum_{n=0}^{\infty}\: \pi^n\: P(\sqrt{3}, n)$.

Report $\lfloor \mathbf{Ans}\times 10^5\rfloor$.

$\lfloor a\rfloor$ denotes the Greatest Integer Function of a.