Problem Statement

There is a triangle $\triangle ABC$ satisfying $AB=a,\ BC=b,\ CA=c$.

penguinman will choose a point $P$ on side $AB$, a point $Q$ on side $BC$, and a point $R$ on side $CA$ completely at random, and form a new triangle $\triangle PQR$.

More precisely, penguinman randomly draws real numbers $p,\ q,\ r$ from continuous uniform distributions over the ranges $[0,\ a),\ [0,\ b),\ [0,\ c)$ respectively, and constructs $\triangle PQR$ by taking the $3$ points $P,\ Q,\ R$ on $AB,\ BC,\ CA$ respectively so that $AP=p,\ BQ=q,\ CR=r$.

What is the expected value of the area of $\triangle PQR$?

Input

\(a\) \(b\) \(c\)

• $1\leq a,\ b,\ c\leq 1000$
• There exists a triangle whose $3$ sides have lengths $a,\ b,\ c$.
• All inputs are integers.

Output

Output the expected value of the area of $\triangle PQR$, followed by a newline.

Your answer is considered correct if its error from the expected solution is at most $10^{-6}$.

Sample

2 4 5

0.9499177596

923 945 843

87798.3473442793