Rectangular Pie Game#4336
The Chief Great Hole Punch and the Chief Great Wallet are engaged in an intriguing game. They start with a rectangular pie, and take turns making moves, with the Great Hole Punch going first. Each move involves cutting one of the existing pieces of the pie into two parts. The game concludes after each chief has made moves. At the end of the game, the Great Wallet consumes the largest piece of the pie by area, while the Great Hole Punch eats all the remaining pieces.
Both chiefs aim to maximize their respective gains and play optimally. What will be the area of the piece that the Great Wallet will claim?
The input consists of a natural number (1 \le n \le 2012), representing the number of pairs of moves in the game, and natural numbers and (1 \le h, w \le 2012), which are the dimensions of the rectangular pie.
Output the area of the piece that will be taken by the Great Wallet, with a precision of at least 10^{-6} either relatively or absolutely.
Example 1