2369: Temple Build

The Dwarves of Middle Earth are renowned for their delving and smithy ability, but they are

also master builders. During the time of the dragons, the dwarves found that above ground the

buildings that were most resistant to attack were truncated square pyramids (a square pyramid

that does not go all the way up to a point, but instead has a flat square on top).

The dwarves knew what the ideal building shape should be based on the height they wanted

and the size of the square base at the top and bottom. They typically had three different sizes of

cubic bricks with which to work. Their goal was to maximize the volume of such a building based

on the following rules:

The building is constructed of layers; each layer is a single square of bricks of a single size.

No part of any brick may extend out from the ideal shape, either to the sides or at the top. The

resulting structure will have jagged sides and may be shorter than the ideal shape, but it must fit

completely within the ideal design. The picture at the right is a vertical cross section of one such

tower.There is no limit on how many bricks of each type can be used.

Each line of input will contain six entries, each separated by a single space. The entries represent

the ideal temple height, the size of the square base at the bottom, the size of the square base at the

top (all three as non-negative integers less than or equal to one million), then three sizes of cubic

bricks (all three as non-negative integers less than or equal to ten thousand). Input is terminated

upon reaching end of file.

For each line of input, output the maximum possible volume based on the given rules, one output

per line.

500000 800000 300000 6931 11315 5000

160293750000000000