Mini-Tetris 3023

A guy named Gry found a new game called "Mini-Tetris 3023". This small
version of Tetris is played on a very long grid only  cells high and has
just three types of tile:
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  A square made out of  tiles in a  grid.
  An S-tile made out of  tiles,  on one row and  slightly offset on the other
  A corner made out of  tiles,  on one row and  on the other
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Tiles may be rotated , , , or  degrees to fit amongst each
other, however, they cannot overlap or go outside the vertical boundary of the
grid.

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Mini-Tetris.png
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This game provides  squares,  S-tiles, and  corners.
Gry would like to beat the high score by creating the largest-possible
contiguous  rectangle out of some or all of the provided tiles,
without any tiles overlapping or sticking out of the rectangle.

Input

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  The sole line of input contains three integers ,
, and  () - the number of squares, S-tiles, and corners,
respectively.
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Output
Output the maximum possible width of the grid, , that can be perfectly
filled by some or all of the given tiles without overlapping or overstepping
the boundaries.