Mini-Tetris 3023

Time limit2sMemory limit1024 MB

Summary

Given counts of square, S-tile, and corner tiles, find the widest 2 x n rectangle that some or all of them can tile exactly without overlap.

Level: Medium4 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

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 $2$ cells high. It has just three types of tile:

A square made out of $4$ tiles in a $2 \times 2$ grid.
An S-tile made out of $4$ tiles, $2$ on one row and $2$ slightly offset on the other.
A corner made out of $3$ tiles, $1$ on one row and $2$ on the other.

Tiles may be rotated $0$ , $90$ , $180$ , or $270$ degrees to fit amongst each other. However, they cannot overlap or go outside the vertical boundary of the grid.

This game provides $a$ squares, $b$ S-tiles, and $c$ corners. Gry would like to beat the high score by creating the largest possible contiguous $2 \times n$ rectangle out of some or all of the provided tiles, without any tiles overlapping or sticking out of the rectangle.

Input

The sole line of input contains three integers $a$ , $b$ , and $c$ ( $0 \leq a, b, c \leq 50$ ): the number of squares, S-tiles, and corners, respectively.

Output

Output the maximum possible width of the grid, $n$ , that can be perfectly filled by some or all of the given tiles without overlapping or overstepping the boundaries.

Examples3

Example 1
Input
```
2 2 2
```
Expected output
```
11
```
Example 2
Input
```
1 1 1
```
Expected output
```
2
```
Example 3
Input
```
0 0 0
```
Expected output
```
0
```