Your problem is to find the highest score that can be achieved with any six particular triangles.

The input file will contain one or more data sets. Each data set is a sequence of six lines with three integers from 1 to 100 separated by blanks on each line. Each line contains the numbers on the triangles in clockwise order. Data sets are separated by a line containing only an asterisk. The last data set is followed by a line containing only a dollar sign.

For each input data set, the output is a line containing only the word "none" if there are no legal hexagons or the highest score if there is a legal hexagon.

**Sample Input**

`1 4 20`
`3 1 5`
`50 2 3`
`5 2 7`
`7 5 20`
`4 7 50`
`*`
`10 1 20`
`20 2 30`
`30 3 40`
`40 4 50`
`50 5 60`
`60 6 10`
`*`
`10 1 20`
`20 2 30`
`30 3 40`
`40 4 50`
`50 5 60`
`10 6 60`
`$`

**Sample Output**

`152`
`21`
`none`

The submit project tag for this assignment is `game`.
For your convenience, here is a submission form for this assignment.