A certain charity recruits twelve volunteers each year to spearhead its fundraising efforts.

Each volunteer is assigned one month to take the lead organizing events. As these are

volunteers, the charity does it best to accommodate everyones schedule as much as

possible. Before the year begins, each volunteer is asked to give his or her top three

choices for a month to serve. These preferences are likely to overlap. For example:

Susan John Mary

first choice December December March

second choice February March May

third choice April February April

Obviously both Susan and John cannot be assigned December; one of them will need to

be assigned a different month. The best possible assignment for the three volunteers

$($ignoring the other nine for the moment$)$ would be

Susan $=$ February John $=$ December Mary $=$ March

as John and Mary get their first choice and Susan receives her second. For twelve

volunteers, the task above is humanly unmanageable, and so the charity has contacted

you to automate this process for them.

The charity proposes that the following point system be used when determining the

desirability of a particular month assignment to its volunteers:

$3$ points for each volunteer assigned his or her first choice

$2$ points for each volunteer assigned his or her second choice

$1$ point for each volunteer assigned his or her third choice

$0$ points for each volunteer not assigned any of his or her choices

Thus, each of the $12!$ possible assignments of months to volunteers will have a

desirability between $0$ and $36.$ Your task is to find the best calendar assignmen