The game of Yahtzee involves 5 dice, which are thrown in 13 rounds. A score card contains 13 categories; each round may be scored in a category of the player's choosing, but each category may be scored only once in the game. The 13 categores are scored as follows:
ones - sum of all ones thrown
twos - sum of all twos thrown
threes - sum of all threes thrown
fours - sum of all fours thrown
fives - sum of all fives thrown
sixes - sum of all sixes thrown
chance - sum of all dice
three of a kind - sum of all dice, provided at least three have same value
four of a kind - sum of all dice, provided at least four have same value
five of a kind - 50 points, provided all five dice have same value
short straight - 25 points, provided four of the dice form a sequence (that is, 1,2,3,4 or 2,3,4,5 or 3,4,5,6)
long straight - 35 points, provided all dice form a sequence (1,2,3,4,5 or 2,3,4,5,6)
full house - 40 points, provided three of the dice are equal and the other two dice are also equal. (for example, 2,2,5,5,5)
Each of the last six categories may be scored as 0 if the criteria are not met.
The score for the game is the sum of all 13 categories plus a bonus of 35 points if the sum of the first six categores is 63 or greater.
Your job is to compute the best possible score for a sequence of rounds.