Zero Escape, is a visual novel adventure video game directed by Kotaro Uchikoshi (you may hear about ever17?) and developed by Chunsoft.
Stilwell is enjoying the first chapter of this series, and in this chapter digital root is an important factor.
This is the definition of digital root on Wikipedia:
The digital root of a non-negative integer is the single digit value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.
For example, the digital root of $65536$ is $7$, because $6 + 5 + 5 + 3 + 6 = 25$ and $2 + 5 = 7$.
In the game, every player has a special identifier. Maybe two players have the same identifier, but they are different players. If a group of players want to get into a door numbered $X(1\leq X\leq 9)$, the digital root of their identifier sum must be $X$.
For example, players $\{1,2,6\}$ can get into the door $9$, but players $\{2,3,3\}$ can't.
There is two doors, numbered $A$ and $B$. Maybe $A=B$, but they are two different door.
And there is $n$ players, everyone must get into one of these two doors. Some players will get into the door $A$, and others will get into the door $B$.
For example:
players are $\{1,2,6\}$, $A=9$, $B=1$
There is only one way to distribute the players: all players get into the door $9$. Because there is no player to get into the door $1$, the digital root limit of this door will be ignored.
Given the identifier of every player, please calculate how many kinds of methods are there, $mod~258280327$.