$($IJBA$)$ Consider two sets S$1=\{$dates$,$eggs,kumquat,melon,plum$\}$ and S$2=\{$berries$,$cherries,dates,eggs,food,grapes,jelly,kumquat,lemon,melon,nectarine,orange,plum$\}.$ How many Partial functions $($mappings$)$ are there from set S$1$ to set S$2?$ The answer must be just an integer consisting only of digits with no extra punctuation, parentheses, or characters.