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Is there a way to automate a priority table in Google Sheets based on another table?

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I have a shared sheet where I have people list their classes by priority like below:

StudentA  StudentB  StudentC  StudentD
Math      Math      Sci       Eng
Sci       Eng       Eng       Math
Eng       Sci       Math      Sci

And I have a second table which I am currently making manually based on the above data. I would like to ask if this can be somehow automated via formula/function to save me the time (as in reality I am dealing with way more students and classes).

There may also be times where a student does not select from all the class options (it's provided in a dropdown) and only has a few on their column.

Math                 Eng                 Sci
StudentA/StudentB    StudentD            StudentC
StudentD             StudentB/StudentC   StudentA
StudentC             StudentA            StudentB/StudentD

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