Deranged Rearrangements
CJam, score: ∞

Each line is of the form

];Lx+:L{__(f&lt;0+:+\,,(;1+:**\(;}h]:+


where x is a number from 0 to n-1. The result is in the range 0 to n!-1.

Try it online! (For n=3.)

Credits to jimmy23013 for the code that computes the actual permutation index. I've only replaced the bit that reads the input with ];Lx+:L which discards the result from the previous line and then adds the index of the current line to the variable L (which is initially an empty array).