It's hard to believe that you really need the position in the array after switching to hashes.
But well, lets continue this road...
As long as the order isn't random but systematic you should be able to calculate this position.
So plz search the internet or math books for algorithms generating all permutations by combination of two permutations named sigma and tau and reverse the process to get the index.
This approach would limit time and space complexity considerably!
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