Terusky

Ancient civilizations often used letters to represent numbers.

In the Roman numeral system, $7$ letters were used: C, D, I, L, M, V, and X, allowing them to write numbers from $1$ to $3999$.

The Etruscans, neighbors of the Romans, also used seven letters: A, E, I, J, O, U, and Y. This system enabled them to represent numbers from $1$ to $5040$. Each number was written as a string of seven letters, with each letter used exactly once. The list of all such strings is sorted alphabetically, and the position of a string in this list is the number it represents. For example: AEIJOUY = 1, AEIJOYU = 2, AEIJUOY = 3, and YUOJIEA = 5040.

Write a program to determine how the Etruscans would have represented a given number.