Marching Orders

Dean Bob Roberts is in charge of the order in which the professors of his college march in the graduation ceremonies. After complaints from some professors in the newly created DEI Studies Department about seniority-based ordering, the dean decided the marching order should be random. Bob thinks this is fine. To be transparent, he has published the method he uses to build the marching list.

He starts with an alphabetically ordered list of $n$ professors numbered $0, 1, \ldots, n-1$ and a non-negative integer $m < 10^{9}$. The first person in the marching list is the one at position $m \bmod n$ in the alphabetic list. That person is removed, which shortens the list by one and shifts down everyone at positions greater than $m \bmod n$. The second person is the one at position $m \bmod (n-1)$, and so on.

For example, assume there are six professors A, B, C, D, E and F. If $m = 11679$, the marching list is created as follows:

The method sounds fair, but it is hard to verify. Dean Roberts does not publish the value of $m$ he uses, so the faculty cannot tell whether he follows the stated method or picked the order by personal preference. The faculty wants to know whether some value of $m$ produces a given marching order.

The first line contains a single decimal integer $n$ ($5 \leq n \leq 20$), the number of professors who will march. The second line contains a string, a permutation of the first $n$ uppercase letters of the alphabet, giving the proposed marching order.

If the given marching order could not have come from the algorithm, print a single line containing NO. Otherwise, print two lines. The first line contains YES. The second line contains the smallest non-negative value of $m$ that produces the given marching order.