A problem set ordering is considered well-indexed if the first letter of the title of the problem is the same as its index. For example, if the title of the problem is Well-indexed?
, its index must be W
(the $23$rd problem).
As you can see, the problem set of JCPC 2019 is not well-indexed as it contains less than $23$ problems.
Indexing of a set of problems is done uniquely starting from A
for the first problem, B
for the second problem, and so on.
You are given the first letter of the titles of $13$ problems. Determine if it is possible to rearrange the problems such that the ordering of the problem set is well-indexed.