Childrens Game

There are many number games for children. These games are easy to play, but creating them is not so simple. Here is one interesting game: each player is given $n$ positive integers. By concatenating these numbers in any order, the player can form a large number. For example, if given $4$ numbers: $123$, $124$, $56$, $90$, one can form numbers like $1231245690$, $1241235690$, $5612312490$, $9012312456$, $9056124123$, etc. In total, $24$ such numbers can be formed. However, $9056124123$ is the largest possible number.

It may seem easy for you to find the answer, but is it just as simple for a child who is just learning numbers?