The fragments of a positive integer are the numbers seen when reading one or more of its digits in order. The fragment sum equals the sum of all the fragments, including the number itself. For example, the fragment sum of $2022$ is $2022+202+022+20+02+22+2+0+2+2 = 2296$. There is another four-digit number with the same fragment sum. What is it? As the example shows, if a fragment occurs multiple times, then all its occurrences are added, and the fragments beginning with $0$ also count (for instance, $022$ is worth $22$).