The team at a TomTom International factory has been assigned a critical optimization task aimed at improving the efficiency of packing a set of boxes, each labeled with a unique ID. These boxes are initially arranged in a single row from left to right, where the ID of the i-th box is represented by the string s_id, which consists of digits ranging from 0 to 9, inclusive.

To streamline the packing process, the team has been granted the ability to perform a specific operation an arbitrary number of times, including zero times if necessary. The operation is defined as follows:

Given the initial arrangement of boxes represented by the string s_id, the goal is to determine the lexicographically minimal string that can be achieved by applying the allowed operations optimally.

Clarification on Lexicographic Order:

A string X is considered lexicographically smaller than another string Y of the same length if and only if, at the first position where X and Y differ, the corresponding digit in X is smaller than the corresponding digit in Y.

Objective: Find and return the lexicographically smallest possible string that can be formed by performing the given operation any number of times.