You are given a string S which consists of numerical characters only. You need to calculate the sum of all the augustic values that are possible for string S$.$ You can use the following method to calculate the augustic values of a given string. You can insert any number of signs between the characters of a string to create a new string and then convert it into an integer to make it an augustic value. For example the given string is $432$ so all the possible augustic values of the string $432$ are : $4+32,43=2,4+3+2$ and $432.$ Which are $36,45,9$ and $32.$ Your task is to find and return a string representing the sum of all possible augustic values for the given string.Input:$111$ Output:$138$ Explanation: Here the given string is $111$ So$,$ the possible values for this string are: $(1+1111+11+1+1111)$ which is$(12,12,3$ and $111).$Therefore the sum of all these augustic values is $138.$Please provide java code.