: A string vec
used as a vector of integer values,
in which each element vec[i]
represents the number of digits
in the group at position i
starting with position 0 as the rightmost group.
If vec.size() <= i
the number is the same as group (i - 1)
if (i < 0 || vec[i] <= 0 || vec[i] == CHAR_MAX)
the size of the digit group is unlimited.