Counting Substhreengs

Substrings are strings formed by choosing a subset of contiguous characters from a string. This is well known. A little more obscure is the definition of substhreengs. A substhreeng is a substring which complies to the following additional requirements:

1. It is non-empty, and composed entirely of base 10 digits.

2. Interpreted in base 10 (allowing extra leading zeros), the resulting integer is a multiple of 3.

For instance, the string “130a303” contains 9 substhreengs: the substhreeng “3” three times, the substhreengs “30” and “0” twice each, and the substhreengs “303” and “03” once each. The substring “30a3” is not a substhreeng because it is not composed entirely of base 10 digits, while the substring “13” is not a substhreeng because 13 is not a multiple of 3.

Notice that two substhreengs are considered different if they are different in length or start at a different position, even if the selected characters are the same.

Given a string, you are asked to count the number of substhreengs it contains.