A humongous Query

Let's define a 10-string as a string that contains only characters '1' and '0', starts with '1' and ends with '0'. For example, "10101010", "100" or "1010" are 10-strings, while "011", "11120" or "10101" are not. A subsequence of any 10-string is called humongous if it is of the form "1010...10" ("10" concatenated an arbitrary number of times). For example, the 10-string "110" contains exactly 2