You are given a string word that was produced by typing some original string, where during typing the key for a character may have been held down, causing that character to appear multiple times consecutively in word. Each maximal block of identical consecutive characters in word must correspond to at least one occurrence of that character in the original string.

Return the number of distinct original strings that could have resulted in word.

Constraints:

• $1 \leq$ word.length $\leq 100$

• word consists only of lowercase English letters.

Input: word = "a"-str
Output: 1-int
Explanation: There is one block "a" of length 1, so the original must contain exactly one 'a', and only "a" is possible.

Input: word = "aa"-str
Output: 2-int
Explanation: There is one block "aa" (length 2). The original could have had 1 'a' (held to make "aa") or 2 'a's (no hold), so the possible originals are "a" and "aa".

Input: word = "abbccc"-str
Output: 6-int
Explanation: The blocks are "a" (len 1), "bb" (len 2), and "ccc" (len 3), and each block in the original can contain between 1 and the block length occurrences: 'a' has 1 choice, 'b' has 2 choices (1 or 2), and 'c' has 3 choices (1, 2, or 3), for a total of 1 * 2 * 3 = 6 distinct originals.

Input: word = "aaaa"-str
Output: 4-int
Explanation: There is one block of 'a' with length 4, so the original could have 1, 2, 3, or 4 'a' characters, giving 4 possible originals.

Input: word = "aabbaa"-str
Output: 8-int
Explanation: The blocks are "aa" (len 2), "bb" (len 2), and "aa" (len 2). Each block contributes 2 choices (the original count can be 1 or 2), so the total is 2 * 2 * 2 = 8.

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