With respect to a given puzzle string, a word is valid if both the following conditions are satisfied:

• word contains the first letter of puzzle.
• For each letter in word, that letter is in puzzle.
For example, if the puzzle is “abcdefg”, then valid words are “faced”, “cabbage”, and “baggage”; while invalid words are “beefed” (doesn’t include “a”) and “based” (includes “s” which isn’t in the puzzle).

Return an array answer, where answer[i] is the number of words in the given word list words that are valid with respect to the puzzle puzzles[i].

Example :

Input:
words = ["aaaa","asas","able","ability","actt","actor","access"],
puzzles = ["aboveyz","abrodyz","abslute","absoryz","actresz","gaswxyz"]
Output: [1,1,3,2,4,0]
Explanation:
1 valid word for "aboveyz" : "aaaa"
1 valid word for "abrodyz" : "aaaa"
3 valid words for "abslute" : "aaaa", "asas", "able"
2 valid words for "absoryz" : "aaaa", "asas"
4 valid words for "actresz" : "aaaa", "asas", "actt", "access"
There're no valid words for "gaswxyz" cause none of the words in the list contains letter 'g'.


Constraints:

• 1 <= words.length <= 10^5
• 4 <= words[i].length <= 50
• 1 <= puzzles.length <= 10^4
• puzzles[i].length == 7
• words[i][j]puzzles[i][j] are English lowercase letters.
• Each puzzles[i] doesn’t contain repeated characters.

## Solution: Subsets

Preprocessing:
Compress each word to a bit map, and compute the frequency of each bit map.
Since there are at most |words| bitmaps while its value ranging from 0 to 2^26, thus it’s better to use a hashtable instead of an array.

Query:
Use the same way to compress a puzzle into a bit map.
Try all subsets (at most 128) of the puzzle (the bit of the first character is be must), and check how many words match each subset.

words = [“aaaa”,”asas”,”able”,”ability”,”actt”,”actor”,”access”],
puzzle = “abslute”
bitmap(“aaaa”) = {0}
bitmap(“asas”) = {0, 18}
bitmap(“able”) = {0,1,4,11}
bitmap(“actt”) = {0, 2, 19}
bitmap(“actor”) = {0, 2, 14, 17, 19}
bitmap(“access”) = {0, 2, 4, 18}

bitmap(“abslute”) = {0, 1, 4, 11, 18, 19, 20}

Time complexity: O(sum(len(w_i)) + |puzzles|)
Space complexity: O(|words|)

## C++

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