The beauty of a string is the difference in frequencies between the most frequent and least frequent characters.

• For example, the beauty of "abaacc" is 3 - 1 = 2.

Given a string s, return the sum of beauty of all of its substrings.

 

Example 1:

Input: s = "aabcb"
Output: 5
Explanation: The substrings with non-zero beauty are ["aab","aabc","aabcb","abcb","bcb"], each with beauty equal to 1.

Example 2:

Input: s = "aabcbaa"
Output: 17

 

Constraints:

• 1 <= s.length <= 500
• s consists of only lowercase English letters.