Find The Sum of the First n Bouncy Numbers Terminology

An increasing number is one where each digit is greater than or equal to all the digits to the left of it (ex. 12239)

A decreasing number is one where each digit is less than or equal to all the digits to the left of it (ex. 95531)

A bouncy number is any number that is not increasing or decreasing. Since this requires at least 3 digits, the first bouncy number is 101

The task

Given an integer n greater than or equal to 1, find the sum of the first n bouncy numbers

Rules


This is code golf, so the answer with the shortest amount of bytes wins
If your language has limits on integer size (ex. 2^32-1) n will be small enough that the sum will fit in the integer
Input can be any reasonable form (stdin, file, command line parameter, integer, string, etc)
Output can be any reasonable form (stdout, file, graphical user element that displays the number, etc)


Test cases

1 &gt; 101
10 &gt; 1065
44701 &gt; 1096472981
Jelly, 10 8 bytes

ṢeṚƬ¬µ#S


Try it online!

How it works

ṢeṚƬ¬µ#S  Main link. No arguments.

      #   Read an integer n from STDIN and call the chain to the left with argument
          k = 0, 1, 2, ... until n of them return a truthy result.
          Yield the array of successful values of k.
     µ    Monadic chain. Argument: k (integer)
Ṣ           Sort, after promoting k to its digit array.
  ṚƬ        Reverse 'til the results are no longer unique and yield unique results.
            Calling Ṛ on k promotes it to its digit array. If k = 14235, the 
            result is [14235, [5,3,2,4,1], [1,4,2,3,5]].
 e          Check if the result to the left appears in the result to the right.
    ¬       Negate the resulting Boolean.
       S  Take the sum.