Sum of digits equation

We define $DS(n)=n+SOD(n)$ where SOD(n) is the sum of the digits of n (See problem 260)

It can be proved that ${10}^{13}+1$ is the smallest integer such as the equation $DS(x)=n$ has 3 solutions.
$${10}^{13}+1=\{\begin{array}{l}DS(9999999999892)\\ DS(9999999999901)\\ DS(10000000000000)\end{array}$$ It can be proved too that $n={10}^{2222222222224}+10000000000002$ is the smallest integer with 6 solutions.

Obviously, if x is a solution we must have $x<n$. Thus, we can write a solution as $n-x_i$

Find these solutions.

Answer format: $x_1,x_2,x_3,x_4,x_5,x_6$ // $x_i$ in ascending order

Example : 1,100,109 // For ${10}^{13}+1$

[My timing: < 1 sec]

Thanks to sinan who helped me to improve this problem.