Kiriti's number

Let NN be the smallest positive integer such that the product of 9999 and NN is a number with all digits 11. What is the digit sum of NN?

This problem is posed by Kiriti M.

Details and assumptions

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is 1+1+2+3=71 + 1 + 2 + 3 = 7.

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