Adding 0 makes no change, Really ?

Given that in the 8-digit number ABCDEFGH\overline{\mathrm{ABCDEFGH}},

(i) ABCD=EFGH\overline{\mathrm{ABCD}}=\overline{\mathrm{EFGH}}
(ii) The numbers ABCDEFGH\overline{\mathrm{ABCDEFGH}} and ABCD0EFGH\overline{\mathrm{ABCD0EFGH}} are both divisible by 1111.
Let the sum of all possible values of ABCDEFGH\overline{\mathrm{ABCDEFGH}} be NN.

Find the digit sum of NN.


Details and assumptions:-

  • ABC\overline{\mathrm{ABC}} means the number in decimal representation with digits A,B,CA,B,C i.e. ABC=100A+10B+C\overline{\mathrm{ABC}} = \mathrm{100A+10B+C}
  • The letters AA to HH do not necessarily stand for distinct digits.
  • In the second number, the digit 00 is added in the middle of the 8-digit number, which makes it a 9-digit number.
  • Digit sum is sum of all digits in decimal representation, digit sum of 1202312023 is 1+2+0+2+3=81+2+0+2+3=8
  • 00123 is not a 5-digit number.
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