Hatred of Eleven II

We define an "Eleven Hater" as a number that is not a multiple of eleven, but becomes a multiple of 1111 when any one digit is removed.

For clarity, consider a 3 digit number abc \overline {abc} . if abc \overline {abc} is an "Eleven Hater", then ab,ac, \overline {ab}, \overline{ac}, and bc\overline{bc} should all be multiples of 1111. Note that the order of the digits are not to be altered.

How many 5-digit Eleven Haters are there?

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