Find the sum of all 9-digit positive integers having all nine numbers 1 through 9 and satisfying the following conditions:

- Sum of digits between 1 and 2 exclusive is 9.
- Sum of digits between 2 and 3 exclusive is 18.
- Sum of digits between 3 and 4 exclusive is 27.
- Sum of digits between 4 and 5 exclusive is 36.

**Note**: For example, for the number 135792468, the sum of digits between 1 and 2 exclusive is \(3+5+7+9=24\).

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