A number N fulfills the following conditions:

1, It consists of nine distinct digits.

2. The inclusive sum of digits between the digits 1 and 2 is 12.

3. The inclusive sum of digits between the digits 2 and 3 is 23.

4. The inclusive sum of digits between the digits 3 and 4 is 34.

5. The inclusive sum of digits between the digits 4 and 5 is 45.

What are the lowest and the highest values of N?