Sum the Digits of All Integers 0 to 10^n - 1

Create a function that takes an integer parameter, n, and returns the sum of all the digits in each integer in the range 0 to 10^n - 1 inclusive.

• If n is 1, the range is 0 to 9.
• if n is 2, the range is 0 to 99.
• if n is 12, the range is 0 to 999999999999.

n will always be >= 0. For this challenge, the value of n will be limited to 10000, but the solution should theoretically work for numbers as large as 500000.

Examples

sum_digits_in_range(1) ➞ 45

sum_digits_in_range(2) ➞ 900

sum_digits_in_range(3) ➞ 13500

sum_digits_in_range(8) ➞ 3600000000

sum_digits_in_range(13) ➞ 585000000000000

Notes

• If n is 0, return 0.
• The function must take less than 12 seconds to run.