Origin

The *origin* of a positive integer is determined by iteratively summing its digits until only a single digit remains. For instance, to compute the *origin* of $129$, - The sum of digits of $129$ is $1+2+9 = 12$. - The sum of digits of $12$ is $1+2 = 3$. So, the *origin* of $129$ is $3$. Given a positive integer $N$, calculate the sum of the *origin* values of every integer from $1$ to $N$. #