Let $f(n)$ be the largest positive integer $x$ less than ${10}^9$ such that the last $9$ digits of $n^x$ form the number $x$ (including leading zeros), or zero if no such integer exists.

For example:

• $f(4)=411728896$ ($4^{411728896}=\cdots 490\underset{―}{411728896}$)
• $f(10)=0$
• $f(157)=743757$ (${157}^{743757}=\cdots 567\underset{―}{000743757}$)
• $\sum _{2\le n\le {10}^3}f(n)=442530011399$

Find $\sum _{2\le n\le {10}^6}f(n)$.