For fixed integers $a,b,c$, define the crazy function $F(n)$ as follows:
$F(n)=n-c$ for all $n>b$
$F(n)=F(a+F(a+F(a+F(a+n))))$ for all $n\le b$.

Also, define $S(a,b,c)=\sum _{n=0}^{b}F(n)$.

For example, if $a=50$, $b=2000$ and $c=40$, then $F(0)=3240$ and $F(2000)=2040$.
Also, $S(50,2000,40)=5204240$.

Find the last $9$ digits of $S({21}^7,7^{21},{12}^7)$.