Two positive integers $x$ and $y$ ($x>y$) can generate a sequence in the following manner:

• $a_x=y$ is the first term,
• $a_{z+1}=a_z^{2}modz$ for $z=x,x+1,x+2,\dots$ and
• the generation stops when a term becomes $0$ or $1$.

The number of terms in this sequence is denoted $l(x,y)$.

For example, with $x=5$ and $y=3$, we get $a_5=3$, $a_6=3^{2}mod5=4$, $a_7=4^{2}mod6=4$, etc. Giving the sequence of 29 terms:
$3,4,4,2,4,7,9,4,4,3,9,6,4,16,4,16,16,4,16,3,9,6,10,19,25,16,16,8,0$
Hence $l(5,3)=29$.

$g(x)$ is defined to be the maximum value of $l(x,y)$ for $y<x$. For example, $g(5)=29$.

Further, define $f(n)$ to be the maximum value of $g(x)$ for $x\le n$. For example, $f(100)=145$ and $f(10000)=8824$.

Find $f(3000000)$.