$N$ disks are placed in a row, indexed $1$ to $N$ from left to right.
Each disk has a black side and white side. Initially all disks show their white side.

At each turn, two, not necessarily distinct, integers $A$ and $B$ between $1$ and $N$ (inclusive) are chosen uniformly at random.
All disks with an index from $A$ to $B$ (inclusive) are flipped.

The following example shows the case $N=8$. At the first turn $A=5$ and $B=2$, and at the second turn $A=4$ and $B=6$.

Let $E(N,M)$ be the expected number of disks that show their white side after $M$ turns.
We can verify that $E(3,1)=10/9$, $E(3,2)=5/3$, $E(10,4)\approx 5.157$ and $E(100,10)\approx 51.893$.

Find $E({10}^{10},4000)$.
Give your answer rounded to $2$ decimal places behind the decimal point.