Let $F_5(n)$ be the number of strings $s$ such that:

• $s$ consists only of '0's and '1's,
• $s$ has length at most $n$, and
• $s$ contains a palindromic substring of length at least $5$.

For example, $F_5(4)=0$, $F_5(5)=8$, $F_5(6)=42$ and $F_5(11)=3844$.

Let $D(L)$ be the number of integers $n$ such that $5\le n\le L$ and $F_5(n)$ is divisible by $87654321$.

For example, $D({10}^7)=0$ and $D(5\cdot {10}^9)=51$.

Find $D({10}^{18})$.