Records in Good Sequences

A sequence $S$ of positive integers, not necessarily distinct is a good sequence if:
- when $k\in S$, then $(k-1)\in S$ for $k\ge 2$
- the first occurence of $k-1$ in $S$ appears before the last occurence of $k$

Examples:
$\{3,1,3,1,2\}$ is not a good sequence: the 1st occurence of 2 is after the last 3.

The following sequences are good:
$\{2,2,1,3,2\}$
$\{1,3,2,1,3\}$
$\{3,1,1,2,3\}$
$\{3,2,3,1,2\}$
$\{1,2,1,3,1\}$

In a sequence $S=\{a_1,a_2,a_3,\dots ,a_n\},a_j$ is a record if it is greater than all elements before it : $\mathrm{\forall }i<j,a_i<aj$

The sequence $\{4,7,5,1,6,8,2,3\}$ contains 3 records: $4,7,8$

Amongst all good sequences with 100 elements in $\{1,2,3,\dots ,100\}$, how many have 3 records?

Answer format: Give the last 10 significant digits (before trailing 0s)