Multiplicative persistence

Given a positive integer, we multiply all its digits; we obtain a new number.
We repeat the process until a fixed point.

Example :
Starting with $n=277777788888899$ , we have the following sequence:
$277777788888899\Rightarrow 4996238671872\Rightarrow 438939648\Rightarrow 4478976\Rightarrow 338688\Rightarrow \dots$
$\dots 27648\Rightarrow 2688\Rightarrow 768\Rightarrow 336\Rightarrow 54\Rightarrow 20\Rightarrow 0$
In this case, we have a chain of length 11.

This value is called the multiplicative persistence of n
$P(277777788888899)=11$

277777788888899 is actually the smallest integer with a multiplicative persistence of 11.

There are 5 15-digits numbers with a multiplicative persistenceof 11:
$277777788888899$
$367777778888889$
$447777778888899$
$466777777888889$
$666677777788888$

We only consider number in their canonical representation : digits in ascending order (as any permutation of a given number has the same multiplicative persistence as the original)

How many 25-digits numbers with a multiplicative persistence of 11 are there?
Answer format: count,sum

Example : $5,2226788902344464$ // For 15-digits numbers

[My timing: 60 sec]