Let the system of equations
$
x + 5y - z = 1
$
$
4x + 3y - 3z = 7
$
$
24x + y + \lambda z = \mu
$
where $ \lambda, \mu \in \mathbb{R} $, have infinitely many solutions. Then the number of the solutions of this system, if $x, y, z$ are integers and satisfy $7 \leq x + y + z \leq 77$, is: