It is known that there is a number $S$ such that if $ a+b+c+d = S$ and $\frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}+ \frac{1}{d} = S$ $(a, b, c, d$ are different from zero and one$)$, then $\frac{1}{a- 1} ++ \frac{1}{b- 1} + \frac{1}{c- 1} + \frac{1}{d -1} = S.$ Find $S$.