Let $$\begin{array}{c}p(x)=x^3-3x^2+2x,x\in \mathbb{R},\\ f_0(x)=\{\begin{array}{ll}{\int }_0^{x}p(t)dt,& x\ge 0,\\ -{\int }_x^{0}p(t)dt,& x<0,\end{array}\\ f_1(x)=e^{f_0(x)},f_2(x)=e^{f_1(x)},\dots ,f_n(x)=e^{f_{n-1}(x)}\end{array}$$ How many roots does the equation $\frac{d{f}_n(x)}{dx}=0$ have in the interval $(-\mathrm{\infty },\mathrm{\infty })?$