Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by
$ f_1(x)=\int_0^x \prod_{j=1}^{21}(t-j)^j d t, x>0 $
and
$ f_2(x)=98(x-1)^{50}-600(x-1)^{49}+2450, x>0 $
where, for any positive integer $n$ and real numbers $a_1, a_2, \ldots, a_n, \prod_{i=1}^n a_i$ denotes the product of $a_1, a_2, \ldots, a_n$. Let $m_i$ and $n_i$, respectively, denote the number of points of local minima and the number of points of local maxima of function $f_{\mathrm{i}}, \mathrm{i}=1,2$, in the interval $(0, \infty)$

The value of $2 m_1+3 n_1+m_1 n_1$ is $\_\_\_\_$ .