Application Of Integration

Let f₁ : (0, \(\infty\)) \(\to\) R and f₂ : (0, \(\infty\)) \(\to\) R be defined by \({f_1}(x) = \int\limits_0^x {\prod\limits_{j = 1}^{21} {{{(t - j)}^j}dt} }\), 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 a₁, a₂, ....., a_n, \(\prod\nolimits_{i = 1}^n {{a_i}}\) denotes the product of a₁, a₂, ....., 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_i, i = 1, 2 in the interval (0, \(\infty\)).

The value of \(2{m_1} + 3{n_1} + {m_1}{n_1}\) is ___________.