Let $(2, 3)$ be the largest open interval in which the function $f(x) = 2\log_{\mathrm{e}}(x - 2) - x^{2} + ax + 1$ is strictly increasing and $(\mathrm{b}, \mathrm{c})$ be the largest open interval, in which the function $\mathrm{g}(x) = (x - 1)^{3}(x + 2 - \mathrm{a})^{2}$ is strictly decreasing. Then $100(a + b - c)$ is equal to:\\
(1) 420\\
(2) 360\\
(3) 160\\
(4) 280