Let \((2,3)\) be the largest open interval in which the function \(f(x)=2 \log _{\mathrm{e}}(x-2)-x^2+a x+1\) is strictl…

Let \((2,3)\) be the largest open interval in which the function \(f(x)=2 \log _{\mathrm{e}}(x-2)-x^2+a x+1\) is strictly increasing and \((b, c)\) 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 :

[JEE Main 2025, 24 Jan (Shift 2)]