JEE Advanced 2023 Mathematics question on Definite Integrals and Areas

Let $n \geq 2$ be a natural number and $f:[0,1] \to \mathbb{R}$ be the function defined by
$$f(x) = \begin{cases} n(1-2nx) & \text{if } 0 \leq x \leq \dfrac{1}{2n} \\ 2n(2nx-1) & \text{if } \dfrac{1}{2n} \leq x \leq \dfrac{3}{4n} \\ 4n(1-nx) & \text{if } \dfrac{3}{4n} \leq x \leq \dfrac{1}{n} \\ \dfrac{n}{n-1}(nx-1) & \text{if } \dfrac{1}{n} \leq x \leq 1 \end{cases}$$
If $n$ is such that the area of the region bounded by the curves $x = 0$, $x = 1$, $y = 0$ and $y = f(x)$ is $4$, then the maximum value of the function $f$ is