Lets call $$$k$$$ the number of indices $$$i$$$ that satisfy $$$i \leq \frac{n}{2}$$$ and $$$p[i] \leq \frac{n}{2}$$$. Then the number of indices $$$i\leq \frac{n}{2}, p[i] \gt \frac{n}{2}$$$ is $$$\frac{n}{2}-k$$$, the number of indices $$$i \gt \frac{n}{2}, p[i] \leq \frac{n}{2}$$$ is $$$\frac{n}{2}-k$$$, and the number of indices $$$i \gt \frac{n}{2}, p[i] \gt \frac{n}{2}$$$ is $$$k$$$. This gives us a way to do it in exactly 2 operations.

Since we want the minimum number of operations, we only need to figure out if it is possible in 1 operation. Hopefully you are able to solve this case :)