You are given an integer array, nums of size $n$, where each number is distinct and falls within the range $[1, n]$. Your task is to sort the array in place while ensuring a time complexity of $O(n)$ and using only $O(1)$ extra space.

Constraints:

• $n ==$ nums.length

• $1 \leq$ $n$ $\leq10^3$

• Each element in nums is unique and within the range $[1, n]$.