Given an integer array arr, replace each element with its rank when the distinct values of arr are sorted in strictly increasing order.

The rank rules are:
The smallest distinct value has rank $1$.
If a value is the $k$ th smallest distinct value, its rank is $k$.
Equal values must receive the same rank.

Return the resulting array of ranks in the same order as arr.

Note: Ranks are assigned based only on the sorted order of distinct values, not on the original indices.

Constraints:

• $0 \leq$ arr.length $\leq 10^5$

• $-10^9 \leq$ arr[i] $\leq 10^9$

Input: arr = [40, 10, 20, 30]-List[int]
Output: [4, 1, 2, 3]-List[int]
Explanation: The sorted distinct values are [10, 20, 30, 40], so the ranks are 10→1, 20→2, 30→3, and 40→4. Mapping back to the original order gives [4, 1, 2, 3].

Input: arr = [100, 100, 100]-List[int]
Output: [1, 1, 1]-List[int]
Explanation: The only distinct value is 100, which gets rank 1, and all equal elements share the same rank.

Input: arr = [37, 12, 28, 9, 100, 56, 80, 5, 12]-List[int]
Output: [5, 3, 4, 2, 8, 6, 7, 1, 3]-List[int]
Explanation: The sorted distinct values are [5, 9, 12, 28, 37, 56, 80, 100], which get ranks 5→1, 9→2, 12→3, 28→4, 37→5, 56→6, 80→7, and 100→8; each element is then replaced accordingly.

Input: arr = [-10, 0, -10, 5]-List[int]
Output: [1, 2, 1, 3]-List[int]
Explanation: The sorted distinct values are [-10, 0, 5], so -10→1, 0→2, and 5→3. Both -10 values map to rank 1.

Input: arr = []-List[int]
Output: []-List[int]
Explanation: An empty array has no elements to rank, so the result is also empty.

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