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# 1331. Rank Transform of an Array

<https://leetcode.com/problems/rank-transform-of-an-array>

## Description

Given an array of integers `arr`, replace each element with its rank.

The rank represents how large the element is. The rank has the following rules:

* Rank is an integer starting from 1.
* The larger the element, the larger the rank. If two elements are equal, their rank must be the same.
* Rank should be as small as possible.

**Example 1:**

```
**Input:** arr = [40,10,20,30]
**Output:** [4,1,2,3]
**Explanation**: 40 is the largest element. 10 is the smallest. 20 is the second smallest. 30 is the third smallest.
```

**Example 2:**

```
**Input:** arr = [100,100,100]
**Output:** [1,1,1]
**Explanation**: Same elements share the same rank.
```

**Example 3:**

```
**Input:** arr = [37,12,28,9,100,56,80,5,12]
**Output:** [5,3,4,2,8,6,7,1,3]
```

**Constraints:**

* `0 <= arr.length <= 105`
* `-109 <= arr[i] <= 109`

## ac

```java
```