Given an `m x n`

`matrix`

, return *a new matrix *`answer`

* where *`answer[row][col]`

* is the ***rank** of `matrix[row][col]`

.

The **rank** is an **integer** that represents how large an element is compared to other elements. It is calculated using the following rules:

- The rank is an integer starting from
`1`

. - If two elements
`p`

and`q`

are in the**same row or column**, then:- If
`p < q`

then`rank(p) < rank(q)`

- If
`p == q`

then`rank(p) == rank(q)`

- If
`p > q`

then`rank(p) > rank(q)`

- If
- The
**rank**should be as**small**as possible.

It is guaranteed that `answer`

is unique under the given rules.

**Example 1:**

Input:matrix = [[1,2],[3,4]]Output:[[1,2],[2,3]]Explanation:The rank of matrix[0][0] is 1 because it is the smallest integer in its row and column. The rank of matrix[0][1] is 2 because matrix[0][1] > matrix[0][0] and matrix[0][0] is rank 1. The rank of matrix[1][0] is 2 because matrix[1][0] > matrix[0][0] and matrix[0][0] is rank 1. The rank of matrix[1][1] is 3 because matrix[1][1] > matrix[0][1], matrix[1][1] > matrix[1][0], and both matrix[0][1] and matrix[1][0] are rank 2.

**Example 2:**

Input:matrix = [[7,7],[7,7]]Output:[[1,1],[1,1]]

**Example 3:**

Input:matrix = [[20,-21,14],[-19,4,19],[22,-47,24],[-19,4,19]]Output:[[4,2,3],[1,3,4],[5,1,6],[1,3,4]]

**Example 4:**

Input:matrix = [[7,3,6],[1,4,5],[9,8,2]]Output:[[5,1,4],[1,2,3],[6,3,1]]

**Constraints:**

`m == matrix.length`

`n == matrix[i].length`

`1 <= m, n <= 500`

`-10`

^{9}<= matrix[row][col] <= 10^{9}

class Solution {
public int[][] matrixRankTransform(int[][] matrix) {
}
}