Description

Given a m x n matrix of distinct numbers, return all lucky numbers in the matrix in any order. A lucky number is an element that is minimum in its row and maximum in its column.

Examples

Input:matrix = [[3,7,8],[9,11,13],[15,16,17]]
Output:[15]
Explanation:

15 is min in row and max in column.

Input:matrix = [[7,8],[1,2]]
Output:[7]
Explanation:

7 is the minimum in its row [7,8] and also the maximum in its column [7,1]. The number 1 is minimum in row [1,2] but not maximum in column [7,1]. The number 2 is maximum in column [8,2] but not minimum in its row.

Input:matrix = [[1,2,3,4,5]]
Output:[1,2,3,4,5]
Explanation:

In a single row matrix, every element is both the minimum of its row and the maximum of its column (since each column has only one element). Therefore, all elements [1,2,3,4,5] are lucky numbers.

Constraints

  • 1 ≤ m, n ≤ 50

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