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Water Flow


Problem Description

Given an N x M matrix A of non-negative integers representing the height of each unit cell in a continent, the "Blue lake" touches the left and top edges of the matrix and the "Red lake" touches the right and bottom edges.

Water can only flow in four directions (up, down, left, or right) from a cell to another one with height equal or lower.

Find the number of cells from where water can flow to both the Blue and Red lake.



Problem Constraints

1 <= M, N <= 1000

1 <= A[i][j] <= 109



Input Format

First and only argument is a 2D matrix A.



Output Format

Return an integer denoting the number of cells from where water can flow to both the Blue and Red lake.



Example Input

Input 1:

 A = [
       [1, 2, 2, 3, 5]
       [3, 2, 3, 4, 4]
       [2, 4, 5, 3, 1]
       [6, 7, 1, 4, 5]
       [5, 1, 1, 2, 4]
     ]

Input 2:

 A = [
       [2, 2]
       [2, 2]
     ]



Example Output

Output 1:

 7

Output 2:

 4



Example Explanation

Explanation 1:

 Blue Lake ~   ~   ~   ~   ~ 
        ~  1   2   2   3  (5) *
        ~  3   2   3  (4) (4) *
        ~  2   4  (5)  3   1  *
        ~ (6) (7)  1   4   5  *
        ~ (5)  1   1   2   4  *
           *   *   *   *   * Red Lake
 Water can flow to both lakes from the cells denoted in parentheses.

Explanation 2:

 Water can flow from all cells.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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