You are given an m x n binary matrix image where 0 represents a white pixel and 1 represents a black pixel.

The black pixels are connected (i.e., there is only one black region). Pixels are connected horizontally and vertically.

Given two integers x and y that represents the location of one of the black pixels, return the area of the smallest (axis-aligned) rectangle that encloses all black pixels.

You must write an algorithm with less than O(mn) runtime complexity

 

Example 1:

Input: image = [["0","0","1","0"],["0","1","1","0"],["0","1","0","0"]], x = 0, y = 2
Output: 6

Example 2:

Input: image = [["1"]], x = 0, y = 0
Output: 1

 

Constraints:

• m == image.length
• n == image[i].length
• 1 <= m, n <= 100
• image[i][j] is either '0' or '1'.
• 0 <= x < m
• 0 <= y < n
• image[x][y] == '1'.
• The black pixels in the image only form one component.