Maximum Connected Component Sum in a Grid

You are given a grid of non-negative integers with m rows and n columns. A cell with value 0 is blocked. A cell with a positive value belongs to a component.

A component is a maximal group of positive cells connected 4-directionally (up, down, left, or right). The sum of a component is the total of its cell values.

Return the largest component sum in the grid, or 0 if every cell is 0.

Examples

Example 1

Input:  grid = [[0, 2, 1, 0],
                [4, 0, 0, 3],
                [1, 0, 0, 4],
                [0, 3, 2, 0]]
Output: 7
Explanation: The largest connected group of positive cells has values 3 and 4, for a total of 7.

Example 2

Input:  grid = [[1, 0, 0, 0],
                [0, 0, 0, 0],
                [0, 0, 0, 0],
                [0, 0, 0, 1]]
Output: 1
Explanation: Two separate single-cell components each have value 1, so the largest sum is 1.