CF1829E The Lakes

You are given an $ n \times m $ grid $ a $ of non-negative integers. The value $ a_{i,j} $ represents the depth of water at the $ i $ -th row and $ j $ -th column. A lake is a set of cells such that: - each cell in the set has $ a_{i,j} > 0 $ , and - there exists a path between any pair of cells in the lake by going up, down, left, or right a number of times and without stepping on a cell with $ a_{i,j} = 0 $ . The volume of a lake is the sum of depths of all the cells in the lake. Find the largest volume of a lake in the grid.

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