642. As Far from Land as Possible

Given an n x n grid of 0s (water) and 1s (land), find the water cell whose distance to the nearest land is maximized, and return that distance (Manhattan). Return -1 if the grid is all land or all water. The input is JSON {grid}.

Input: JSON {grid}.

Output: Integer — the maximum distance, or -1.

Examples

Input: {"grid":[[1,0,1],[0,0,0],[1,0,1]]}
Output: 2
Explanation: The center is distance 2 from land.

Input: {"grid":[[1,0,0],[0,0,0],[0,0,0]]}
Output: 4
Explanation: The far corner.

Input: {"grid":[[0,0,0],[0,0,0]]}
Output: -1
Explanation: No land.

Constraints

• 1<=n<=100

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