There are some utility poles on the plane, which is addressed by a lattice an of size (n+1)×(m+1). There is a utility pole at (x,y) if ax,y=1. For each point (x,y), characterize S(x,y) as the square of the Euclidean distance between the closest post and (x,y). Officially, the square of the Euclidean distance between two focuses (x1,y1) and (x2,y2) is (x2−x1)2+(y2−y1)2.  To streamline the structure plan, the task director asks you

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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There are some utility poles on the plane, which is addressed by a lattice an of size (n+1)×(m+1). There is a utility pole at (x,y) if ax,y=1. For each point (x,y), characterize S(x,y) as the square of the Euclidean distance between the closest post and (x,y). Officially, the square of the Euclidean distance between two focuses (x1,y1) and (x2,y2) is (x2−x1)2+(y2−y1)2. 

To streamline the structure plan, the task director asks you the amount of all S(x,y) for each 0≤x≤n and 0≤y≤m. Help him by discovering the worth of ∑nx=0∑my=0S(x,y). 

Input :The main line contains two integers n and m (0≤n,m<2000) — the size of the framework. Then, at that point (n+1) lines follow, each containing (m+1) integers ai,j (0≤ai,j≤1) — the lattice signifying the places of utility poles in the plane. There is no less than one utility pole in the given lattice. 

Output :Output an integer meaning the worth of ∑nx=0∑my=0S(x,y).

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