Magic Square Transformation

You are given a 3×3 grid of integers. Your task is to convert this grid into a magic square with minimum cost. A magic square is a 3×3 grid in which every row, column, and both main diagonals all add up to the same constant. The cost of changing a number is defined as the absolute difference between the original and the new value. In other words, if you change an element from s_i to m_i, then the cost incurred is |s_i - m_i|. The overall cost is the sum of the individual costs, i.e.,

\[ \text{cost} = \sum_{i=0}^{8} |s_i - m_i| \]

Find the minimum cost required to convert the given grid into any magic square. There are only eight possible 3×3 magic squares, which can be precomputed and used to solve the problem.

inputFormat

The input consists of 3 lines. Each line contains 3 space-separated integers representing a row of the grid.

outputFormat

Output a single integer, which is the minimum cost to convert the input grid into a magic square.

4 9 2
3 5 7
8 1 6

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