#47Hitori

Hitori is a number-grid puzzle in which you must shade certain cells black so that the remaining white cells follow specific rules. You are given an n x n integer matrix called grid. Your task is to solve the Hitori puzzle and return an n x n matrix representing the solution.

Each cell in the resulting matrix must contain:

• 0 : The cell is shaded black.
• 1 : The cell remains white.

The resulting grid must satisfy all the following rules:

• No Repeated Numbers in Rows: No number should appear more than once among the white cells of any row.
• No Repeated Numbers in Columns: No number should appear more than once among the white cells of any column.
• No Adjacent Black Cells: Two black cells must never share an edge. Diagonal adjacency is allowed.
• All White Cells Must Be Connected: Every white cell must be reachable from every other white cell by moving up, down, left, or right through white cells.
• Only Duplicate Cells Can Be Shaded: A cell can be shaded black only if its number occurs more than once in its row or column.

Return the resulting matrix representing the solved puzzle. Note: Every puzzle is guaranteed to have exactly one valid solution.