class SudokuSolver:
    @staticmethod
    def solve(puzzle):
        sudoku_dict = {}
        r = 'ABCDEFGHI'
        c = '123456789'
        for i in range(9):
            for j in range(9):
                sudoku_dict[r[i]+c[j]] = str(puzzle[i][j]) if puzzle[i][j] != 0 else c
        square = [[x+y for x in i for y in j] for i in ('ABC','DEF','GHI') for j in ('123','456','789')]
        peers = {}
        for key in sudoku_dict.keys():
            value = [i for i in square if key in i][0]
            row = [[x+y for x in i for y in j][0] for i in key[0] for j in c]
            col = [[x+y for x in i for y in j][0] for i in r for j in key[1]]
            peers[key] = set(x for x in value+row+col if x != key)
        for i in range(9):
            sudoku_dict = SudokuSolver.Check(sudoku_dict,peers)
        sudoku_dict = SudokuSolver.search(sudoku_dict, peers)
        solution = []
        for i in r:
            solution.append([])
            for j in c:
                solution[r.find(i)].append(int(sudoku_dict[i+j]))
        return solution

    @staticmethod
    def Check(sudoku_dict, peers):
        for k,v in sudoku_dict.items():
            if len(v) == 1:
                for s in peers[k]:
                    sudoku_dict[s] = sudoku_dict[s].replace(v,'')
                    if len(sudoku_dict[s])==0:
                        return False
        return sudoku_dict

    @staticmethod
    def search(sudoku_dict,peers):
        if SudokuSolver.Check(sudoku_dict,peers)==False:
            return False
        if all(len(sudoku_dict[s]) == 1 for s in sudoku_dict.keys()): 
            return sudoku_dict
        n,s = min((len(sudoku_dict[s]), s) for s in sudoku_dict.keys() if len(sudoku_dict[s]) > 1)
        res = []
        for value in sudoku_dict[s]:
            new_sudoku_dict = sudoku_dict.copy()
            new_sudoku_dict[s] = value
            ans = SudokuSolver.search(new_sudoku_dict, peers)
            if ans:
                res.append(ans)
        if len(res) > 1:
            raise Exception("Error")
        elif len(res) == 1:
            return res[0]