#include<stdio.h>
int main()
{
	bool fill(int board_[9][9]);
	int JudgeMent(int board[9][9]);
	bool judge = 1; 
	int result = 0;
	int b_0[9][9];
	for ( int i=0;i<9;i++)
	{
		for(int j=0;j<9;j++)
		{
			scanf("%d",&b_0[i][j]); 			
		}
		
	}//读取数组
	
	 
	judge=JudgeMent(b_0);
	if(judge==1)
	{
		
		if(!fill(b_0))
		{
			printf("No solution");
		}
		else
		{
			printf("|-----------------------|\n");
			for(int i=0;i<9;i++)
			{
				printf("| ");
				for (int  j=0;j<9;j++)
				{
					printf("%d ",b_0[i][j]);
					if(j==2||j==5)printf("| ");
					if(j==8) printf("|\n");
				}
				if(i==2||i==5||i==8)printf("|-----------------------|\n");		
			}
		}
	}
	
	return 0;
	
}
bool fill(int board_[9][9])
{
	bool isValid(int board[9][9], int row, int col, int k);
	int JudgeMent(int board[9][9]);
	int Judgement(int board[9][9]);
	for ( int i=0;i<9;i++)
	{
		for(int j=0;j<9;j++)
		{
			if(board_[i][j]!=0)
			{
				//b_0[i][j]++;
				continue;
			} 
			for(int k=1;k<=9;k++)
			{
				if(isValid( board_,  i,  j,  k)) {
                    board_[i][j] = k;
                    /* 判断下一层递归之后是否找到一种解法，是则返回true */
                    if (fill(board_)) 
					{
                        return true;
                    }
                    /* 回溯，将当前位置清零 */
                    board_[i][j] = 0;
                }
				
			}
			return 0;			
		}
		
	}
	return 1;
}

int JudgeMent(int board[9][9])
{
	int parallel[9][9]={0};//用于计数，计算每行1-9出现的次数 
	int vertical[9][9]={0}; //用于计数，计算每列1-9出现的次数 
	int a[9][9]={0}; //用于计数，计算每块1-9出现的次数 
	int element,line=0, column=0, block =0;
	int i,j,k;//用于控制循环 
	int err01,err02,err12,err11,err21,err22;//记录数据出错的位置 
	bool judgement=0;
	printf("The original Sudoku matrix: \n") ;
	printf("|-----------------------|\n");
	for(i=0;i<9;i++)
	{
		printf("| ");
		for ( j=0;j<9;j++)
		{
			printf("%d ",board[i][j]);
			if(j==2||j==5)printf("| ");
			if(j==8) printf("|\n");
		}
		if(i==2||i==5||i==8)printf("|-----------------------|\n");		
	}//输出数组； 
	
	for ( i=0;i<9;i++)
	{
		for( j=0;j<9;j++)
		{
			if(board[i][j]>=1&&board[i][j]<=9)
			{
				element=board[i][j];
				parallel[i][element-1]++;
			}
			
		}
		
	}//统计各行各个数字出现的次数 
	for ( i=0;i<9;i++)
	{
		for( j=0;j<9;j++)
		{
			if(parallel[i][j]>1)
			{
				line=parallel[i][j];
				err01=j+1;
				err02=i+1;
				goto end;
			}			
		}
		
	}//判断行 
	for ( i=0;i<9;i++)
	{
		for( j=0;j<9;j++)
		{
			if(board[i][j]>=1&&board[i][j]<=9)
			{
				element=board[i][j];
				vertical[element-1][j]++;
			}
			
		}
		
	}
	for ( i=0;i<9;i++)
	{
		for( j=0;j<9;j++)
		{
			if(vertical[i][j]>1)
			{
				column=vertical[i][j];
				err11=j+1;
				err12=i+1;
				goto end;
			}			
		}
		
	}
	//判断列 
	for (i=0;i<9;i++)
	{
		for(j=0;j<9;j++)
		{
			if(board[i][j]>=1&&board[i][j]<=9)
			{
				element=board[i][j];
				k=i/3*3+j/3; 
				a[k][element-1]++;
			}
			
		}
	}
	for ( i=0;i<9;i++)
	{
		for( j=0;j<9;j++)
		{
			if(a[i][j]>1)
			{
				block=a[i][j];
				err21=i+1;
				err22=j+1;
				goto end;
			}			
		}
		
	}
	//判断块 
	end:
	if(line>1)
	{
		printf("False:Invalid initial Sudoku matrix!\n");
		printf("The number %d in the line %d has been used!",err01,err02);
	}
	else if(column>1)
	{
		printf("False:Invalid initial Sudoku matrix!\n");
		printf("The number %d in the column %d has been used!",err12,err11);
	}	
	else if(block>1)
	{
		printf("False:Invalid initial Sudoku matrix!\n");
		printf("The number %d in the block %d has been used!",err22,err21);
	}
	else
	{
			printf("True:Valid initial Sudoku matrix!\n");
			judgement=1;
	}
	return judgement;

}
bool isValid(int board[9][9], int row, int col, int k) {
    // 判断当前行是否有重复元素 
    for (int i = 0; i < 9; i++) {
        if (board[i][col] == k) {
            return false;
        }
    }
	// 判断当前列是否有重复元素 
    for (int j = 0; j < 9; j++) {
        if (board[row][j] == k) {
            return false;
        }
    }
    // 计算当前9宫格左上角的位置 
    int startRow = (row / 3) * 3;
    int startCol = (col / 3) * 3;
    //判断当前元素所在九宫格是否有重复元素 
    for (int i = startRow; i < startRow + 3; i++) {
        for (int j = startCol; j < startCol + 3; j++) {
            if (board[i][j] == k) {
                return false;
            }
        }
    }
    //满足条件，返回true 
    return true;
}