#include <iostream>
#include<cmath>
#include<ctime>
#include<string>
#include <iomanip>
#include <fstream>

using namespace std;

int octal2Dec(string& octal);
bool validity(int number);
int stringToNum(string number);
int bin2Dec(int binNumber);
int dec2octal(const string& number);



void readASolution(int grid[][9]);
 bool isValid(const int grid[][9]);
 bool isValid(int i, int j, const int grid[][9]);

 int main()
{
	 // Read a Sudoku puzzle
		 int grid[9][9];
	 readASolution(grid);
	
		 cout << (isValid(grid) ? "Valid solution" : "Invalid solution");
	
		 return 0;
		 system("pause");
 }

 // Read a Sudoku puzzle from the keyboard
 void readASolution(int grid[][9])
 {
	 cout << "Enter a Sudoku puzzle:" << endl;
	 for (int i = 0; i < 9; i++)
		 for (int j = 0; j < 9; j++)
		 cin >> grid[i][j];
 }
 bool isValid(const int grid[][9])
	 {
	  for (int i = 0; i < 9; i++) 
		  for (int j = 0; j < 9; j++)
		  if (grid[i][j] < 1 || grid[i][j] > 9 ||
			  !isValid(i, j, grid))
		  return false;
	 
		  return true; // The fixed cells are valid
 }
 
	  // Check whether grid[i][j] is valid in the grid
 bool isValid(int i, int j, const int grid[][9])
 {
	 // Check whether grid[i][j] is valid at the i's row
	 for (int column = 0; column < 9; column++)
		 if (column != j && grid[i][column] == grid[i][j])
			 return false;

	 // Check whether grid[i][j] is valid at the j's column
	 for (int row = 0; row < 9; row++)
		 if (row != i && grid[row][j] == grid[i][j])
			 return false;

	 // Check whether grid[i][j] is valid in the 3-by-3 box
	 for (int row = (i / 3) * 3; row < (i / 3) * 3 + 3; row++)
		 for (int col = (j / 3) * 3; col < (j / 3) * 3 + 3; col++)
			 if (row != i && col != j && grid[row][col] == grid[i][j])
				 return false;

	 return true; // The current value at grid[i][j] is valid
 }