#include <iostream>
using namespace std;

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;
}

/** Read a Sudoku puzzle from the keyboard */
void readASolution(int grid[][9])
{
  cout << "Enter a Sudoku puzzle solution:" << endl;
  for (int i = 0; i < 9; i++)
    for (int j = 0; j < 9; j++)
      cin >> grid[i][j];
}

// Check whether the fixed cells are valid in the grid 
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
}