How to apply openMP to a C++ function to validate all rows of a sudoku puzzle solution?

I am designing a program that will test to see whether a valid sudoku puzzle solution is given to the program or not. I first designed it in C++ but now I want to try to make it parallel. The program compiles fine without errors.

First I had to figure out a way to deal with using a return statement inside of a structured block. I just decided to make an array of bool's that are initialized to true. However the output from this function is false and I know for a fact the solution I am submitting is true. I am new to openMP and was wondering if anyone could help me out?

I have a feeling the issue is with my variable a getting set back to 0 and maybe also with my other variable nextSudokuNum getting set back to 1.

bool test_rows(int sudoku[9][9])
{
   int i, j, a;
   int nextSudokuNum = 1;
   bool rowReturn[9];

#pragma omp parallel for private(i)
   for(i = 0; i < 9; i++)
   {
      rowReturn[i] = true;
   }

#pragma omp parallel for private(i,j) \
   reduction(+: a, nextSudokuNum)
   for(i = 0; i < 9; i++)
   {
      for(j = 0; j < 9; j++)
      {
         a = 0;
         while(sudoku[i][a] != nextSudokuNum) {
            a++;
            if(a > 9) {
               rowReturn[i] = false;
            }
         }

         nextSudokuNum++;
      }
      nextSudokuNum = 1;
   }

   for(i = 0; i < 9; i++)
   {
      if(rowReturn[i] == false) {
         cout << "Invalid Sudoku Solution(Next Valid Sudoku Number Not Found)" << endl;
         cout << "Check row " << (i+1) << endl;
         return false;
      }
   }

   cout << "Valid sudoku rows(Returning true)" << endl;
   return true;
}