class Solution {
  private static final int SQUARE_SIZE = 3;

  private int sum(int[][] grid, int y, int x, int dy, int dx) {
    int total = 0;
    for (int d = 0; d < SQUARE_SIZE; ++d) {
      total += grid[y + d * dy][x + d * dx];
    }
    return total;
  }

  private static final int ALL_DIGITS = (~(((~0) >> 9) << 9));

  private boolean isMagicSquare(int[][] grid, int y, int x) {
    // check the digits
    int seen = 0;
    for (int d = 0; d < SQUARE_SIZE * SQUARE_SIZE; ++d) {
      int dy = d / SQUARE_SIZE, dx = d % SQUARE_SIZE;

      int digit = grid[y + dy][x + dx];
      if (digit < 1 || digit > 9) {
        // out of range
        return false;
      }

      seen |= 1 << (digit - 1);
    }

    if (seen != ALL_DIGITS) {
      // repeated digits
      return false;
    }

    // check the sums
    int expectedSum = sum(grid, y, x, 1, 1);
    int diag2 = sum(grid, y, x + 2, 1, -1);
    if (diag2 != expectedSum) {
      // diagonals are broken
      return false;
    }

    for (int d = 0; d < SQUARE_SIZE; ++d) {
      if (sum(grid, y + d, x, 0, 1) != expectedSum) {
        return false;
      }

      if (sum(grid, y, x + d, 1, 0) != expectedSum) {
        return false;
      }
    }

    return true;
  }

  public int numMagicSquaresInside(int[][] grid) {
    int squares = 0;

    for (int y = 0; y + 2 < grid.length; ++y) {
      for (int x = 0; x + 2 < grid[y].length; ++x) {
        if (isMagicSquare(grid, y, x)) {
          ++squares;
        }
      }
    }

    return squares;
  }
}