import java.util.ArrayList;
import java.util.concurrent.ThreadLocalRandom;

class Grid {

private int dimension;
private Point currentPoint;
private ArrayList<Point> path;
private ArrayList<Point> nextPoints;
private int length;

Grid(int dimension) {
   this.dimension = dimension;
   this.length = 0;

   if (this.dimension == 2) {
         // Create 2 dimensional path for this grid. And start with origin (0, 0) point.
         this.currentPoint = new Point2D(0, 0);

   } else if (this.dimension == 3) {
         // Create 3 dimensional path for this grid. And start with origin (0, 0, 0) point.
         this.currentPoint = new Point3D(0, 0, 0);

   } else if (this.dimension == 4) {
         // Create 4 dimensional path for this grid. And start with origin (0, 0, 0, 0) point.
         this.currentPoint = new Point4D(0, 0, 0, 0);

   } else {
         System.out.println("Invalid dimension. Only supports [2, 3, 4]");
         System.exit(-1);
   }

   // Initialize list to store points on the path.
   this.path = new ArrayList<>();

   // Add origin point to the path.
   this.path.add(currentPoint);

   // Generate available next moves.
   this.updateNextPoints();

}

void move() {
   // If there is any point which is free, move to that point.
   if (canMove()) {
         // Get random number (use the size of available points as limit of random generation.)
         int r = ThreadLocalRandom.current().nextInt(nextPoints.size());
         // Get the next point using generated random number.
         Point nextPoint = nextPoints.get(r);
         // Add next point to the path.
         path.add(nextPoint);
         // Update the current point.
         currentPoint = nextPoint;
         // Increase the length of the path by 1.
         length++;
         // Update next available points to move.
         updateNextPoints();
   }
}

private boolean isFreePoint(Point point) {
   // Return true if given point is not in the path, false if already exists.
   for (Point p : path) {
         if (p.isEqual(point))
            return false;
   }
   return true;
}

boolean canMove() {
   // Return true if there is any free point to move.
   return nextPoints.size() > 0;
}

int getLength() {
   // Return the current length of the path.
   return length;
}

double getDistance() {
   // Return the End-to-end squared distance of current point.
   return currentPoint.getDistance();
}

private void updateNextPoints() {
   // Clear the current next point array and create new one.
   nextPoints = new ArrayList<>();
   Point point;

   if (dimension == 2) {
         // If the dimension is 2, generate all possible 4 points and add only free points to the nextPoints list.
         Point2D cp = (Point2D) currentPoint;

         point = new Point2D(cp.x + 1, cp.y);
         if (isFreePoint(point))
            nextPoints.add(point);

         point = new Point2D(cp.x - 1, cp.y);
         if (isFreePoint(point))
            nextPoints.add(point);

         point = new Point2D(cp.x, cp.y + 1);
         if (isFreePoint(point))
            nextPoints.add(point);

         point = new Point2D(cp.x, cp.y - 1);
         if (isFreePoint(point))
            nextPoints.add(point);

   } else if (dimension == 3) {
         // If the dimension is 3, generate all possible 6 points and add only free points to the nextPoints list.
         Point3D cp = (Point3D) currentPoint;

         point = new Point3D(cp.x + 1, cp.y, cp.z);
         if (isFreePoint(point))
            nextPoints.add(point);

         point = new Point3D(cp.x - 1, cp.y, cp.z);
         if (isFreePoint(point))
            nextPoints.add(point);

         point = new Point3D(cp.x, cp.y + 1, cp.z);
         if (isFreePoint(point))
            nextPoints.add(point);

         point = new Point3D(cp.x, cp.y - 1, cp.z);
         if (isFreePoint(point))
            nextPoints.add(point);

         point = new Point3D(cp.x, cp.y, cp.z + 1);
         if (isFreePoint(point))
            nextPoints.add

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