bool intersected(Ball ball) {
    for (int i = 0; i < balls.size(); i++) {
        double dx = balls[i].x - ball.x;
        double dy = balls[i].y - ball.y;
        double distance = sqrt(dx * dx + dy * dy);
        if (distance < balls[i].radius + ball.radius) return true;
    }
    return false;
}