### Database Schema
CREATE TABLE Physician (
  EmployeeID INTEGER NOT NULL,
  Name VARCHAR(30) NOT NULL,
  Position VARCHAR(30) NOT NULL,
  SSN INTEGER NOT NULL,
  CONSTRAINT pk_physician PRIMARY KEY(EmployeeID)
)

CREATE TABLE Department (
  DepartmentID INTEGER NOT NULL,
  Name VARCHAR(30) NOT NULL,
  Head INTEGER NOT NULL,
  CONSTRAINT pk_Department PRIMARY KEY(DepartmentID),
  CONSTRAINT fk_Department_Physician_EmployeeID FOREIGN KEY(Head) REFERENCES Physician(EmployeeID)
)

CREATE TABLE Affiliated_With (
  Physician INTEGER NOT NULL,
  Department INTEGER NOT NULL,
  PrimaryAffiliation BOOLEAN NOT NULL,
  CONSTRAINT fk_Affiliated_With_Physician_EmployeeID FOREIGN KEY(Physician) REFERENCES Physician(EmployeeID),
  CONSTRAINT fk_Affiliated_With_Department_DepartmentID FOREIGN KEY(Department) REFERENCES Department(DepartmentID),
  PRIMARY KEY(Physician, Department)
)

CREATE TABLE Procedures (
  Code INTEGER PRIMARY KEY NOT NULL,
  Name VARCHAR(30) NOT NULL,
  Cost REAL NOT NULL
)

CREATE TABLE Trained_In (
  Physician INTEGER NOT NULL,
  Treatment INTEGER NOT NULL,
  CertificationDate DATETIME NOT NULL,
  CertificationExpires DATETIME NOT NULL,
  CONSTRAINT fk_Trained_In_Physician_EmployeeID FOREIGN KEY(Physician) REFERENCES Physician(EmployeeID),
  CONSTRAINT fk_Trained_In_Procedures_Code FOREIGN KEY(Treatment) REFERENCES Procedures(Code),
  PRIMARY KEY(Physician, Treatment)
)

CREATE TABLE Patient (
  SSN INTEGER PRIMARY KEY NOT NULL,
  Name VARCHAR(30) NOT NULL,
  Address VARCHAR(30) NOT NULL,
  Phone VARCHAR(30) NOT NULL,
  InsuranceID INTEGER NOT NULL,
  PCP INTEGER NOT NULL,
  CONSTRAINT fk_Patient_Physician_EmployeeID FOREIGN KEY(PCP) REFERENCES Physician(EmployeeID)
)

CREATE TABLE Nurse (
  EmployeeID INTEGER PRIMARY KEY NOT NULL,
  Name VARCHAR(30) NOT NULL,
  Position VARCHAR(30) NOT NULL,
  Registered BOOLEAN NOT NULL,
  SSN INTEGER NOT NULL
)

CREATE TABLE Appointment (
  AppointmentID INTEGER PRIMARY KEY NOT NULL,
  Patient INTEGER NOT NULL,    
  PrepNurse INTEGER,
  Physician INTEGER NOT NULL,
  Start DATETIME NOT NULL,
  End DATETIME NOT NULL,
  ExaminationRoom TEXT NOT NULL,
  CONSTRAINT fk_Appointment_Patient_SSN FOREIGN KEY(Patient) REFERENCES Patient(SSN),
  CONSTRAINT fk_Appointment_Nurse_EmployeeID FOREIGN KEY(PrepNurse) REFERENCES Nurse(EmployeeID),
  CONSTRAINT fk_Appointment_Physician_EmployeeID FOREIGN KEY(Physician) REFERENCES Physician(EmployeeID)
)

CREATE TABLE Medication (
  Code INTEGER PRIMARY KEY NOT NULL,
  Name VARCHAR(30) NOT NULL,
  Brand VARCHAR(30) NOT NULL,
  Description VARCHAR(30) NOT NULL
)

CREATE TABLE Prescribes (
  Physician INTEGER NOT NULL,
  Patient INTEGER NOT NULL, 
  Medication INTEGER NOT NULL, 
  Date DATETIME NOT NULL,
  Appointment INTEGER,  
  Dose VARCHAR(30) NOT NULL,
  PRIMARY KEY(Physician, Patient, Medication, Date),
  CONSTRAINT fk_Prescribes_Physician_EmployeeID FOREIGN KEY(Physician) REFERENCES Physician(EmployeeID),
  CONSTRAINT fk_Prescribes_Patient_SSN FOREIGN KEY(Patient) REFERENCES Patient(SSN),
  CONSTRAINT fk_Prescribes_Medication_Code FOREIGN KEY(Medication) REFERENCES Medication(Code),
  CONSTRAINT fk_Prescribes_Appointment_AppointmentID FOREIGN KEY(Appointment) REFERENCES Appointment(AppointmentID)
)

CREATE TABLE Block (
  BlockFloor INTEGER NOT NULL,
  BlockCode INTEGER NOT NULL,
  PRIMARY KEY(BlockFloor, BlockCode)
)

CREATE TABLE Room (
  RoomNumber INTEGER PRIMARY KEY NOT NULL,
  RoomType VARCHAR(30) NOT NULL,
  BlockFloor INTEGER NOT NULL,  
  BlockCode INTEGER NOT NULL,  
  Unavailable BOOLEAN NOT NULL,
  CONSTRAINT fk_Room_Block_PK FOREIGN KEY(BlockFloor, BlockCode) REFERENCES Block(BlockFloor, BlockCode)
)

CREATE TABLE On_Call (
  Nurse INTEGER NOT NULL,
  BlockFloor INTEGER NOT NULL, 
  BlockCode INTEGER NOT NULL,
  OnCallStart DATETIME NOT NULL,
  OnCallEnd DATETIME NOT NULL,
  PRIMARY KEY(Nurse, BlockFloor, BlockCode, OnCallStart, OnCallEnd),
  CONSTRAINT fk_OnCall_Nurse_EmployeeID FOREIGN KEY(Nurse) REFERENCES Nurse(EmployeeID),
  CONSTRAINT fk_OnCall_Block_Floor FOREIGN KEY(BlockFloor, BlockCode) REFERENCES Block(BlockFloor, BlockCode) 
)

CREATE TABLE Stay (
  StayID INTEGER PRIMARY KEY NOT NULL,
  Patient INTEGER NOT NULL,
  Room INTEGER NOT NULL,
  StayStart DATETIME NOT NULL,
  StayEnd DATETIME NOT NULL,
  CONSTRAINT fk_Stay_Patient_SSN FOREIGN KEY(Patient) REFERENCES Patient(SSN),
  CONSTRAINT fk_Stay_Room_Number FOREIGN KEY(Room) REFERENCES Room(RoomNumber)
)

CREATE TABLE Undergoes (
  Patient INTEGER NOT NULL,
  Procedures INTEGER NOT NULL,
  Stay INTEGER NOT NULL,
  DateUndergoes DATETIME NOT NULL,
  Physician INTEGER NOT NULL,
  AssistingNurse INTEGER,
  PRIMARY KEY(Patient, Procedures, Stay, DateUndergoes),
  CONSTRAINT fk_Undergoes_Patient_SSN FOREIGN KEY(Patient) REFERENCES Patient(SSN),
  CONSTRAINT fk_Undergoes_Procedures_Code FOREIGN KEY(Procedures) REFERENCES Procedures(Code),
  CONSTRAINT fk_Undergoes_Stay_StayID FOREIGN KEY(Stay) REFERENCES Stay(StayID),
  CONSTRAINT fk_Undergoes_Physician_EmployeeID FOREIGN KEY(Physician) REFERENCES Physician(EmployeeID),
  CONSTRAINT fk_Undergoes_Nurse_EmployeeID FOREIGN KEY(AssistingNurse) REFERENCES Nurse(EmployeeID)
)

### Question
Find the number of distinct room types available.

### SQL
SELECT count(DISTINCT roomtype) FROM room