I have an issue with my switch statement

I've been trying to figure this code out for a while, but no matter what you type "north" "south" "east" or "west" it only displays the current case over and over again.

For example

You are in Hospital you can go north or west

north
Nope
You are in Hospital you can go north or west

south
Nope
You are in Hospital you can go north or west


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  #include<iostream>
#include<string>
#include<ctime>
#include<cstdlib>
///////////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////Variables///////////////////////////////////////////////////////
using namespace std;
int randomNumber;
int Monster();
int num;
int monsterNum;
int Inventory();
string inventory[5];
///////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////////////

int main(){
string input = "a";
int room = 1;

	while (input.compare("quit")!=0){

		switch (room){

			

		case 1:

cout<<"                    Terrorist Toad of the Mushroom Kingdom\n\n\n\n";		
cout << "Your name is Toad.\n";
cout<< "You were assigned a top secret mission deep in the land of the Bomb-ombs.\n\n\n";
cout<<"Your squad deserted you, left you to die. You decide to strike back\n";
cout<<"You are now... TERRORIST TOAD"<<endl;
cout<<"Type 'west', 'east', 'north', and 'south' to navigate these desolate lands"<<endl;


	

			cout << "You are at the downed helicopter\nYou can go east or west or north\n";
			getline(cin, input);

			Inventory();

			if (input.compare("west") != 0)
				room = 2;
			else if (input.compare("east") != 0)
				room = 5;
			else if (input.compare("north") != 0)
				room = 6;
			else if (input.compare("south") != 0)
				cout << "Nope" << endl;

			break;


		case 2:

			cout << "You are in a home\n You can go west or north or east\n" << endl;
			getline(cin, input);

			if (input.compare("south") != 0)
				cout << "Nope" << endl;
			else if (input.compare("west") != 0)
				room = 3;
			else if (input.compare("east") != 0)
				cout << "Nope" << endl;
			else if (input.compare("north") != 0)
				room = 4;

			

			break;
		case 3:
			


			cout << "You are on the shore\n You can only go east\n" << endl;
			getline(cin, input);
			if (input.compare("east") != 0)
				cout << "Nope " << endl;
			else if (input.compare("south") != 0)
				room = 2;
			else if (input.compare("west") != 0)
				room = 4;
				
			else if (input.compare("north") != 0)
				cout << "Nope " << endl;


			break;
		case 4:

		


			cout << "You are in a parking lot. It kinda smells, you can go south or east\n" << endl;
			getline(cin, input);
			if (input.compare("south") != 0)
				room = 2;
			else if (input.compare("west") != 0)
				cout << "Nope" << endl;
			else if (input.compare("north") != 0)
				cout << "Nope" << endl;
			else if (input.compare("east") != 0)
				room = 6;
			break;


		case 5:
			


			
			
			
			cout << "You are in a Hospital You can go north or west\n" << endl;
			getline(cin, input);
			if (input.compare("east") != 0)
				cout<<"Nope"<<endl;
			else if (input.compare("south") != 0)
				cout << "Nope" << endl;
			else if (input.compare("west") != 0)
				room = 1; 
			else if (input.compare("north") != 0)
				room = 7;
			
			

			break;

		case 6:
			



			
			
			cout << "You are in a Hotel You can go east or west or south\n" << endl;
			getline(cin, input);
			if (input.compare("west") != 0)
				room = 4;
			else if (input.compare("south") != 0)
				room = 1;
			else if (input.compare("east") != 0)
				room = 7;
			else if (input.compare("north") != 0)
				cout << "Nope" << endl;


			

			break;

		case 7:
			

	
			

			
		cout << "You are in the Armory You can go east or north or west or south\n" << endl;
			getline(cin, input);
			if (input.compare("west") != 0)
				room = 1;
			else if (input.compare("south") != 0)
				room = 5;
			else if (input.compare("west") != 0)
				room = 6;
			else if (input.compare("north") != 0)
				room = 10;
				
			

			break;

		case 8:
			


			if (monsterNum == 1)
				inventory[0] = "Ruby";
			else if (monsterNum == 2)
				inventory[1] = "Emerald";
			else if (monsterNum == 3)
				inventory[2] = "Diamond";
			else if (monsterNum == 4)
				inventory[3] = "Sapphire";
			else if (monsterNum == 5)
				inventory[4] = "Gold";

			cout << "Look out! There are bad guys. You have no choice but to fight\nIn order to battle the president, you need the lucky dice\nYou can go north or west\n" << endl;
			Monster();

			getline(cin, input);
			if (input.compare("west") != 0)
				room = 7;
			else if (input.compare("south") != 0)
				cout << "Nope" << endl;
			else if (input.compare("west") != 0)
				cout << "Nope" << endl;
			else if (input.compare("north") != 0)
				room = 9;
			

			

			break;

		case 9:
			


			
			
			cout << "You are in the at the US Castle, You need to have the lucky dice! You can only go east\n" << endl;
			getline(cin, input);
			if (input.compare("west") != 0)
				room = 1;
			else if (input.compare("south") != 0)
				cout << "Nope" << endl;
			else if (input.compare("west") != 0)
				cout << "Nope" << endl;
			else if (input.compare("north") != 0)
				cout << "Nope" << endl;

			

			break;

		case 10:
			

			
			cout << "Welcome to Bass Pro! \n" << endl;
			getline(cin, input);
			if (input.compare("west") != 0)
				room = 1;
			else if (input.compare("south") != 0)
				cout << "Nope" << endl;
			else if (input.compare("west") != 0)
				cout << "Nope" << endl;
			else if (input.compare("north") != 0)
				cout << "Nope" << endl;

			break;

		}


		}

	}


int Monster(){



	

		
		srand(static_cast<unsigned> (time(0)));
		randomNumber = rand();
		num = (randomNumber % 100) + 1;


		cout << "Theres a bad guy he has a " << endl;


		if (num > 5 && num <= 10){
			cout << "Tank" <<endl;
			return 1;
		}
		else if (num > 11 && num <= 15){
			cout << "Rocket Launcher" << endl;
			return 2;
		}
		
		else if (num > 16 && num <= 30){
			cout << "Machine Gun" << endl;
			return 3;
		}
			
		else if (num > 31 && num <= 50){
			cout << "Pistol" << endl;
			return 4;
		}
		else if (num > 51 && num <= 100){
			cout << "Knife" << endl;
			return 5;
		}
}


int Inventory(){



	for (int i = 0; i < 5; i++){

		inventory[i] = 5;
	}
	for (int i = 0; i < 5; i++)
		cout << "This is your inventory, " << inventory[i] << endl;
	 return 1;
}
if (input.compare("west") != 0) This reads as "if input is not west". Compare returns 0 if strings are equal. Better use == operator for clarity:

if(input == "west")
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