While loop excutes else statement before ending

So I thought I made a while loop that would not run when I typed in "done" or "quit". But it turns out it runs the else statement at the very bottom of my code before it stops. How can I change this to stop this from happening?

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 #include <iostream>
#include <string>
#include <cmath>
#include "error.h"
using namespace std;
 
 
const double pi = 3.14159; // Global constant pi accurate to 5 decimal points
 
// Fucntion to get positive number.
// Function must be greather than zero to count as a positive number.
double get_postivie_numb(const string& prompt= "")
{
        cout << prompt;
        double x;
        cin >> x;
        while (x <= 0)            
        {
            cout << "Sorry, You can only enter positive numbers.\n";
            cin >> x;
        }
        return x;
}
 
// Funciton to convert input to lowercase.
// Precondition: String must not contain numbers. Only letters.
string convert_to_lowercase(const string& s)
{
	string result = "";
	for(int i = 0; i < s.size(); i++)
	{
		int x = 0;
		x = static_cast<int>(s[i]);
		char y = x;
		if (x < 97)
		{
			x += 32;
			y = x;
		}
		result +=y;		
	}
	return result;
}
 
// Circle Functions:
 
void circle_information(double& radius)
{
	radius = get_postivie_numb("What is the radius of the circle?");
}
double circle_area(double& radius)
{
    double area = pi * radius * radius;
    return area;
}
double circle_perimeter(double& radius)
{
    double perimeter = 2 * pi * radius;
	return perimeter;
}
 
 
// Square Functions:
 
void square_information(double& height)
{
   height = get_postivie_numb("What is the height of the square? \n");
}
double square_area(double& height)
{
    double area = height * height;
    return area;
}
double square_perimeter(double& height)
{
    double perimeter = height * 4;
    return perimeter;
}
 
// Rectangle Functions:
 
void rectangle_information(double& height, double& width)
{
    height = get_postivie_numb("Enter the height of the rectangle.\n");
    width = get_postivie_numb("Enter the width of the rectangle.\n");
}
double rectangle_area(double& height, double& width)
{
    double area = height * width;
    return area;
}
double rectangle_perimeter(double& height, double& width)
{
    double perimeter = (2 * height) + (2 * width);
    return perimeter;
}
 
// Triangle Functions:
 
void triangle_information(double& a, double& b, double& c)
{
	cout << "Please enter the side lengths from least to greatest.\n";
   	a = get_postivie_numb("Enter side length a. \n");
    b = get_postivie_numb("Enter side length b. \n");
    c = get_postivie_numb("Enter side length c. \n");
    
}

//Precondition: Triangle must be a real triangle. NO impossible triangles.
// Example : traingle with sides 3,4,54 is not a real triangle.
double triangle_area(double& a, double& b, double& c, double s)  // Heron's Formula
{
        double area = sqrt((s-a)*(s-b)*(s-c)*s);
        return area;
}
double triangle_perimeter(double& a, double& b, double& c)
{
        double perimeter = a + b + c;
        return perimeter;
}

 
int main()
{
	string s = "";
	
	while (s != "done" || s!= "quit")
	{
  	  	cout << "Enter the name of a geometric shape. (Type \"done\" or \"quit\" to exit):";
		cin >> s;
        if (convert_to_lowercase(s) == "circle" || convert_to_lowercase(s) == "cir")
        {
        	double radius = 0.0;
        	circle_information(radius);
        	cout << "The area of the circle is " << circle_area(radius) << ".\n";
        	cout << "The perimeter of the circle is " << circle_perimeter(radius) <<".\n\n";
		}
		else if (convert_to_lowercase(s) == "square" || convert_to_lowercase(s) == "sq")
        {
        	double height = 0;
            square_information(height);
            cout << "The area of the square is " << square_area(height) << ". \n";
            cout << "The perimeter of the square is " << square_perimeter(height) << ". \n\n";
		}
        else if (convert_to_lowercase(s) == "rectangle" || convert_to_lowercase(s) == "rect")
        {
            double height = 0;
            double width = 0;
            rectangle_information(height, width);
            cout << "The area of the rectangle is " << rectangle_area(height, width) << ".\n";
            cout << "The perimeter of the rectangle is " << rectangle_perimeter(height, width) << ".\n\n";
        }
        else if (convert_to_lowercase(s) == "triangle" || convert_to_lowercase(s) == "tri")
        {
        	double a = 0;
            double b = 0;
            double c = 0;
            
            triangle_information(a, b, c);
            double semi = triangle_perimeter(a,b,c)/2.0;   //semiperimeter of triangle
            
            while(a > b || a > c || b > c)
  		  	{
    			cout << "It seems you did not type the numbers from least to greatest."
    				 << "Please try again.\n";
    				 triangle_information(a, b, c);
  		  	}
  			
  			double x = a + b;

  			if (c > x)
  			{
  				cout << "This will produce an impossible trianlge.\n\n";
  			}
  			else
  			{
            	cout << "The area of the triangle is " << triangle_area(a, b, c, semi) << ".\n";
            	cout << "The perimeter of the rectangle is " << triangle_perimeter(a, b, c) << ".\n\n";
  			}

        }
        else
        {
        	cout << "Sorry. Program doesn't know that shape. Please try again.\n\n";
        }
    }
}
add else if(s == "done" || s== "quit") break; before else
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#include <iostream>
#include <cctype> //// tolower
using namespace std;

int main( )
{
	char str[] = "Hello World!";
	
	for(int i=0; str[i]; i++)	
		str[i] =  tolower(str[i]);	
		
	cout << str;
	
	return 0;
}
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