Sorting string with if-else

My lecturer asked us to write a program that sorts three strings alphabetically using only if-else (no sorting algorithms, usage of arrays whatsover). I'm fairly new to C++ programming but I've come up with this program and would like to know if there's any way to make this more efficient while only using if-else? Any help or suggestions would be appreciated. Thank you!

#include <iostream>
using namespace std;

int main()
{
    string word1, word2, word3;
    string temp;
    
    cout << "Enter three words separated by a space: ";
    cin >> word1 >> word2 >> word3; 
    
    if (word1 > word2 && word1 > word3 && word3 > word2) 
    {
        temp = word1; 
        word1 = word2; 
        word2 = word3; 
        word3 = temp; 
    } 
        
        else if (word1 > word2 && word1 > word3 && word2 > word3) 
        {
            temp = word1; 
            word1 = word3;
            word3 = temp; 
        }
        
            else if (word2 > word1 && word2 > word3 && word1 > word3)
            {
                temp = word2; 
                word1 = word3; 
                word2 = word1; 
                word3 = temp;
            }
            
            else if (word2 > word1 && word2 > word3 && word3 > word1)
            {
                temp = word2; 
                word2 = word3; 
                word3 = temp; 
            }
            
                else if (word3 > word1 && word3 > word2 && word1 > word2)
                {
                    temp = word1; 
                    word1 = word2; 
                    word2 = temp; 
                }

    
    cout << "The correct sort is " << word1 << ", " << word2 << ", " << word3 << endl;
    
    return 0;
}