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C++ If-else Branch wont produce an output

hope all is well. I was working on some code (C++) that would determine the season depending on the users input. The user is meant to type in a valid month and date in a year and from that the code is supposed to determine the season. Per instructions provided by my professor:

The dates for each season are:
Spring: March 20 – June 20
Summer: June 21 – September 21
Autumn: September 22 – December 20
Winter: December 21 – March 19

I was working on Spring for now, and this is the code I have. Just a little heads up, when inputting values March 20 – March 31, the code runs to my expectation and prints what is being looked for. However, when I type in any value such as June 1 – June 20 the program compiles, but it does not produce an output.

Here is the link to my code: https://repl.it/repls/FlippantAgileTheory

And here is the code:

 using namespace std;

 int main() {
   string inputMonth;
   int inputDay;

   cin >> inputMonth;
   cin >> inputDay;

  if (inputMonth == "March" || inputMonth == "June"){
    if (inputMonth == "March"){
     if (inputDay > 19 && inputDay < 32){
        cout << "Spring\n";
     }
     else if (inputMonth == "June"){  // this is the aspect of the code that doesn't work
        if ((inputDay > 0) && (inputDay < 21)){ 
           cout << "Spring\n";
        }
     }
  }

}
}

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