calling constructor from member function

Here's the question:

Define a class called Month that is an abstract data type for a month. Your class will have one member variable of type int to represent a month (1 for January, 2 for February, and so forth). Include all the following member functions: a constructor to set the month using the first three letters in the name of the month as three arguments, a constructor to set the month using an integer as an argument (1 for January, 2 for February, and so forth), a default constructor, an input function that reads the month as an integer, an input function that reads the month as the first three letters in the name of the month, an output function that outputs the month as an integer, an output function that outputs the month as the first three letters in the name of the month, and a member function that returns the next month as a value of type Month . Embed your class definition in a test program.

#include <iostream>
using namespace std;

class Month
{
public:
    Month (char letter1, char letter2, char letter3);
    Month (int numOfMonth);
    Month ();
    void inputAsNum(); // read month as integer
    void inputAsCh(); //  read first three chars of month
    void outputAsCh() const;
    void outputAsNum() const;
    Month nextMonth();
private:
    int month;
};

int main()
{
    Month test(5);
    //test.inputAsNum();
    cout << "Current month is " << endl;
    test.outputAsCh();
    test.outputAsNum();
    cout << endl;
    test.nextMonth();
    cout << "Next month is " <<endl;
    test.outputAsCh();
    test.outputAsNum();
    cout << endl;

    Month test2('a','p','r');
    //test2.inputAsCh();
    cout << "Current month is " << endl;
    test2.outputAsCh();
    test2.outputAsNum();
    cout << endl;
    test2.nextMonth();
    cout << "Next month is " <<endl;
    test2.outputAsCh();
    test2.outputAsNum();
    cout << endl;


    Month test3;
    test3.inputAsNum();
    cout << "Current month is " << endl;
    test3.outputAsCh();
    test3.outputAsNum();
    cout << endl;
    test3.nextMonth();
    cout << "Next month is " <<endl;
    test3.outputAsCh();
    test3.outputAsNum();
    cout << endl;

    Month test4;
    test4.inputAsCh();
    cout << "Current month is " << endl;
    test4.outputAsCh();
    test4.outputAsNum();
    cout << endl;
    test4.nextMonth();
    cout << "Next month is " <<endl;
    test4.outputAsCh();
    test4.outputAsNum();
    cout << endl;

    return 0;
}

Month::Month (char letter1, char letter2, char letter3)
{
    if ((letter1 == 'j')&&(letter2 == 'a')&&(letter3 == 'n'))
        month= 1;
    else if ((letter1 == 'f')&&(letter2 == 'e')&&(letter3 == 'b'))
        month= 2;
    else if ((letter1 == 'm')&&(letter2 == 'a')&&(letter3 == 'r'))
        month= 3;
    else if ((letter1 = 'a')&&(letter2 == 'p')&&(letter3 == 'r'))
        month= 4;
    else if ((letter1 == 'm')&&(letter2 == 'a')&&(letter3 == 'y'))
        month= 5;
    else if ((letter1 == 'j')&&(letter2 == 'u')&&(letter3 == 'n'))
        month= 6;
    else if ((letter1 == 'j')&&(letter2 == 'u')&&(letter3 == 'l'))
        month= 7;
    else if ((letter1 == 'a')&&(letter2 == 'u')&&(letter3 == 'g'))
        month= 8;
    else if ((letter1 == 's')&&(letter2 == 'e')&&(letter3 == 'p'))
        month= 9;
    else if ((letter1 == 'o')&&(letter2 == 'c')&&(letter3 == 't'))
        month= 10;
    else if ((letter1 == 'n')&&(letter2 == 'o')&&(letter3 == 'v'))
        month= 11;
    else if ((letter1 == 'd')&&(letter2 == 'e')&&(letter3 == 'c'))
        month= 12;
}
Month::Month (int numOfMonth)
                    :month(numOfMonth)
{ }
Month::Month ()
                    :month(1)
{ }
void Month::inputAsNum()
{
    int num;
    cout << "Enter num of month => ";
    cin  >> num;
    month = num;
}
void Month::inputAsCh()
{
    char c1,c2,c3;
    cout << "Enter three letters of month => ";
    cin  >> c1 >> c2 >> c3;
    Month::Month(c1,c2,c3);
}
void Month::outputAsCh() const
{
    if (month == 1)
        cout << "Jan ";
    else if (month == 2)
        cout << "Feb ";
    else if (month == 3)
        cout << "Mar ";
    else if (month == 4)
        cout << "Apr ";
    else if (month == 5)
        cout << "May ";
    else if (month == 6)
        cout << "Jun ";
    else if (month == 7)
        cout << "Jul ";
    else if (month == 8)
        cout << "Aug ";
    else if (month == 9)
        cout << "Sep ";
    else if (month == 10)
        cout << "Oct ";
    else if (month == 11)
        cout << "Nov ";
    else if (month == 12)
        cout << "Dec ";
}
void Month::outputAsNum() const
{
    cout << month;
}
Month Month::nextMonth()
{
    if (month < 12)
        month++;
    else if (month == 12)
        month = 1;
    return Month(month);
}

The code runs just fine. I try that calling constructor Month::Month (char letter1, char letter2, char letter3) from member function void Month::inputAsCh() . I can solve the problem by changing definition of Month::inputAsCh() and copy paste definitions of the constructor into the function. But, just out of curiosity, can be a constructor called from member function ? If it's okey, Month::inputAsCh() works wrong, I also try on Month test4 variable.

Output                                  Expected Output
-------------                           -----------------
Current month is                        Current month is 
Nov 11                                  Nov 11
Next month is                           Next month is 
Dec 12                                  Dec 12
Current month is                        Current month is 
Apr 4                                   Apr 4
Next month is                           Next month is 
May 5                                   May 5
Enter num of month => 2                 Enter num of month => 2
Current month is                        Current month is 
Feb 2                                   Feb 2
Next month is                           Next month is 
Mar 3                                   Mar 3
Enter three letters of month => apr     Enter three letters of month => apr
Current month is                        Current month is 
Jan 1                                   Apr 4
Next month is                           Next month is 
Feb 2                                   May 5