Weekdays

Write a program that reads a sequence of dates, and for each one prints the corresponding weekday, or prints that the date is not correct according to the Gregorian calendar.

Implement the functions

    bool is_leap_year(int year);
    bool is_correct_date(int day, int month, int year);
    string weekday(int day, int month, int year);

Given a year @y@, @is_leap_year(y)@ tells if @y@ is a leap year or not. Given a date defined with @d@, @m@ and @y@, @is_correct_date(d, m, y)@ tells if the date is correct or not according to the Gregorian calendar. Given a correct date defined with @d@, @m@ and @y@, @weekday(d, m, y)@ returns the corresponding weekday (that is, “Monday”, “Tuesday”, …).

To know the weekday, use the congruence of Zeller: Given a date defined by the triple $(d,m,y)$, where $d$ is the day, $m$ is the month, and $y$ is the year,

1. Subtract two units to the month $m$, and if the result is zero or less, add 12 to the month and subtract a unit to the year. Call $m'$ the new month and call $y'$ the new year.

2. Compute the century $c$ (the first two digits of the year) from the year $y'$.

3. Compute the year inside the century $a$ (the two last digits of the year) from the year $y'$.

4. Compute $$f = \lfloor 2.6m' - 0.2 \rfloor + d + a + \lfloor a/4 \rfloor + \lfloor c/4 \rfloor - 2c.$$

5. Finally, $f$ modulo 7 give us the desired result: 0 represents Sunday, 1 represents Monday, 2 represents Tuesday...

You can find the rule about leap years in the exercise  problem://problemsjutge.org:problems/p1/jpetit/traspas-elemental .

Precondition

For the functions @is_leap_year()@ and @is_correct_date()@, the value of the year is always between 1800 and 9999 (both included). For the function @weekday()@, the given date is always correct w.r.t. the function @is_correct_date()@.

Input

Each date of the input is composed by three integers, corresponding respectively to the day, the month and the year. All the years are between 1800 and 9999.

Output

For each date of the input, print in a line the corresponding weekday (“Monday”, …, “Sunday”) if it is a correct date according to the Gregorian calendar, or “Incorrect Date” if it is not.

Author

Jordi Petit (en: Carlos Molina)

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