Easter Sunday is a mobile holiday corresponding to the first Sunday after the first full moon of the spring. Write a program to compute the day D and the month M of the Easter Sunday of every given year Y.

Below, := indicates assignment, div indicates integer division, and mod indicates the remainder of the integer division. To solve this problem, use the Gauss method:

- Compute
- k := Y div 100
- x := Y mod 19
- b := Y mod 4
- c := Y mod 7
- q := k div 4
- p := (13+8k) div 25
- y := (15−p+k−q) mod 30
- z := (19x+y) mod 30
- n := (4+k−q) mod 7
- e := (2b+4c+6z+n) mod 7

- If z+e ≤ 9, then D := 22+z+e and M := 3.
- Otherwise, if z=29 and e=6, then D := 19 and M := 4.
- Otherwise, if z=28 and e=6 and x>10, then D := 18 and M := 4.
- Otherwise, D := z+e−9 and M := 4.

Input

Input consists of several natural numbers between 1800 and 9999.

Output

Print the day and the month of the Easter Sunday of each year.

Public test cases

**Input**

2006 1999

**Output**

16/4 4/4

Information

- Author
- Jordi Petit
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++ Java Pascal Python
- User solutions
- C C++ Java Python