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Language: Lucky and Good Months by Gregorian Calendar
Description Have you ever wondered why normally an year has 365 days, not 400 days? Why August have 31 days, but February have only 28 days? Why there are 7 days, not 6 days, in a week? Do people in ancient time use the same calendar as we do? There are many interesting conjectures and theories about those problems. Now we will tell you one story that may help explaining plausible answers to these questions. Using information in the story, you are then ask to solve an interesting problem using computer. Note that there are many theories about the calendar system discussed. This problem set will tell only one of them in a simplified way. Throughout history, people keep track of time by observing the relative positions of the earth, the moon and the sun. A Depending on how accurate you can measure the period of the earth orbiting the sun, you need to invent different formulas for leap years. Several famous Western calendar systems have been invented, not to mention the more complex Oriental systems. In order to save programmers’ efforts, we will not discuss the Oriental, such as Chinese, calendar systems. We will focus on major Western calendar systems. The earliest one may be the Julian calendar created by Julius Caesar in 46 BC. It is not accurate enough and will have one day off every 128 years. The next one is the Astronomical Julian calendar invented by Joseph Justus Scaliger around the 16th century. Both have simple formulas to determine which year is a leap year. The next major one is called Gregorian calendar that was invented at the year 1582 because the synchronization of the earth’s orbiting and the calendar is finally noticed by people. In this system, a leap year is dropped every 100 years unless it is every 400 years. By doing this modification, the average number of days in a calendar year is 365.2425. Note that this system is also not perfect. It adds one more day every 3289 years. There are other more modifications suggested, such as the one by Astronomer John Herschel, the Greek Orthodox, and the SPAWAR group in the US Navy. For simplicity, people use Gregorian calendar system though it may not be perfect. The following is the formula for the Gregorian calendar to determine whether an year is a leap year or not. An year *y*is divisible by 4, and*y*is not divisible by 100 unless it is divisible by 400.
An year *y*is divisible by 4.
Hence year 4 is a leap year, year 100 is a leap year, year 1900 is not a leap year, but year 2000 is a leap year. A leap year has 366 days with the extra day February 29. A non-leap year has 365 days. During your computation, you may also want to observe the following facts about Gregorian calendar. Many calendar systems were used by people in different areas in the Western world at the same time. The current Western calendar system, primarily follows Gregorian calendar, and is so called the Gregorian Reformation, was adopted by Britain and the possessions on September 3, 1752. For lots of reasons that we are sure you do not want to read in this problem description, 11 days are eliminated starting September 3, 1752 in order for people not to rewrite history. That is, in the Gregorian calendar, there is no days in between September 3, 1752 and September 13, 1752. Note that Rome adopted the Gregorian calendar at the year 1582, when it was invented. Also for historical reasons, the year 1700 is declared a leap year in the Gregorian calendar. There are other variations about the Gregorian calendar system, however, we will use the one that is defined above. A lunar In ancient time, a Throughout history, people believe the relative positions of the stars can decide their fate. This is also true for people living in an island Also from ancient tales, a month is called Given a period of time, your task is to report the number of lucky months and the number good months during this period of time using the described Gregorian calendar system. Input The first line contains the number of test cases
M _{s}Y _{e}M_{e}where two numbers are separated by a single blank, Y < 10000, denoting the starting year in western style, _{s}M is an integer, 1 ≤ _{s}M ≤ 12, denoting the starting month, _{s}Y is an integer, 0 < _{e}Y < 10000, denoting the ending year in western style, _{e}M is an integer, 1 ≤ _{e}M ≤ 12, denoting the ending month._{e}Note that you can be sure the month indicated by Y is never after the month indicated by _{s}M, _{e}Y._{e}Output For each test case, output the number of lucky months and the number of good month in between the month Y (including this month) and the month _{s}M of the year _{e}Y (including this month) in one line. The two numbers are separated by a single blank._{e}Sample Input 2 2006 9 2006 9 2006 7 2006 9 Sample Output 1 0 1 1 Source |

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