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 day is
the amount of time the earth completes a self rotation. An year
is defined to be the amount of time the earth orbits the sun. The
earth takes roughly 365.242190 days to orbit the sun with some small
variations. For practical purpose, a calendar year needs to have an
integral number of days. Hence people need to add leap days to
keep the calendar synchronized with the sun. If you keep a calendar
year to have 365 years, you need to add one more day in a leap year
roughly about every 4 years. However, this kind of calendar will not
be in perfect synchronization with the earth’s position orbiting the
sun because it advanced 365.25 days in average, which is slightly more
than the actual period. 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, y >
1582 and y ≠ 1700, is a leap year if and only if
y is divisible by 4, and
y is not divisible by 100 unless it is divisible by 400. An year y, 0 < y < 1582 is a leap year if and
only if 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 month is defined to be the average time between
successive new or full moons which is 29.531 days. People observe in
average 12.368 full moons in an year. Unfortunately, this is also not
an integral number in terms of days. Hence if we set an year to have
12 months with each month having 30 days, we need to add several days
each year. To save the trouble, an alternative way is to have the
number of days in a month to alternative between 30 and 31. However,
this introduces one extra day. After lots of struggle, the Gregorian
calendar defined the numbers of days in each month during a non-leap
year to be 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31,
respectively from the first month to the 12th month. One more day is
added on February in the leap year. The names for the months in
sequence from the first month — January, February, March, April, May,
June, July, August, September, October, November, and December, are
also very interesting and have lots of stories associated with them.
For example, the Roman Senate named the month of July after Julius
Caesar to honor him for reforming their calendar. However, we do not
have time to cover them here. In ancient time, a week may have different number of days, say
from 4 to 10 days. In the Gregorian calendar system, a week
corresponds roughly to the moon’s quarter phase whose position can be
clearly observed by people. Hence people can easily measure a week.
Also for some other reasons, such as religion, it is defined as 7
days. The names of the 7 days in sequence — Sunday, Monday, Tuesday,
Wednesday, Thursday, Friday and Saturday, all have interesting
stories. However, we also do not have time to cover them here. Throughout history, people believe the relative positions of the
stars can decide their fate. This is also true for people living in an
island T. In island T, people are working from Monday
through Friday every week and enjoy holidays on every Saturday and
Sunday without exceptions. There is no other holidays. From ancient
tales, a month is called lucky if the last working day in this
month is Friday. For examples, the last working day of September, 2006
is September 29, 2006 — which is Friday. Hence it is lucky. The last
working day of July, 2006 is July 31, 2006 — which is Monday. Hence it
is not lucky. The last working day of August, 2006 is August 31, 2006
— which is Thursday. Hence it is also not lucky. It is believed that
if one eats only vegetable everyday during a lucky month, he/she will
have a good fortune in getting rich. Also from ancient tales, a month is called good if the first
working day in this month is Monday. For examples, the first working
day of July, 2006 is July 3, 2006 — which is Monday. Hence it is good.
The first working day of October, 2006 is October 2, 2006 — which is
Monday. Hence it is also good. The first working day of August, 2006
is August 1, 2006 — which is Tuesday. Hence it is not good. The first
working day of September, 2006 is September 1, 2006 — which is Friday.
Hence it is also not good. It is believed that if one goes to bed
before 10 PM every day during a good month, he/she will be very
healthy. A month can be both good and lucky at the same time. 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. The first line contains the number of test cases w, 1 ≤
w ≤ 10. Then the w test cases are listed one by one.
Each test case consists of 1 line with four numbers:
Ys
Ms
Ye
Me
where two numbers are separated by a single blank, Ys
is an integer, 0 < Ys
< 10000, denoting the starting year in western style, Ms
is an integer, 1 ≤ Ms
≤ 12, denoting the starting month, Ye
is an integer, 0 < Ye
< 10000, denoting the ending year in western style, Me
is an integer, 1 ≤ Me
≤ 12, denoting the ending month. Note that you can be sure the month indicated by Ms
, Ys
is never after the month indicated by Me
, Ye
. For each test case, output the number of lucky months and the number
of good month in between the month Ms
of the year Ys
(including this month) and the month Me
of the year Ye
(including this month) in one line. The two numbers are separated
by a single blank.
输入描述
输出描述
输入例子
2
2006 9 2006 9
2006 7 2006 9
输出例子
1 0
1 1