Ambiguous Dates

Time Limit: 2 Seconds
Memory Limit: 65536 KB

**Background**

More than 200 companies in more than 50 countries all over the world contribute
towards the success of the Merck Group. You can imagine that every day Merck
Group Headquarters at Darmstadt gets loads of mail from all over the world,
the layout of all the letters following the customary style of their origin.
In particular, the representation of a date is often ambiguous if you do not
know in what order day, month, and year are given.

For example, if you read 01-02-03, you do not know if that represents the first
of February 1903, or 2003, or if it is the third of February 1901, or 2001.
It might even be the second of March 2001, or some other permutation of the
three numbers. Instead of the hyphens, there could also be slashes, backslashes,
dots, commas, or no delimiters at all.

**Problem**

You are hired to write a program that converts dates given in an unknown format
to the format of the Adjusted Calender of Merck (ACM). The latter specifies
the number of days relative to November 4, 2001, an important day in Merck��s
history.

**Input**

The first line contains the number of scenarios.

Every scenario contains a single date on a line by itself. A date consists of
three parts: A day, a month, and a year given in any order, separated either
by exactly two identical delimiters, or not separated by delimiters at all.
Delimiters can be slashes ��/��, backslashes ��\��, hyphens ��-��, dots ��.��, or commas
��,��. The day and month are represented by a single digit, or by two digits,
the first of which can be a leading zero. Valid years are in the range 1700
. . . 2299; either all four digits are given, or just the last two that specify
the year relative to the century. In the latter case, a leading zero may be
omitted.

Dates are considered illegal if no valid interpretation exists. More precisely,
a date is illegal if no classification of the digits as day, month, and year
results in a valid date in the range January 1, 1700, to December 31, 2299.
However, you can be sure that all dates given contain 3 to 8 digits, and no
other characters except for maybe the two delimiters.

Remember that February 29 is a valid date for leap-years only. A year is a leap-year
if and only if either its number is divisible by four, but not by one hundred,
or if its number is divisible by four hundred. So, in particular, 2000 is a
leap-year, while 1700, 1800, 1900, 2100, or 2200 are not.

**Output**

The output for every scenario begins with a line containing ��Scenario #i:��,
where i is the number of the scenario starting at 1.

For every scenario, print all possible interpretations of the given date in
the format of the Adjusted Calender of Merck (ACM), each interpretation in a
single line, in ascending order and with duplicates removed. If no valid interpretation
exists, print a line containing Illegal date instead.

Terminate the output for each scenario with a single blank line.

**Sample Input**

3

1631/02/29

2001-11-03

010203

**Sample Output**

Scenario #1:

Illegal date

Scenario #2:

-238

-1

Scenario #3:

-109847

-109820

-109513

-109456

-109149

-109119

-73323

-73296

-72989

-72932

-72625

-72595

-36799

-36772

-36465

-36408

-36101

-36071

-274

-247

60

117

424

454

36250

36277

36584

36641

36948

36978

72774

72801

73108

73165

73472

73502

Source:

**Northwestern Europe 2001**
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