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Collections are a way for you to organize kata so that you can create your own training routines. Every collection you create is public and automatically sharable with other warriors. After you have added a few kata to a collection you and others can train on the kata contained within the collection.
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Input range in random tests is
1-4000, but month, week and day of week are calendar concepts, Gregorian calendar starts from late 1582, and the tests does not use the proper calendar functions in PHP for its calculation (dateis a timestamp function; at best you can only say it's Julian Day). So whatever calculated is wrong/invalid in some of the input range.