[POJ2084]Game of Connections

Description

This is a small but ancient game. You are supposed to write down the numbers 1, 2, 3, . . . , 2n - 1, 2n consecutively in clockwise order on the ground to form a circle, and then, to draw some straight line segments to connect them into number pairs. Every number must be connected to exactly one another. 
And, no two segments are allowed to intersect. 
It‘s still a simple game, isn‘t it? But after you‘ve written down the 2n numbers, can you tell me in how many different ways can you connect the numbers into pairs? Life is harder, right?

Input

Each line of the input file will be a single positive number n, except the last line, which is a number -1. 
You may assume that 1 <= n <= 100.

Output

For each n, print in a single line the number of ways to connect the 2n numbers into pairs.

Sample Input

2
3
-1

Sample Output

2
5

Source

Shanghai 2004 Preliminary

Thinking

　　高精度卡特兰数，如果不想写高精度就像我一样打表吧。记得用超长字符串。

　　PS：卡特兰数第一百项需用恒河沙记（10^57），你考虑考虑什么能存的下。

const a:array[1..100] of ansistring  =
(‘1‘,
 ‘2‘,
 ‘5‘,
 ‘14‘,
 ‘42‘,
 ‘132‘,
 ‘429‘,
 ‘1430‘,
 ‘4862‘,
 ‘16796‘,
 ‘58786‘,
 ‘208012‘,
 ‘742900‘,
 ‘2674440‘,
 ‘9694845‘,
 ‘35357670‘,
 ‘129644790‘,
 ‘477638700‘,
 ‘1767263190‘,
 ‘6564120420‘,
 ‘24466267020‘,
 ‘91482563640‘,
 ‘343059613650‘,
 ‘1289904147324‘,
 ‘4861946401452‘,
 ‘18367353072152‘,
 ‘69533550916004‘,
 ‘263747951750360‘,
 ‘1002242216651368‘,
 ‘3814986502092304‘,
 ‘14544636039226909‘,
 ‘55534064877048198‘,
 ‘212336130412243110‘,
 ‘812944042149730764‘,
 ‘3116285494907301262‘,
 ‘11959798385860453492‘,
 ‘45950804324621742364‘,
 ‘176733862787006701400‘,
 ‘680425371729975800390‘,
 ‘2622127042276492108820‘,
 ‘10113918591637898134020‘,
 ‘39044429911904443959240‘,
 ‘150853479205085351660700‘,
 ‘583300119592996693088040‘,
 ‘2257117854077248073253720‘,
 ‘8740328711533173390046320‘,
 ‘33868773757191046886429490‘,
 ‘131327898242169365477991900‘,
 ‘509552245179617138054608572‘,
 ‘1978261657756160653623774456‘,
 ‘7684785670514316385230816156‘,
 ‘29869166945772625950142417512‘,
 ‘116157871455782434250553845880‘,
 ‘451959718027953471447609509424‘,
 ‘1759414616608818870992479875972‘,
 ‘6852456927844873497549658464312‘,
 ‘26700952856774851904245220912664‘,
 ‘104088460289122304033498318812080‘,
 ‘405944995127576985730643443367112‘,
 ‘1583850964596120042686772779038896‘,
 ‘6182127958584855650487080847216336‘,
 ‘24139737743045626825711458546273312‘,
 ‘94295850558771979787935384946380125‘,
 ‘368479169875816659479009042713546950‘,
 ‘1440418573150919668872489894243865350‘,
 ‘5632681584560312734993915705849145100‘,
 ‘22033725021956517463358552614056949950‘,
 ‘86218923998960285726185640663701108500‘,
 ‘337485502510215975556783793455058624700‘,
 ‘1321422108420282270489942177190229544600‘,
 ‘5175569924646105559418940193995065716350‘,
 ‘20276890389709399862928998568254641025700‘,
 ‘79463489365077377841208237632349268884500‘,
 ‘311496878311103321137536291518809134027240‘,
 ‘1221395654430378811828760722007962130791020‘,
 ‘4790408930363303911328386208394864461024520‘,
 ‘18793142726809884575211361279087545193250040‘,
 ‘73745243611532458459690151854647329239335600‘,
 ‘289450081175264899454283846029490767264392230‘,
 ‘1136359577947336271931632877004667456667613940‘,
 ‘4462290049988320482463241297506133183499654740‘,
 ‘17526585015616776834735140517915655636396234280‘,
 ‘68854441132780194707888052034668647142985206100‘,
 ‘270557451039395118028642463289168566420671280440‘,
 ‘1063353702922273835973036658043476458723103404520‘,
 ‘4180080073556524734514695828170907458428751314320‘,
 ‘16435314834665426797069144960762886143367590394940‘,
 ‘64633260585762914370496637486146181462681535261000‘,
 ‘254224158304000796523953440778841647086547372026600‘,
 ‘1000134600800354781929399250536541864362461089950800‘,
 ‘3935312233584004685417853572763349509774031680023800‘,
 ‘15487357822491889407128326963778343232013931127835600‘,
 ‘60960876535340415751462563580829648891969728907438000‘,
 ‘239993345518077005168915776623476723006280827488229600‘,
 ‘944973797977428207852605870454939596837230758234904050‘,
 ‘3721443204405954385563870541379246659709506697378694300‘,
 ‘14657929356129575437016877846657032761712954950899755100‘,
 ‘57743358069601357782187700608042856334020731624756611000‘,
 ‘227508830794229349661819540395688853956041682601541047340‘,
 ‘896519947090131496687170070074100632420837521538745909320‘
 );
var n:longint;
begin
    while true do
        begin
            read(n);
            if n=-1 then halt;
            writeln(a[n]);
        end;
end.