A super-int calculator

Define an object that represents an unlimited size integer.
It must have an array of ints to represent the digits, one int per digit.
It must be like a vector because the number of digits can change unpredictably,
but it should not use the <vector>, remember the do-it-yourself rule. It
must be able to handle negatives effectively.

These methods are required:
  a constructor that takes a string for initialisation, e.g.
    bigint a("-473827346472372344747785");
  a constructor that copies another bigint, e.g.
    bigint b(a);
  the ability to be printed on an ostream, e.g.
    cout << "a = " << a << "\n";
  efficient increment and decrement operators, e.g.
    a++;
  or if you prefer
    ++a;
  addition, subtraction, and multiplication as update operators, e.g.
    a += b;
    a -= b;
    a *= b;
  the usual comparison operations:
    a == b, a != b, a < b, a > b, a <= b, a >= b
  a factorial method that replaces the number with its own factorial, e.g.
    a.factorial();
  and a destructor.

You must follow the requirements stated in class, which I shall remind you
of if wanted, but note-taking should not be neglected.

Serious tests of course, not just repeating my examples.
When testing the factorial operation think a little about how quickly the
result will grow otherwise you may waste a lot of time trying to correct
what seems to be wrong but isn't.

    bigint a("123456789"), b("1000000000"), c("987654321");
    a *= b;
    a += c;
    cout << a << "\n";

 123456789987654321

    bigint d("1234567890987654321"), e("98765432123456789");
    d *= e;
    cout << d << "\n";

 121932631239140373304069513112635269

    bigint f("121932631239140373304069513112635269");
    f *= f;
    cout << f << "\n\n";
    f *= f;
    cout << f << "\n\n";
    f *= f;
    cout << f << "\n";

 14867566560900190847762835625434958044951725287785
 745795594697822702361
 
 22104453544279752829244391507338290807340055284920
 13202016632312590959378730055466635911713035488161
 66757871928926950884970918798408794974321

 48860686649122172677174869503848501015860366194743
 27146917069435387336624013258542752906736994972007
 79737611113907886646033318541177017396733483105675
 80188142155832397185305548876683919018674473485203
 23393748934688389843135214858801124243915991742452
 2794753887485703346107049411041

    bigint g("1000");
    g.factorial();
    cout << g << "\n";

 40238726007709377354370243392300398571937486421071
 46325437999104299385123986290205920442084869694048
 00479988610197196058631666872994808558901323829669
 94459099742450408707375991882362772718873251977950
 59509952761208749754624970436014182780946464962910
 56393887437886487337119181045825783647849977012476
 63288983595573543251318532395846307555740911426241
 74743493475534286465766116677973966688202912073791
 43853719588249808126867838374559731746136085379534
 52422158659320192809087829730843139284440328123155
 86110369768013573042161687476096758713483120254785
 89320767169132448426236131412508780208000261683151
 02734182797770478463586817016436502415369139828126
 48102130927612448963599287051149649754199093422215
 66832572080821333186116811553615836546984046708975
 60290095053761647584772842188967964624494516076535
 34081989013854424879849599533191017233555566021394
 50399736280750137837615307127761926849034352625200
 01588853514733161170210396817592151090778801939317
 81141945452572238655414610628921879602238389714760
 88506276862967146674697562911234082439208160153780
 88989396451826324367161676217916890977991190375403
 12746222899880051954444142820121873617459926429565
 81746628302955570299024324153181617210465832036786
 90611726015878352075151628422554026517048330422614
 39742869330616908979684825901254583271682264580665
 26769958652682272807075781391858178889652208164348
 34482599326604336766017699961283186078838615027946
 59551311565520360939881806121385586003014356945272
 24206344631797460594682573103790084024432438465657
 24501440282188525247093519062092902313649327349756
 55139587205596542287497740114133469627154228458623
 77387538230483865688976461927383814900140767310446
 64025989949022222176590433990188601856652648506179
 97023561938970178600408118897299183110211712298459
 01641921068884387121855646124960798722908519296819
 37238864261483965738229112312502418664935314397013
 74285319266498753372189406942814341185201580141233
 44828015051399694290153483077644569099073152433278
 28826986460278986432113908350621709500259738986355
 42771967428222487575867657523442202075736305694988
 25087968928162753848863396909959826280956121450994
 87170124451646126037902930912088908694202851064018
 21543994571568059418727489980942547421735824010636
 77404595741785160829230135358081840096996372524230
 56085590370062427124341690900415369010593398383577
 79394109700277534720000000000000000000000000000000
 00000000000000000000000000000000000000000000000000
 00000000000000000000000000000000000000000000000000
 00000000000000000000000000000000000000000000000000
 00000000000000000000000000000000000000000000000000
 000000000000000000

    bigint h("25");
    bigint i("10000");
    h -= i;
    cout << h << "\n";

-9975