Doctor JS is a genius. He’ll analyze your JavaScript code, complete with: polymorphism, prototypes, exceptions, and callbacks.

DoctorJS is a static analysis tool developed by my PRL lab neighbor, Dimitris Vardoulakis. It’s an implementation of Vardoulakis and Olin Shivers‘ CFA2—a context-free approach to control flow analysis.

Brendan Eich, CTO of Mozilla and creator of JS, recently blogged about DoctorJS (Static Analysis FTW) and called static analysis one of the best “researchy” investments Mozilla has made over the past few years.

This exercise is a continuation of me throwing some of my favorite functional programs at JavaScript to see what they look like. This one is the meta-circular evaluator, a staple of PL textbooks and classrooms. (These evaluators aren’t quite meta-circular since they can’t evaluate themselves, but maybe we’ll get there someday.)

Writing programs always starts with designing data definitions, so let’s start with data definitions for the abstract syntax trees of our language. Our core language is expression based and an expression is either a variable, a number, a function constructor, or an application. We represent each variant of an expression as a record. Records in Scheme vary among dialects. SRFI 9 Records are widely supported and simple, and although R6RS has a sophisticated record facility, we rely on a very simple subset of PLT Scheme’s define-struct syntax:

;; An Exp is one of
;; - (make-var Symbol)
;; - (make-num Number)
;; - (make-lam Name Exp)
;; - (make-app Exp Exp)
;; And Name = Symbol.

(define-struct var (name))
(define-struct num (val))
(define-struct lam (var body))
(define-struct app (left right))

This defines constructor functions, e.g. a variable is represented by a (make-var 'x), accessors (var-name, lam-body, etc.), and predicates (var?, lam?, etc.).

In JavaScript, functions (invoked with the keyword new) are used to construct records:

// An Exp is one of
// - new Var(Name)
// - new Num(Number)
// - new Lam(String, Exp)
// - new App(Exp, Exp)
// And Name = String.

function Var(name) { this.name = name }
function Num(val)  { this.val = val }

function Lam(variable, body) {
  this.variable = variable;
  this.body = body }

function App(left, right) {
  this.left = left;
  this.right = right }

Notice we had to do the field initialization by hand above. Also, record definitions won’t provide predicates by default, unlike in Scheme, so we build these by hand, too:

function isVar(exp) { return exp instanceof Var }
function isNum(exp) { return exp instanceof Num }
function isLam(exp) { return exp instanceof Lam }
function isApp(exp) { return exp instanceof App }

(If JavaScript included a hygienic macro facility, we could have baked in all this syntactic sugar easily.)

Now let’s sketch data definitions for the values (denotations) of our language. These are the results of evaluation. Since our language is functional, we have function values (closures), and since we have number expressions, we’ll include number values. So we have:

;; A Val is one of
;; - (make-closure Lam Env) [Scheme]
;; | makeClosure(Lam, Env)  [JavaScript]
;; - Number

More will be said about the representation of closures later. With data definitions in place, we can now give the heart of the evaluator. First, in Scheme:

;; evaluate : Exp Env -> Val
;; Evaluate the given expression in the given environment,
;; which must close the expression.
(define (evaluate exp env)
  (cond ((var? exp) (lookup exp env))
        ((num? exp) (num-val exp))
        ((lam? exp) (make-closure exp env))
        ((app? exp) (let ((fun (evaluate (app-left exp) env))
                          (arg (evaluate (app-right exp) env)))
                      (fun arg)))))

And now in JavaScript:

// evaluate : Exp Env -> Val
// Evaluate the given expression in the given environment,
// which must close the expression.
function evaluate(exp, env) {
  return isVar(exp) ? lookup(exp, env) :
         isNum(exp) ? exp.val :
         isLam(exp) ? makeClosure(exp, env) :
         isApp(exp) ? (function () {
                        var fun = evaluate(exp.left, env);
                        var arg = evaluate(exp.right, env);
                        return fun(arg) })() :
         undefined }

Evaluation is defined by structural recursion on expressions. A variable evaluates to the value it is bound to in the environment. (We have not chosen a representation for environments, or defined lookup, yet. These things are on the proverbial wish list.) A number evaluates to the number it represents. A lambda expression evaluates to a closure: the term closed by the current environment. An application evaluates its operator and operand, then evaluates to the application of the operator value to the operand value. You can see here that a closure is being applied (note (fun arg) in the Scheme, and fun(arg) in the JavaScript), so we’ve committed to representing closures with functions in the implementing language (seems just as natural as representing number values with numbers, after all).

One thing you might notice in the JavaScript is the (function () {...})(). This is an idiom to create block scope in a language without let. This is done by creating a function of no arguments, which creates a block of scope in which fun and arg are bound. The function is then immediately applied, so its body is evaluated. Thus we can “fake” let (x = y) e as (function () {var x = y; e})(). (Again, macros would alleviate the syntactic tax here. It seems embarrassing that JavaScript doesn’t have let; maybe more modern dialects do? and maybe the next revision of the language will include it?)

Returning to closures, we know that a closure is a (make-closure Lam Env). Since the evaluator applies closure values, we are committed to a functional representation of closures. Closures are applied to single arguments, so they will be represented a functions expecting one argument. When applied, a closure should evaluate the body of the lambda expression in the environment in which it was created, extended with the formal parameter of the lambda expression being bound to the given argument. So we arrive at the following:

;; make-closure : Lam Env -> (Val -> Val)
(define (make-closure lam env)
  (lambda (v)
    (evaluate (lam-body lam) (extend env (lam-var lam) v))))

The analogous JavaScript is:

// makeClosure : Lam Env -> (Val -> Val)
function makeClosure(lam, env) {
  return function (v) {
    return evaluate(lam.body, extend(env, lam.variable, v))}}

All that is left is dismissing our wish list items: we need to choose a representation for environments and implement lookup and extend. We just to use association lists, which are lists of pairs.

;; A [Listof T] is one of
;; - '(), the empty list
;; - (cons T [Listof T])
;; And Env = [Listof (cons Name Val)]

In JavaScript, we use arrays with two elements to represent pairs, arriving at the following data definitions. Type parameterization is written in curly braces so as not to be confused with the array notation:

// A {Listof T} is one of
// - [], the empty array
// - [T, {Listof T}]
// And Env = {Listof [Name, Val]}

The operations lookup and extend are straightforward:

;; lookup : Var Env -> Val
;; Produces the binding of the given variable
;; in the given environment.
(define (lookup var env)
  (cond ((eq? (first (first env)) (var-name var))
         (rest (first env)))
        (else (lookup var (rest env)))))

;; extend : Env Name Val -> Env
;; Produces an extended environment
;; with the given name bound to the given value.
(define (extend env name val)
  (cons (cons name val) env))

JavaScript:

// lookup : Var Env -> Val
// Produces the binding of the given variable
// in the given environment.
function lookup(variable, env) {
  return variable.name === first(first(env))
       ? rest(first(env))
       : lookup(variable, rest(env))}

// extend : Env Name Val -> Env
// Produces an extended environment
// with the given name bound to the given value.
function extend(env, name, value) {
  return [[name, value], env]}

This relies on the obvious definitions of first and rest to emphasize the correspondence:

function first(p) { return p[0] }
function rest(p)  { return p[1] }

The evaluator is complete now, but we still don’t have a concise notation for writing programs in the implemented language. A cheap and traditional solution is to use S-Expressions:

;; An S-Exp is one of
;; - Name
;; - Number
;; - (list 'fun Name S-Exp) [Scheme]
;; | ["fun", Name, S-Exp]   [JavaScript]
;; - (list S-Exp S-Exp) [Scheme]
;; | [S-Exp, S-Exp]     [JavaScript]

Some examples in Scheme:

• '(fun x x),
• '(add1 4),
• '(((fun x (fun y x)) 3) 7).

Some examples in JavaScript:

• ["fun", "x", "x"],
• ["add1", 4],
• [[["fun", "x", ["fun", "y", "x"]], 3], 7].

S-Expressions are parsed into abstract syntax trees as follows. This is a brain-dead application of the design recipe for functions that consume self-referential data (in this case S-Exps), where the template for such functions is:

;; template : S-Exp -> ?
(define (template sexp)
  (cond ((number? sexp) ...)
        ((symbol? sexp) ...)
        (else
          (cond ((eq? 'fun (first sexp))
                 ...(second sexp)...
                 ...(template (third sexp))...)
                (else
                 ...(template (first sexp))...
                 ...(template (second sexp)...))))))

And the following examples guide filling in the dots for our particular function, parse:

• (parse 5) => (make-num 5)
• (parse 'x) => (make-var 'x)
• (parse '(fun x x)) => (make-lam 'x (parse 'x))
• (parse '(add1 4)) => (make-app (parse 'add1) (parse 4))

In Scheme:

;; parse : S-Exp -> Exp
(define (parse sexp)
  (cond ((number? sexp) (make-num sexp))
        ((symbol? sexp) (make-var sexp))
        (else
         (cond ((eq? 'fun (first sexp))
                (make-lam (second sexp)
                          (parse (third sexp))))
               (else
                (make-app (parse (first sexp))
                          (parse (second sexp))))))))

And JavaScript:

// parse : S-Exp -> Exp
function parse(sexp) {
  return isString(sexp) ? new Var(sexp) :
         isNumber(sexp) ? new Num(sexp) :
         sexp[0] === "fun" ? new Lam(sexp[1], parse(sexp[2])) :
         new App(parse(sexp[0]), parse(sexp[1]))}

Where,

function isString(sexp) { return typeof sexp === "string" }
function isNumber(sexp) { return typeof sexp === "number" }

Finally, we can evaluate some example programs in Scheme:

• (evaluate (parse 3) '())
  => 3
• (evaluate (parse '(fun x x)) '())
  => (make-closure (parse '(fun x x)) '())
• (evaluate (parse '(((fun x (fun y x)) 3) 7)) '())
  => 3

Or in JavaScript:

• evaluate(parse(3), [])
  => 3
• evaluate(parse(["fun", "x", "x"]), [])
  => makeClosure(parse(["fun", "x", "x"]),[])
• evaluate(parse([[["fun", "x", ["fun", "y", "x"]], 3], 7]), [])
  => 3

We can also embed values from the implementing language into the implemented language via the initial environment, in Scheme:

(define initial-env (cons (cons 'add1 add1) '()))

In JavaScript:

var initial_env = ["add1", (function (n) {return n+1}), []]

This brings us back to yesterday’s functional program, iterative doubling, which we can evaluate in Scheme:

(evaluate
 (parse '((fun double (((((double double) double) double) add1) 0))
          (fun f (fun x (f (f x))))))
 initial-env)

=> 65536

Or in JavaScript:

evaluate(
  parse([["fun", "d", [[[[["d", "d"], "d"], "d"], "add1"], 0]],
         ["fun", "f", ["fun", "x", ["f", ["f", "x"]]]]]),
  initial_env)

=> 65536

And we are done. Complete code is available here [Scheme] and here [JavaScript].

I’ve always had a strong respect for Mozilla. Their commitment to openness and support for standards and free software makes the world a better place to live in. Literally. And Eich’s candor and fluency in research really impressed me. The fact that they fund fundamental research in the theory of hygienic macros speaks to their seriousness in academic work. (And if they had a research lab, I’d take half as much money to get a job there.)

I had known for a long time that JavaScript was the Schemer’s hidden gem in the overwhelmingly turdish world of real-world technologies. But I didn’t realize the extent to which Scheme itself had influenced its design. Eich describes his days at Netscape building the first JavaScript implementation as the “Scheme in the Browser” project. You might go so far as to say JavaScript is the world’s most ubiquitous dialect of Scheme.

So today, I thought I’d give JavaScript a test run and throw some of my favorite functional programs at it to see how far the Scheme in the Browser analogy went. Here’s the transcript of one of my favorites: iterative doubling.

>>> function add1(n) {return n+1;}
>>> add1(0);
1
>>> function double(f) {return function (x) {return f(f(x));}}
>>> double(add1);
function()
>>> double(add1)(0);
2
>>> double(double)(add1)(0);
4
>>> double(double)(double)(add1)(0);
16
>>> double(double)(double)(double)(add1)(0);
65536
>>> double(double)(double)(double)(double)(add1)(0);
error: too much recursion

OK, so there’s really no “recursion” going on here, but that’s forgiveable. The point is, if you’re used to programming in a dynamically typed, higher-order programming language with a REPL (I’m using Firebug), this little exercise should make you feel right at home.

(You might miss having big numbers. This isn’t all that satisfying:

>>> Math.pow(2,Math.pow(2,2));
16
>>> Math.pow(2,Math.pow(2,Math.pow(2,2)));
65536
>>> Math.pow(2,Math.pow(2,Math.pow(2,Math.pow(2,2))));
Infinity

The correct answer to that last one is much, much smaller than infinity:

200352993040684646497907235156025575044782547556975141926501
697371089405955631145308950613088093334810103823434290726318
182294938211881266886950636476154702916504187191635158796634
721944293092798208430910485599057015931895963952486337236720
300291696959215610876494888925409080591145703767520850020667
156370236612635974714480711177481588091413574272096719015183
628256061809145885269982614142503012339110827360384376787644
904320596037912449090570756031403507616256247603186379312648
470374378295497561377098160461441330869211810248595915238019
533103029216280016056867010565164675056803874152946384224484
529253736144253361437372908830379460127472495841486491593064
725201515569392262818069165079638106413227530726714399815850
881129262890113423778270556742108007006528396332215507783121
428855167555407334510721311242739956298271976915005488390522
380435704584819795639315785351001899200002414196370681355984
046403947219401606951769015611972698233789001764151719005113
346630689814021938348143542638730653955296969138802415816185
956110064036211979610185953480278716720012260464249238511139
340046435162386756707874525946467090388654774348321789701276
445552940909202195958575162297333357615955239488529757995402
847194352991354376370598692891375715374000198639433246489005
254310662966916524341917469138963247656028941519977547770313
806478134230959619096065459130089018888758808473362595606544
488850144733570605881709016210849971452956834406197969056546
981363116205357936979140323632849623304642106613620022017578
785185740916205048971178182040018728293994344618622432800983
732376493181478984811945271300744022076568091037620399920349
202390662626449190916798546151577883906039772075927937885224
129430101745808686226336928472585140303961555856433038545068
865221311481363840838477826379045960718687672850976347127198
889068047824323039471865052566097815072986114143030581692792
497140916105941718535227588750447759221830115878070197553572
224140001954810200566177358978149953232520858975346354700778
669040642901676380816174055040511767009367320280454933902799
249186730653993164072049223847481528061916690093380573212081
635070763435166986962502096902316285935007187419057916124153
689751480826190484794657173660100589247665544584083833479054
414481768425532720731558634934760513741977952519036503219802
010876473836868253102518337753390886142618480037400808223810
407646887847164755294532694766170042446106331123802113458869
453220011656407632702307429242605158281107038701834532456763
562595143003203743274078087905628366340696503084422585596703
927186946115851379338647569974856867007982396060439347885086
164926030494506174341236582835214480672667684180708375486221
140823657980296120002744132443843240233125740354501935242877
643088023285085588608996277445816468085787511580701474376386
797695504999164399828435729041537814343884730348426190338884
149403136613985425763557710533558020662218557706008255128889
333222643628198483861323957067619140963853383237434375883085
923372228464428799624560547693242899843265267737837317328806
321075321123868060467470842805116648870908477029120816110491
255559832236624486855665140268464120969498259056551921618810
434122683899628307165486852553691485029953967550395493837185
340590009618748947399288043249637316575380367358671017578399
481847179849824694806053208199606618343401247609663951977802
144119975254670408060849934417825628509272652370989865153946
219300460736450792621297591769829389236701517099209153156781
443979124847570623780460000991829332130688057004659145838720
808801688744583555792625846512476308714856631352893416611749
061752667149267217612833084527393646924458289257138887783905
630048248379983969202922221548614590237347822268252163995744
080172714414617955922617508388902007416992623830028228624928
418267124340575142418856999427233160699871298688277182061721
445314257494401506613946316919762918150657974552623619122484
806389003366907436598922634956411466550306296596019972063620
260352191777674066877746354937531889958786628212546979710206
574723272137291814466665942187200347450894283091153518927111
428710837615922238027660532782335166155514936937577846667014
571797190122711781278045024002638475878833939681796295069079
881712169068692953824852983002347606845411417813911064856023
654975422749723100761513187002405391051091381784372179142252
858743209852495787803468370333781842144401713868812424998441
861812927119853331538256732187042153063119774853521467095533
462633661086466733229240987984925669110951614361860154890974
024191350962304361219612816595051866602203071561368473236466
086890501426391390651506390819937885231836505989729912540447
944342516677429965981184923315155527288327402835268844240875
281128328998062591267369954624734154333350014723143061275039
030739713525206933817384332295070104906186753943313078479801
565513038475815568523621801041965025559618193498631591323303
609646190599023611268119602344184336333459492763194610171665
291382371718239429921627253846177606569454229787707138319881
703696458868981186321097690035573588462446483570629145305275
710127887202796536447972402540544813274839179412882642383517
194919720979714593688753719872913083173803391101612854741537
737771595172808411162759718638492422280237344192546999198367
219213128703558530796694271341639103388275431861364349010094
319740904733101447629986172542442335561223743571582593338280
498624389249822278071595176275784710947511903348224141202518
268871372819310425347819612844017647953150505711072297431456
991522345164312184865757578652819756484350895838472292353455
946452121583165775147129870822590929265563883665112068194383
690411625266871004456024370420066370900194118555716047204464
369693285006004692814050711906926139399390273553454556747031
490388602202463994826050176243196930564066636662609020704888
743889890749815286544438186291738290105182086993638266186830
391527326458128678280660133750009659336462514609172318031293
034787742123467911845479131110989779464821692250562939995679
348380169915743970053754213448587458685604728675106542334189
383909911058646559511364606105515683854121745980180713316361
257307961116834386376766730735458349478978831633012924080083
635682593915711313097803051644171668251834657367593419808495
894794098329250008638977856349469321247342610306271374507728
615692259662857385790553324064184901845132828463270926975383
086730840914224765947443997334813081098639941737978965701068
702673416196719659159958853783482298827012560584236558953969
030647496558414798131099715754204325639577607048510088157829
140825077773855979012912940730946278594450585941227319481275
322515232480150346651904822896140664689030510251091623777044
848623022948896671138055560795662073244937337402783676730020
301161522700892184351565212137921574820685935692079021450227
713309998772945959695281704458218195608096581170279806266989
120506156074232568684227130629500986442185347081040712891764
690655083612991669477802382250278966784348919940965736170458
678624255400694251669397929262471452494540885842272615375526
007190433632919637577750217600519580069384763578958687848953
687212289855780682651819270363209948015587445557517531273647
142129553649408438558661520801211507907506855334448925869328
385965301327204697069457154695935365857178889486233329246520
273585318853337094845540333656535698817258252891805663548836
374379334841184558016833182767683464629199560551347003914787
680864032262961664156066750815371064672310846196424753749055
374480531822600271021640098058449752602303564003808347205314
994117296573678506642140084269649710324191918212121320693976
914392336837470922826773870813223668008692470349158684099115
309831541206356612318750430546753698323082796645741762080659
317726568584168183796610614496343254411170694170022265781735
835125982108076910196105222926387974504901925431190062056190
657745241619191318753398404934397682331029846589331837301580
959252282920682086223033258528011926649631444131644277300323
779227471233069641714994553226103547514563129066885434542686
978844774298177749371011761465162418361668025481529633530849
084994300676365480610294009469375060984558855804397048591444
958444507997849704558355068540874516331646411808312307970438
984919050658758642581073842242059119194167418249045270028826
398305795005734171148703118714283418449915345670291528010448
514517605530697144176136858238410278765932466268997841831962
031226242117739147720800488357833356920453393595325456489702
855858973550575123512953654050284208102278524877660357424636
667314868027948605244578267362623085297826505711462484659591
421027812278894144816399497388188462276824485162205181707672
216986326570165431691974265123004175732990447353767253684579
275436541282655358185804684006936771860502007054724754840080
553042495185449526724726134731817474218007857469346544713603
697588411802940803961674694628854067917213860122541950381970
453841726800639882065632879283958270851091995883944829777564
715202613287108952616341770715164289948795356485455355314875
497813400996485449863582484769059003311696130376612792346432
312970662841130742704620203201336835038542536031363676357521
260470742531120923340283748294945310472741896928727557202761
527226828337674139342565265328306846999759709775000556088993
268502504921288406827413988163154045649035077587168007405568
572402175868543905322813377070741583075626962831695568742406
052772648585305061135638485196591896864959633556821697543762
143077866593473045016482243296489127070989807667662567151726
906205881554966638257382927418208227896068448822298339481667
098403902428351430681376725346012600726926296946867275079434
619043999661897961192875051944235640264430327173734159128149
605616835398818856948404534231142461355992527233006488162746
672352375123431189344211888508507935816384899448754475633168
921386967557430273795378526254232902488104718193903722066689
470220425883689584093999845356094886994683385257967516188215
941098162491874181336472696512398067756194791255795744647142
786862405375057610420426714936608498023827468057598259133100
691994190465190653117190892607794911921794640735512963386452
303567334558803331319708036545718479155043265489955970586288
828686660661802188224860214499997312216413817065348017551043
840662441282280361664890425737764095632648282525840766904560
843949032529052633753231650908768133661424239830953080654966
187938194912003391948949406513239881664208008839555494223709
673484007264270570116508907519615537018626479745638118785617
545711340047381076276301495330973517418065547911266093803431
137853253288353335202493436597912934128485497094682632907583
019307266533778255931433111096384805394085928398890779621047
984791968687653998747709591278872747587443980677982496827827
220092644994455938041460877064194181044075826980568803894965
461658798390466058764534181028990719429302177451997610449504
319684150345551404482092893337865736305283061999007774872692
299860827905317169187657886090894181705799340489021844155979
109267686279659758395248392673488363474565168701616624064242
424122896111801061568234253939218005248345472377921991122859
591419187749179382334001007812832650671028178139602912091472
010094787875255126337288422235386949006792766451163475810119
387531965724212147603828477477457170457861041738574791130190
858387789015233434301300528279703858035981518292960030568261
209195094373732545417105638388704752895056396102984364136093
564163258940813798151169333861979733982167076100460798009601
602482309694304380695662012321365014054958625061528258803302
290838581247846931572032323360189946943764772672187937682643
182838260356452069946863021604887452842436359355862233350623
594500289055858161127534178375045593612613085264082805121387
317749020024955273873458595640516083058305377073253397155262
044470542957353836111367752316997274029294167420442324811387
507563131907827218886405337469421384216992886294047963530515
056078812636620649723125757901959887304119562622734372890051
656111109411174527796548279047125058199907749806382155937688
554649882293898540829132512907647838632249478101675349169348
928810420301561028338614382737816094634133538357834076531432
141715065587754782025245478065730134227747061674424196895261
316427410469547462148375628829977180418678508454696561915090
869587425118443583730659095146098045124740941137389992782249
298336779601101538709612974970556630163730720275073475992294
379239382442742118615823616131788639255309511718842129850830
723825972914414225157940388301135908333165185823496722125962
181250705811375949552502274727467436988713192667076929919908
446716122873885845758462272657333075373557282395161696417519
867501268174542932373829414382481437713986190671665757294580
780482055951188168718807521297183263644215533678775127476694
079011705750981957508456356521738954417987507452385445520013
357203333237989507439390531291821225525983379090946363020218
535384885482506289771561696386071238277172562131346054940177
041358173193176337013633225281912754719144345092071184883836
681817426334294961187009150304916533946476371776643912079834
749462739782217150209067019030246976215127852195614207080646
163137323651785397629209202550028896201297014137964003805573
494926907353514596120867479654773369295877362863566014376796
403843079686413856344780132826128458918489852804804884418082
163942397401436290348166545811445436646003249061876303950235
640204453074821024136689519664422133920075747912868380517515
063466256939193774028351207566626082989049187728783385217852
279204577184696585527879044756219266399200840930207567392536
373562839082981757790215320210640961737328359849406665214119
818381088451545977289516457213189779790749194101314836854463
961690460703010759681893374121757598816512700076126278916951
040631585763753478742007022205107089125761236165802680681585
849985263146587808661680073326467683020639169720306489440562
819540619068524200305346315662189132730906968735318164109451
428803660599522024824888671155442910472192913424834643870536
850864874909917881267056566538719104972182004237149274016446
094345984539253670613221061653308566202118896823400575267548
610147699368873820958455221157192347968688816085363161586288
015039594941852948922707441082820716930338781808493620401825
522227101098565344481720747075601924591559943107294957819787
859057894005254012286751714251118435643718405356302418122547
326609330271039796809106493927272268303541046763259135527968
383770501985523462122285841055711992173171796980433931770775
075562705604783177984444763756025463703336924711422081551997
369137197516324130274871219986340454824852457011855334267526
471597831073124566342980522145549415625272402891533335434934
121786203700726031527987077187249123449447714790952073476138
542548531155277330103034247683586549609372232400715451812973
269208105842409055772564580368146223449318970813889714329983
134761779967971245378231070373915147387869211918756670031932
128189680332269659445928621060743882741691946516226763254066
507088107103039417886056489376981673415902592519461182364294
565266937220315550470021359884629275801252771542201662995486
313032491231102962792372389976641680349714122652793190763632
613681414551637665655983978848938173308266877990196288693229
659737995193162118721545528739417024366988559388879331674453
336311954151840408828381519342123412282003095031334105070476
015998798547252919066522247931971544033179483683737322082188
577334162385644138070054191353024594391350255453188645479625
226025176292837433046510236105758351455073944333961021622967
546141578112719700173861149427950141125328062125477581051297
208846526315809480663368767014731073354071771087661593585681
409821296773075919738297344144525668877085532457088895832099
382343210271822411476373279135756861542125284965790333509315
277692550584564401055219264450531207375628774499816364633283
581614033017581396735942732769044892036188038675495575180689
005853292720149392350052584514670698262854825788326739873522
045722823929020714482221988558710289699193587307427781515975
762076402395124386020203259659625021257834995771008562638611
823381331850901468657706401067627861758377277289589274603940
393033727187385053691295712671506689668849388088514294360996
201296675907922508227531381284985152690293170026313632894209
579757795932763553116206675348865131732387243874806351331451
264488996758982881292548007642518658649024111112730135719718
138160258317850693224400799865663537154408845486639318170839
573578079905973083909488180406093595919090747396090441015051
632174968141210076571917748376735575100073361692238653742907
945780320004233745280756615304292901449578062963413838355178
359976470885134900485697369796523869584599459559209070905895
689145114141268450546211794502661175016692826025095077077821
195043261738322356243760177679936279609936897519139496503335
850715541843645685261667424368892037103749532842592713161053
783498074073915863381796765842525803673720646935124865223848
134166380806150570482905989069645193644001859712042572300731
641000991698752426037736217776343062161674488493081092990100
951797454156425120482208671458684925513244426677712786372821
133153622430109182439124338021404624222334915355951689081628
848798998827363044537243217428021575577796702166631704796972
817248339284101564227450727177926939992974030807277039501358
154514249404902653610582540937311465310494338248437971860693
721444460082679800247122948940576185389220342560830269705287
662137737359439422411470707407290272546130735854174569141944
648762435768239706570318416846754073346634629367398362000404
140071405427763248013274220268539369886978760700959004868465
062677136307097982100655728510130660101078063374334477307347
865388174268123074376606664331277535646657860371519292276844
045827328324380821284121877613204246046490080105473142674926
082692215563740548624171703102791999694264562095561981645454
766204502241144940474934983220680719135276798674781345820385
957041346617793722853494003163159954409368408957253343870298
671782977037333280680176463950209002394193149911500910527682
111951099906316615031158558283558260717941005252858361136996
130344279017381178741206128818206202326384986151565645123004
779296756361834576810504334176954306753804111392855379252924
134733948105053202570872818630729115891133594201476187266429
156403637192760230628384065042544174233546454998705531872688
792642410214736369862546374715974435494344389973005174252511
087735788639094681209667342815258591992485764048805507132981
429935991146323991911395992675257635900744657281019180584180
734222773472139772321823177171691640010882611254909336118678
057572239101818616854910850088527227437421208652485237245624
869766224538481929867112945294551549703058591930719849710541
418163696897613112674402700964866754593456705993699546450055
892162804797636568613331656390739570327203438917541526750091
501119885687270884819553167693168127289214303137681801644547
736751835349785792427646335416243360112596025210950161226411
034608346564823559793427405686884922445874549377675212032470
380303549115754483129527589193989368087632768543876955769488
142284431199859570072752139317683783177033913042306095899913
731468456901042209516196707050642025673387344611565527617599
272715187766001023894476053978951694570880272873622512107622
409181006670088347473760515628553394356584375627124124445765
166306408593950794755092046393224520253546363444479175566172
596218719927918657549085785295001284022903506151493731010700
944615101161371242376142672254173205595920278212932572594714
641722497732131638184532655527960427054187149623658525245864
893325414506264233788565146467060429856478196846159366328895
429978072254226479040061601975197500746054515006029180663827
149701611098795133663377137843441619405312144529185518013657
555866761501937302969193207612000925506508158327550849934076
879725236998702356793102680413674571895664143185267905471716
996299036301554564509004480278905570196832831363071899769915
316667920895876857229060091547291963638167359667395997571032
601557192023734858052112811745861006515259888384311451189488
055212914577569914657753004138471712457796504817585639507289
5337539755822087777506072339445587895905719156736

Oh well.)