type ref;
type realVar;
type classConst;
// type Field x;
// var $HeapVar : <x>[ref, Field x]x;

const unique $null : ref ;
const unique $intArrNull : [int]int ;
const unique $realArrNull : [int]realVar ;
const unique $refArrNull : [int]ref ;

const unique $arrSizeIdx : int;
var $intArrSize : [int]int;
var $realArrSize : [realVar]int;
var $refArrSize : [ref]int;

var $stringSize : [ref]int;

//built-in axioms 
axiom ($arrSizeIdx == -1);

//note: new version doesn't put helpers in the perlude anymore//Prelude finished 



var int$Random$index0 : int;
var java.lang.String$lp$$rp$$Random$args254 : [int]ref;


// procedure is generated by joogie.
function {:inline true} $neref(x : ref, y : ref) returns (__ret : int) {
if (x != y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $realarrtoref($param00 : [int]realVar) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $modreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



	 //  @line: 5
// <Random: int random()>
procedure int$Random$random$2233() returns (__ret : int)
  modifies int$Random$index0, $stringSize;
 {
var r020 : ref;
var $r119 : [int]ref;
var $i323 : int;
var $i018 : int;
var $i222 : int;
var $i121 : int;
	 //  @line: 6
Block41:
	 //  @line: 6
	$r119 := java.lang.String$lp$$rp$$Random$args254;
	 //  @line: 6
	$i018 := int$Random$index0;
	 assert ($geint(($i018), (0))==1);
	 assert ($ltint(($i018), ($refArrSize[$r119[$arrSizeIdx]]))==1);
	 //  @line: 6
	r020 := $r119[$i018];
	 //  @line: 7
	$i121 := int$Random$index0;
	 //  @line: 7
	$i222 := $addint(($i121), (1));
	 //  @line: 7
	int$Random$index0 := $i222;
	$i323 := $stringSize[r020];
	 //  @line: 8
	__ret := $i323;
	 return;
}


// procedure is generated by joogie.
function {:inline true} $leref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $modint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $gtref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqrealarray($param00 : [int]realVar, $param11 : [int]realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $addint(x : int, y : int) returns (__ret : int) {
(x + y)
}


// procedure is generated by joogie.
function {:inline true} $subref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $inttoreal($param00 : int) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $shrint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $negReal($param00 : realVar) returns (__ret : int);



// <GCD: void <init>()>
procedure void$GCD$$la$init$ra$$2228(__this : ref)  requires ($neref((__this), ($null))==1);
 {
var r01 : ref;
Block16:
	r01 := __this;
	 assert ($neref((r01), ($null))==1);
	 //  @line: 1
	 call void$java.lang.Object$$la$init$ra$$28((r01));
	 return;
}


// procedure is generated by joogie.
function {:inline true} $ushrint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $refarrtoref($param00 : [int]ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $divref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $mulref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $neint(x : int, y : int) returns (__ret : int) {
if (x != y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $ltreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $reftorefarr($param00 : ref) returns (__ret : [int]ref);



// procedure is generated by joogie.
function {:inline true} $gtint(x : int, y : int) returns (__ret : int) {
if (x > y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $reftoint($param00 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $addref($param00 : ref, $param11 : ref) returns (__ret : ref);



	 //  @line: 15
// <GCD: int gcd(int,int)>
procedure int$GCD$gcd$2230($param_0 : int, $param_1 : int) returns (__ret : int) {
var i19 : int;
var i07 : int;
var i210 : int;
Block34:
	i19 := $param_0;
	i210 := $param_1;
	 goto Block35;
	 //  @line: 16
Block35:
	 goto Block36, Block38;
	 //  @line: 16
Block36:
	 assume ($eqint((i210), (0))==1);
	 goto Block37;
	 //  @line: 16
Block38:
	 //  @line: 16
	 assume ($negInt(($eqint((i210), (0))))==1);
	 //  @line: 17
	i07 := i210;
	 //  @line: 18
	 call i210 := int$GCD$mod$2229((i19), (i210));
	 //  @line: 19
	i19 := i07;
	 goto Block35;
	 //  @line: 21
Block37:
	 //  @line: 21
	__ret := i19;
	 return;
}


// procedure is generated by joogie.
function {:inline true} $xorreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $andref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $cmpreal(x : realVar, y : realVar) returns (__ret : int) {
if ($ltreal((x), (y)) == 1) then 1 else if ($eqreal((x), (y)) == 1) then 0 else -1
}


// procedure is generated by joogie.
function {:inline true} $addreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $gtreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



	 //  @line: 2
// <GCD: int mod(int,int)>
procedure int$GCD$mod$2229($param_0 : int, $param_1 : int) returns (__ret : int) {
var i03 : int;
var i14 : int;
Block17:
	i14 := $param_0;
	i03 := $param_1;
	 goto Block18;
	 //  @line: 3
Block18:
	 goto Block19, Block21;
	 //  @line: 3
Block19:
	 assume ($leint((i14), (0))==1);
	 goto Block20;
	 //  @line: 3
Block21:
	 //  @line: 3
	 assume ($negInt(($leint((i14), (0))))==1);
	 goto Block22;
	 //  @line: 4
Block20:
	 //  @line: 4
	__ret := 0;
	 return;
	 //  @line: 4
Block22:
	 goto Block25, Block23;
	 //  @line: 4
Block25:
	 //  @line: 4
	 assume ($negInt(($gtint((i03), (0))))==1);
	 goto Block20;
	 //  @line: 4
Block23:
	 assume ($gtint((i03), (0))==1);
	 goto Block24;
	 //  @line: 5
Block24:
	 goto Block26, Block28;
	 //  @line: 5
Block26:
	 assume ($neint((i14), (i03))==1);
	 goto Block27;
	 //  @line: 5
Block28:
	 //  @line: 5
	 assume ($negInt(($neint((i14), (i03))))==1);
	 goto Block29;
	 //  @line: 8
Block27:
	 goto Block32, Block30;
	 //  @line: 6
Block29:
	 //  @line: 6
	__ret := 0;
	 return;
	 //  @line: 8
Block32:
	 //  @line: 8
	 assume ($negInt(($leint((i14), (i03))))==1);
	 goto Block33;
	 //  @line: 8
Block30:
	 assume ($leint((i14), (i03))==1);
	 goto Block31;
	 //  @line: 9
Block33:
	 //  @line: 9
	i14 := $subint((i14), (i03));
	 goto Block27;
	 //  @line: 11
Block31:
	 //  @line: 11
	__ret := i14;
	 return;
}


// procedure is generated by joogie.
function {:inline true} $eqreal(x : realVar, y : realVar) returns (__ret : int) {
if (x == y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $ltint(x : int, y : int) returns (__ret : int) {
if (x < y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $newvariable($param00 : int) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $divint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $geint(x : int, y : int) returns (__ret : int) {
if (x >= y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $mulint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $leint(x : int, y : int) returns (__ret : int) {
if (x <= y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $shlref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqrefarray($param00 : [int]ref, $param11 : [int]ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $reftointarr($param00 : ref) returns (__ret : [int]int);



// procedure is generated by joogie.
function {:inline true} $ltref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $mulreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $shrref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $ushrreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $shrreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



	 //  @line: 2
// <Random: void <clinit>()>
procedure void$Random$$la$clinit$ra$$2234()
  modifies int$Random$index0;
 {
	 //  @line: 3
Block42:
	 //  @line: 3
	int$Random$index0 := 0;
	 return;
}


// procedure is generated by joogie.
function {:inline true} $divreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $orint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $reftorealarr($param00 : ref) returns (__ret : [int]realVar);



// procedure is generated by joogie.
function {:inline true} $cmpref(x : ref, y : ref) returns (__ret : int) {
if ($ltref((x), (y)) == 1) then 1 else if ($eqref((x), (y)) == 1) then 0 else -1
}


// procedure is generated by joogie.
function {:inline true} $realtoint($param00 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $geref($param00 : ref, $param11 : ref) returns (__ret : int);



// <java.lang.String: int length()>
procedure int$java.lang.String$length$59(__this : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $orreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqint(x : int, y : int) returns (__ret : int) {
if (x == y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $ushrref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $modref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $eqintarray($param00 : [int]int, $param11 : [int]int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $negRef($param00 : ref) returns (__ret : int);



// <java.lang.Object: void <init>()>
procedure void$java.lang.Object$$la$init$ra$$28(__this : ref);



// procedure is generated by joogie.
function {:inline true} $lereal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $nereal(x : realVar, y : realVar) returns (__ret : int) {
if (x != y) then 1 else 0
}


	 //  @line: 24
// <GCD: void main(java.lang.String[])>
procedure void$GCD$main$2231($param_0 : [int]ref)
  modifies $stringSize, java.lang.String$lp$$rp$$Random$args254;
 {
var i013 : int;
var r011 : [int]ref;
var i115 : int;

 //temp local variables 
var $freshlocal0 : int;

Block39:
	r011 := $param_0;
	 //  @line: 25
	java.lang.String$lp$$rp$$Random$args254 := r011;
	 //  @line: 26
	 call i013 := int$Random$random$2233();
	 //  @line: 27
	 call i115 := int$Random$random$2233();
	 //  @line: 28
	 call $freshlocal0 := int$GCD$gcd$2230((i013), (i115));
	 return;
}


// procedure is generated by joogie.
function {:inline true} $instanceof($param00 : ref, $param11 : classConst) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $xorref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $orref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $intarrtoref($param00 : [int]int) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $subreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $shlreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $negInt(x : int) returns (__ret : int) {
if (x == 0) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $gereal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqref(x : ref, y : ref) returns (__ret : int) {
if (x == y) then 1 else 0
}


// <Random: void <init>()>
procedure void$Random$$la$init$ra$$2232(__this : ref)  requires ($neref((__this), ($null))==1);
 {
var r017 : ref;
Block40:
	r017 := __this;
	 assert ($neref((r017), ($null))==1);
	 //  @line: 1
	 call void$java.lang.Object$$la$init$ra$$28((r017));
	 return;
}


// procedure is generated by joogie.
function {:inline true} $cmpint(x : int, y : int) returns (__ret : int) {
if (x < y) then 1 else if (x == y) then 0 else -1
}


// procedure is generated by joogie.
function {:inline true} $andint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $andreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $shlint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $xorint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $subint(x : int, y : int) returns (__ret : int) {
(x - y)
}