var Phi = (Math.sqrt(5)+1)/2 ,  phi = (Math.sqrt(5)-1)/2, Pi=Math.PI;

var myErr=false; 
//self.onerror=function(ErrMsg,URL,LineNb){if(myErr){halt(ErrMsg+"\r");return true}else{return false}};

function halt(msg){alert(msg);ERROR()};
function DoERROR(){return false};
function resetERROR(){self.onerror=DoERROR;return true};
function HALT(msg){alert("**Error**\r"+msg);//self.onerror=resetERROR;
   ERROR();};

function ECHO(txt){alert(txt);return txt};

function getArgs(opts){
  if(arguments.length==0)opts=location.search.substring(1);
  //alert("getArgs "+opts);
  var args=new Object();
  var pairs=opts.split(",");
  //if(pairs.length>0)alert("getArgs "+pairs);
  for(var i=0;i<pairs.length;i++)
  { var pos=pairs[i].indexOf("=");
	if(pos==-1)args[pairs[i]]=true  //allow ids with no values
	else args[pairs[i].substring(0,pos)]=pairs[i].substring(pos+1);
   };
   return args
 };
var outF;

function clearmsg(F){ if(arguments.length==0)F=outF; 
   document.getElementById('msg'+F).innerHTML=''};
   
function putmsg(txt){  
   var olist = document.getElementById('msg'+outF);
        olist.innerHTML += txt+"<br>";
        olist.scrollTop = olist.scrollHeight;
        olist.scrollLeft=0;
};

function isInt(i){return i.toString()!="" && i.toString().indexOf(".")==-1 
     &&i.toString().toLowerCase().indexOf("e")==-1 
     && !isNaN(i) && isFinite(i) && (i+1)!=i};
function isNb(r){return r!="" && !isNaN(r) &&isFinite(r)};
function log10(x){return Math.log(x)/Math.LN10}; 
function logB(B,x){return Math.log(x)/Math.log(B)};


function gcd(a,b){  return gcd1(Math.abs(a),Math.abs(b))  };
function gcd1(a,b){  
   do{     if(a==0) return b
      else if(b==0) return a
      else var aa=a;a=b%a;b=aa
     }while(true)
};

//var test=new Array("gcd(0,2)","gcd(2,0)","gcd(12,15)","gcd(144,89)");
//for(var i=0;i<test.length;i++)alert(test[i]+" = "+eval(test[i]));

function lcm(a,b){ return a/gcd(a,b)*b };
function powmod(Base,Pow,Mod){ 
  var pm;  
       if(Pow==0)pm= 1
  else if(Pow==1)pm= Base%Mod
  else if(Pow>1)
       {var s=powmod(Base,Math.round((Pow-Pow%2)/2),Mod);
        var ss=mul(s,s)%Mod;
        pm= (Pow%2==0 ? ss : (Base*ss)%Mod )  } ;
  return pm     
};
function isprime(N){ 
  if(N%2==0)return (N==2);
  var i=3,L=Math.sqrt(N),ct=0;
  //var stime=(new Date()).getTime();
  while(i<=L && N%i!=0){i=i+2; ct++}; // var inctime=(new Date()).getTime()-stime;  
  return(N>1 && i>L)
};

function primefactors(N){   
    if(N==1)return [1];
    var f=new Array(), II=N,L=Math.sqrt(N);
    while(II%2==0){f=f.concat(2);II=II/2;L=Math.sqrt(II)};
    for(var i=3;i<=L;i=i+2)
       while(i<=L && II%i==0){f=f.concat(i);II=II/i;L=Math.sqrt(II)};
    if(II>1)f=f.concat(II);
    return f
};
function cpfrom(PrevAnss,Li,L,F){ 
   if(L.length==Li)return F(PrevAnss);
   var ans=[];
   for(var i=0;i<=L[Li][1];i++)
      ans=ans.concat(cpfrom(PrevAnss.concat(Math.pow(L[Li][0],i)), Li+1, L, F));
   return ans
};
function ordlistToZbag(L){    
   var s=L[0],ct=1,i,z=[];
   for(var i=1;i<L.length;i++)
     if(L[i]==s)ct++
     else {z=z.concat([[s,ct]]);s=L[i];ct=1};
   z=z.concat([[s,ct]]);
    return z
};
function EulerPhi(N){  
  var pfs=ordlistToZbag(primefactors(N));
  var phi=1,i=0;
  while(i<pfs.length)  {var pr=pfs[i][0],po=pfs[i][1]; i++; phi=phi*Math.pow(pr,po-1)*(pr-1)}; 
 return phi
};

function factors(N){  
  if(N==1)return [1];
  return cpfrom([],0,ordlistToZbag(primefactors(N)),function(L){return eval(L.join('*'))})
   .sort(function(a,b){return a-b});
};


function strip(s,remCh){
  if(arguments.length==1)remCh=" ";
  var i=0;while(i<s.length && s.substring(i,i+1)==remCh)i++;
  return s.substring(i)};
  
function endswith(s,x){if(typeof s != "string")s=s.toString(); if(typeof x != "string")x=x.toString();
  if(s.substring(s.slength-1)==" ")s=revstr(strip(revstr(s)));
  if(s.length>=x.length){return s.substring(s.length-x.length)==x }else{return false}};
  
function beginswith(s,x){ if(typeof s != "string")s=s.toString(); if(typeof x != "string")x=x.toString();
  s=strip(s," ");
  if(s.length>=x.length){return s.substring(0,x.length)==x }else{return false}};
  
function revstr(r){var s="";for(var i=0;i<r.length;i++)s=r.charAt(i)+s;return s};
  
function randint(lo,hi){ with(Math){return floor(random()*(hi-lo+1))+lo} };
function randelt(vals){
   if(arguments.length==1)
      {if(typeof vals=="object")return vals[randint(0,vals.length-1)]
       else if(typeof vals == "string")return randelt(vals.split(""));
      }
   else return arguments[randint(0,arguments.length-1)]
};


function evalstr(fld)
  {try{var i=eval(fld.replace("sqrt","Math.sqrt").replace(/infinity/,"Infinity")
                .replace(/pi/ig,"Math.PI").replace("E","Math.E"))
  }catch(e){}
   return i};
   
function checkinput(fld,nm,opts){  // default: eval input, or include opt "noeval"
   var i,res;//alert("checkinput "+fld+" "+nm);
   var opts=arguments.length<3?new Object():getArgs(opts);
   if(!opts.emptyval)opts.emptyval=""; //Empty always allowed (when clicking on (?) button; use 'emptyval=NaN' otherwise 
   //alert(typeof opts.noeval);
   if(!opts.hasOwnProperty("noeval"))opts.noeval=false;
   //alert(fld);
   fld=fld.replace(/\s/g,"");
   //alert("< "+fld+" "+nm);
   if(fld=="")return opts.emptyval;
   if(!opts.noeval)
       {var xtra=fld.replace(/sqrt/g,"").replace(/[Ii]nfinity/g,"").replace(/pi/gi,"").replace(/[0-9eE\.\-\*\/+\(\)\s]/g,"")
          if(xtra!="" )
              halt(nm+": Only numbers, fractions, E, Pi, sqrt, Infinity and -Infinity are allowed in input boxes\nFound "+xtra)
              // don't allow trig fns etc
          else try{i=evalstr(fld) }
               catch(evt){halt("I do not understand your input to "+nm+"\nPlease change it");return NaN}
         
       if(opts.eval&&isNaN(i))
         {//alert(nm+" is NaN");
            if(fld=="") i=opts.emptyval // empty fields always allowed as input ELSE use:-
           //else if(isemptyinput(fld))halt("The "+nm+" input box must have a value typed in.")
         else halt("No number found for "+nm)};
         res=i
     }
     else res=fld;
   //debug(nm+" Noeval="+opts.noeval+" = "+res);
   return res
 };
 
function isemptyinput(str){return str.replace(/\s/,'')==''};


var maxdps=Math.PI.toString().length-2;

function pad(used,requd){ if(typeof used != "string")used=used.toString();
  used=used.length;
  return (requd<=used?"":"                    ".slice(0,requd-used).replace(/ /g,"&nbsp;"))
};

function fw(n,fwd,pad){ if(arguments.length<3)pad=" ";
   var s=n.toString(); while(s.length<fwd)s=pad+s;  return s};
function fw2(n){  if(n<10){return " "+n   } else return n};


function hideId(nm) { if(arguments.length==0)nm="Soln";
        if (document.getElementById) {document.getElementById(nm).style.visibility = "hidden";}
   else if (document.all) {document.all[nm].style.visibility = "hidden";}
   else if (document.layers) {document[nm].visibility = "hide";}
   else {var w=eval(nm).style;w.visibility="hidden"};
};
function showId(nm) {if(arguments.length==0)nm="Soln";
	     if (document.getElementById) {document.getElementById(nm).style.visibility = "visible"; } 
    else if (document.all) {document.all[nm].style.visibility = "visible"; } 
	else if (document.layers) {document[nm].visibility = "show"; } 
	else {var w=eval(nm).style;w.visibility="visible"};
};
function setStyle(nm,valpair) {if(arguments.length==0)nm="Soln";
   var attr=valpair.slice(0,valpair.indexOf(":")),attrval=valpair.slice(valpair.indexOf(":")+1);
        if (document.getElementById) {document.getElementById(nm).style[attr] = attrval } 
    else if (document.all) {document.all[nm].style[attr] = attrval } 
	else if (document.layers) {document[nm][attr] = attrval } 
	else {var w=eval(nm).style;w[attr]=attrval};
};

function ARR(lo,hi,mt){//JS array type which allows -ve indices
//putmsg("ARR "+lo+" "+hi+" "+mt)
  if(arguments.length<3)mt=0;
  this.empty=mt;
  this.lwb=lo;this.upb=hi;
  this.elts=new Array(hi-lo+1);for(var i=0;i<hi-lo+1;i++)this.elts[i]=this.empty;
  this.length=this.upb-this.lwb+1;
  this.at=function(i){if(this.inrange(i)){return this.elts[i-this.lwb]} else return this.empty};
  this.set=function(ind,val){
          if(ind<this.lwb){var extra=new Array();for(var i=this.lwb-1;i>=ind;i--)extra[i-ind]=this.empty;this.lwb=ind;
                 this.elts=extra.concat(this.elts)}
     else if(ind>this.upb){var extra=new Array();for(var i=0;i<ind-this.upb;i++)extra[i]=this.empty;this.upb=ind;
                 this.elts=this.elts.concat(extra)}
     this.elts[ind-this.lwb]=val};
  this.inc=function(i,addon){var currval=this.at(i);this.set(i,currval+addon)};
  this.inrange=function(i){return i>=this.lwb && i<=this.upb};
  this.toString=function(){return this.elts};
  this.inrng=function(lind,rind){
           return this.elts.slice(lind-this.lwb,rind-this.lwb+1)}
 }
 
 function changeOpac(opacity, id) {
    var object = document.getElementById(id).style;
    object.opacity = (opacity / 100);
     object.KhtmlOpacity = (opacity / 100);
}

function blendimage(divid, imageid, imagefile, millisec) {
    var speed = Math.round(millisec / 100);
    var timer = 0;
    
    //set the current image as background
    document.getElementById(divid).style.backgroundImage = "url(" + document.getElementById(imageid).src + ")";
    
    //make image transparent
    changeOpac(0, imageid);
    
    //make new image
    document.getElementById(imageid).src = imagefile;

    //fade in image
    for(var i = 0; i <= 100; i++) {
        setTimeout("changeOpac(" + i + ",'" + imageid + "')",(timer * speed));
        timer++;
    }
} 
	
function showMoreOrLess(divId,incdec){ //needs a hidden field divId+"depth" containing the depth in em
    var v=document.getElementById(divId+"depth").value;
    if(!isNaN(v))
    {  v=eval(v)+incdec;
       if(v<15)v=15;
       document.getElementById(divId).style.height=v+'em'
}   }