"use strict";
var rollPrep=str=>str.replace(/\+-|-/,"+-").split("+");

function roll(str){
	var parts=rollPrep(str),
	sum=0;
	for(let i of parts){
		if(i.includes(/d/i)){
			i=i.split(/d/i);
			let I=Math.abs(i[0]||1);
			if(i>1e+7)sum+=Math.round(shortRoll(I,i[1]));
			else for(;I>=1;I--)sum+=Math.sign(i[0])*(Math.round(Math.random()*(i[1]-1))+1);
		}
		else sum+=Number(i);
	}
	return sum;
}

function rollP(str,p){
	var parts=rollPrep(str),
	sum=0;
	for(let i of parts){
		if(i.includes(/d/i)){
			i=i.split(/d/i);
			sum+=(i[0]||1)*(i[1]*p+1);
		}
		else sum+=Number(i);
	}
	return sum;
}

function shortRoll(n,s,o){
	var sign=Math.sign(n);
	n=Math.abs(n);
	var t=Math.min(1e+7*o?Math.min(Math.abs(o),10):1,n),
	m=n/t,
	sum=0;
	for(let i=1;i<=t;i++)sum+=m*(Math.round(Math.random()*s+1));
	return sign*sum;
}

var dieDist=(x,n,s)=>n<x<ns?Math.normDist(x,s/n,n*(s+1)/2):0;

/*function dieDistC(x,n,s){
	$ bower install numbers.js
	numbers.calculus.Riemann(t=>{dieDist(t,n,s)},n,x,200)/numbers.calculus.Riemann(t=>{dieDist(t,n,s)},n,ns,200);
	Math.int(x,n,dieDist(t,n,s),t)/Math.int(ns,n,dieDist(t,n,s),t);//????
}*/

Math.normDist=(x,o,u)=>Math.exp(-(x-u)**2/2*o**2)/o*Math.sqrt(2*Math.PI);
Math.between=(v,m,M)=>m<v<M;
Math.PHI=(1+Math.sqrt(5))/2;
Math.invPHI=2/(1+Math.sqrt(5));
Math.silverRatio=1+Math.sqrt(2);
Math.randomNum=(m=1,a=0,c=false)=>Math.random()*m+a-mi*c/2;
Math.randomInt=(mi=1,ai=0,mo=1,ao=0,c=false)=>Math.round(Math.randomNum(mi,ai,c))*mo+ao;
Math.randomBool=()=>Math.random()>=.5;
Math.TAU=2*Math.PI;
Math.sum=()=>attributes.reduce((c,v)=>c+v);
Math.diff=()=>attributes.reduce((c,v)=>c-v);
Math.prod=()=>attributes.reduce((c,v)=>c*v);//First value of c?=0
Math.div=()=>attributes.reduce((c,v)=>c/v);


class shape{
	constructor(){
		this.area={
			difference:s=>this.area-s.area,
			sum:s=>this.area+s.area,
			product:s=>this.area*s.area,
			ratio:s=>this.area/s.area
		}
		this.perimeter={
			difference:s=>this.perimeter-s.perimeter,
			sum:s=>this.perimeter+s.perimeter,
			product:s=>this.perimeter*s.perimeter,
			ratio:s=>this.perimeter/s.perimeter
		}
		this.volume=v=>this.area*v;
	}
}

class circle extends shape{
	constructor(r){
		this.radius=r;
		this.diameter=2*r;
		this.circumference=2*Math.PI*r;
		this.area=Math.PI*r**2;
		this.name=r=1?"unit circle":"circle";
	}
}

Array.prototype.sortN=function(){
	return this.sort((a,b)=>a-b);
}

class ellipse extends shape{
	constructor(a,b){
		super();
		this.axis=[b,a].sortN();
		this.a=a;
		this.b=b;
		this.eccentricity=Math.sqrt(1-b**2/a**2);
		this.semi_latusRectum=b**2/c**2;
		this.area=Math.PI*a*b;
		this.circumference=Math.PI*(3*(a+b)-Math.sqrt((3*a+b)*(a+3*b)));
		this.h=((a-b)/(a+b))**2;
		this.circumferenceAlt=Math.PI*(a+b)*(1+3*this.h/(10+Math.sqrt(4-3*this.h)));
		this.name="ellipse";
	}
	tangent(x,y){
		return [x/this.a**2,y/this.b**2];
	}
}

Math.divBy=(v,d)=>v%d==0;
Number.prototype.divBy=d=>this.valueOf();

class polygon extends shape{
	constructor(s){
		super();
		this.valid=s>2&&s%1==0;
		this.sideCount=s.length;
		this.sides=s;
		this.perimeter=s.reduce((a,v)=>a+v);
		this.interiorAngles=(this.sideCount-2)*Math.PI;
		this.regularAngles=this.interiorAngles/this.sideCount;
		this.exteriorAngles=2*Math.PI;
		this.name=this.sideCount+"-agon";
	}
}

class regularPolygon extends shape{
	constructor(s,n){
		super();
		this.sideCount=n;
		this.side=s;
		this.perimeter=s*n;
		this.apothem=s/(2*Math.tan(Math.PI/2));
		this.area=this.apothem*this.perimeter;
		this.interiorAngle=(this.sideCount-2)*Math.PI;
		this.angle=this.interiorAngles/this.sideCount;
		this.exteriorAngles=2*Math.PI;
		this.name="regular "n+"-agon";
	}
}

class triangle extends polygon{
	constructor(a,b,c){
		super([a,b,c]);
		let S=s=this.perimeter/2;
		this.area=Math.sqrt(S*(S-a)*(S-b)*(S-c));
		this.name="triangle";
	}
}

class equilateralTriangle extends regularPolygon{
	constructor(s){
		super(s,3);
		let S=s=this.perimeter/2;
		this.area=Math.sqrt(S(S-s)**3);
		this.name="equilateralTriangle";
	}
}

class quadragon extends polygon{
	constructor(a,b,c,d){
		super([a,b,c,d]);
		this.perimeter=2*w+2*h;
		this.parallelogram=null;
		this.name="quadragon";
	}
}

class kite extends quadragon{
	constructor(a,b,A){//A is the angle between a,b
		super([a,a,b,b]);
		this.angle=[A,A-Math.PI];
		this.area=a*b*Math.sin(A);
		this.diagonal={
			cross:Math.sqrt(a**2+b**2-2*a*b*Math.cos(A)),
			main:Math.sqrt(2*a**2-2*a**2*Math.cos(this.angle[1]))
		};
		this.parallelogram=false;
		this.name="kite";
	}
}

class rhombus extends kite{
	constructor(s,A){
		super(s,s,A);
		this.diagonal=this.diagonal.main;
		this.parallelogram=true;
		this.name="rhombus";
	}
}

class rectangle extends rhombus{
	constructor(w,h){
		super(w,h,Math.PI/2);
		this.parallelogram=true;
		this.name="rectangle";
	}
}

class square extends regularPolygon{
	constructor(s){
		super(s,4);
		this.angle=Math.PI/2;
		this.parallelogram=true;
		this.name="square";
	}
}

class trapezoid extends quadragon{
	constructor(b,s){
		super([b[0],s[0],b[1],s[1]);
		this.median=(b[0]+b[1])/2;
		let bs=Math.abs(b[0]-b[1])/2,
		S=(bs,s[0],s[1])/2,
		A=Math.sqrt(S*(S-s[0])*(S-s[1])*(S-bs));
		this.height=2*A/bs;
		this.area=this.height*this.median;
		this.parallelogram=false;
		this.name="trapezoid";
	}
}

class regularTrapezoid extends trapezoid{
	constructor(b,s){
		super(b[0],b[1],s,s);
		this.name="regularTrapezoid";
	}
}

class pentagon extends polygon{
	constructor(a,b,c,d,e){
		super([a,b,c,d,e]);
		this.name="pentagon";
	}
}

class regularPentagon extends regularPolygon{
	constructor(s){
		super(s,5);
		this.area=Math.sqrt(5*(5+2*Math.sqrt(5)))*s**2/4;
		this.diagonal=(1+Math.sqrt(5))*s/2;
		this.name="regularPentagon";
	}
}

class hexagon extends polygon{
	constructor(a,b,c,d,e,f){
		super([a,b,c,d,e,f]);
		this.name="hexagon";
	}
}

class regularHexagon extends polygon{
	constructor(s){
		super(s,6);
		this.area=3*s**2*Math.sqrt(3)/2;
		this.diagonal=3*s;
		this.name="regularHexagon";
	}
}

class point{
	constructor(x,y,z){
		this.x=x;
		this.y=y;
		this.xy=x/y;
		if(z){
			this.z=z;
			this.zx=z/x;
			this.zy=z/y;
		}
		else this.r=this.xy;
		let n=!z||z>0?0:4;
		this.quadrant=x>0?y>0?1+n:4+n:y>0?2+n:3+n;
		this.sign=[Math.sign(x),Math.sign(y),Math.sign(z)];
	}
}

class points extends polygon{
	constructor(p){
		let area=0,
		s=x=y=point=[];
		for(let i in p){
			point[i]=new point(...p[i]);
			let next=s[i+1]||s[0],
			v=s[i];
			v=Math.sqrt((v[0]-next[0])**2+(v[1]-next[1])**2);
			area+=v[0]*next[1]-v[1]*next[0];
			[x[i],y[i]]=p[i];
		}
		super(s);
		this.area=Math.abs(area/2);
		this.points=point;
		this.x=x;
		this.y=y;
	}
}

Math.rad=d=>d*Math.PI/180;
Math.deg=d=>d*180/Math.PI;
Math.csc=a=>1/Math.sin(a);
Math.sec=a=>1/Math.cos(a);
Math.cot=a=>1/Math.tan(a);

class angle{
	constructor(A,u="rad"){
		this.a=[A,u];
		switch(A){
			case "rad":
				break;
			case "deg":
				this.deg=A;
				A=Math.rad(A);
				break;
		}
		this.rad=A;
		if(!this.deg)this.deg=Math.deg(A);
		this.sRad=this.rad%(2*Math.PI);
		this.sDeg=this.deg%360;
		this.complement=Math.PI/2-this.sRad;
		this.supplement=Math.PI-this.sRad;

		this.sin=Math.sin(this.sRad);
		this.cos=Math.cos(this.sRad);
		this.tan=Math.tan(this.sRad);
		this.csc=1/this.sin;
		this.sec=1/this.cos;
		this.cot=1/this.tan;
	}
	isSame(a){
		return this.rad==a.rad||this.deg==a.deg;
	}
	isEquivalent(a){
		return this.sRad==a.sRad||this.sDeg==a.sDeg;
	}
}

class color{
	constructor(r=0,b=0,g=0,a,p=false){
		if(typeof(r)=="string")r=parseFloat(r,16);
		if(typeof(b)=="string")b=parseFloat(b,16);
		if(typeof(g)=="string")g=parseFloat(g,16);
		if(typeof(a)=="string")a=parseFloat(a,p?10:16);
		this.color=[r,b,g,p?a*255:a];
		this.dex=[r/255,b/255,g/255,p?a:a/255];
		this.hex=[
			r<16?"0":""+Math.round(r%255).toString(16),
			g<16?"0":""+Math.round(g%255).toString(16),
			b<16?"0":""+Math.round(b%255).toString(16),
			a<16?"0":""+Math.round(this.dex[3]%255).toString(16)
		];
		{
			this.average=(r+b+g)/3;
			this.averageA=(this.average+this.color[3])/2;
			this.number=parseInt(this.hex.join(""),16);
			this.numberA=parseInt(this.hex.join("")+a?"":"00",16);
		}
		this.invalid=[r>255,b>255,g>255,this.dex[3]>255];
		this.transparent=!a;
	}
	combine(c,r=true,g=true,b=true,a=true){
		return new color(
			r?Math.min(this.color[0]+c.color[0],255):this.color[0],
			b?Math.min(this.color[1]+c.color[1],255):this.color[1],
			g?Math.min(this.color[2]+c.color[2],255):this.color[2],
			a?Math.min(this.color[3]+c.color[3],255):this.color[3]
		)
	}
	difference(c,r=true,g=true,b=true,a=true){
		return new color(
			r?Math.max(this.color[0]-c.color[0],0):this.color[0],
			b?Math.max(this.color[1]-c.color[1],0):this.color[1],
			g?Math.max(this.color[2]-c.color[2],0):this.color[2],
			a?Math.max(this.color[3]-c.color[3],0):this.color[3]
		)
	}
	differenceAbs(c,r=true,g=true,b=true,a=true){
		return new color(
			r?Math.abs(this.color[0]-c.color[0]):this.color[0],
			b?Math.abs(this.color[1]-c.color[1]):this.color[1],
			g?Math.abs(this.color[2]-c.color[2]):this.color[2],
			a?Math.abs(this.color[3]-c.color[3]):this.color[3]
		)
	}
	multiply(c,r=true,g=true,b=true,a=true){
		return new color(
			r?this.color[0]*c.dex[0]:this.color[0],
			b?this.color[1]*c.dex[1]:this.color[1],
			g?this.color[2]*c.dex[2]:this.color[2],
			a?this.color[3]*c.dex[3]:this.color[3]
		)
	}
	divide(c,r=true,g=true,b=true,a=true){
		return new color(
			r?Math.min(this.color[0]/c.color[0],255):this.color[0],
			b?Math.min(this.color[1]/c.color[1],255):this.color[1],
			g?Math.min(this.color[2]/c.color[2],255):this.color[2],
			a?Math.min(this.color[3]/c.color[3],255):this.color[3]
		)
	}
}
color.prototype.valueOf=function(){return this.color};

class colorDes extends color{
	constructor(r=0,b=0,g=0,a,p=true){
		super(255*r,255*b,255*g,a,p);
	}
}
colorDes.prototype.valueOf=function(){return this.color};

class grayScale extends color{
	constructor(w,a,p){
		super(w,w,w,a,p);
		this.white=this.color[0];
		this.whiteDec=this.dex[0];
		this.whiteHex=this.hex[0];
	}
	combine(c,w=true,a=true){
		return new grayScale(
			w?Math.min(this.white+c.white,255):this.white,
			a?Math.min(this.alpha+c.alpha,255):this.alpha
		)
	}
	difference(c,w=true,a=true){
		return new grayScale(
			w?Math.max(this.white-c.white,0):this.white,
			a?Math.max(this.alpha-c.alpha,0):this.alpha
		)
	}
	differenceAbs(c,w=true,a=true){
		return new grayScale(
			w?Math.abs(this.white-c.white):this.white,
			a?Math.abs(this.alpha-c.alpha):this.alpha
		)
	}
	multiply(c,w=true,a=true){
		return new grayScale(
			w?this.white*c.whiteDex:this.white,
			a?this.alpha*c.alphaDex:this.alpha
		)
	}
	divide(c,w=true,a=true){
		return new grayScale(
			w?Math.min(this.white/c.white,255):this.white,
			a?Math.min(this.alpha/c.alpha,255):this.alpha
		)
	}
}
grayScale.prototype.valueOf=function(){return this.color};