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i=0;i<100;++i){if(s=(e*Math.exp(-n)+n*n)/(n+1),Math.abs(s-n)<t*Math.abs(s))return s;n=s}throw Error(`Iteration failed to converge: ${e.toString()}`)};function is(e,t=1e-10){let n,s,i,l;if(!Number.isFinite(e.mag)||e===a.dZero)return e;if(e===a.dOne)return p(ys);a.abs(e),n=a.ln(e);for(let r=0;r<100;++r){if(s=a.exp(-n),i=n.sub(e.mul(s)),l=n.sub(i.div(n.add(1).sub(n.add(2).mul(i).div(a.mul(2,n).add(2))))),a.abs(l.sub(n)).lt(a.abs(l).mul(t)))return l;n=l}throw Error(`Iteration failed to converge: ${e.toString()}`)}const C=class{constructor(e){this.sign=Number.NaN,this.mag=Number.NaN,this.layer=Number.NaN,e instanceof C||e!=null&&typeof e=="object"&&"sign"in e&&"mag"in e&&"layer"in e?this.fromDecimal(e):typeof e=="number"?this.fromNumber(e):typeof e=="string"?this.fromString(e):(this.sign=0,this.layer=0,this.mag=0)}get m(){if(this.sign===0)return 0;if(this.layer===0){const e=Math.floor(Math.log10(this.mag));let t;return this.mag===5e-324?t=5:t=this.mag/Wi(e),this.sign*t}else 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C().fromMantissaExponent_noNormalize(e,t)}static fromDecimal(e){return new C().fromDecimal(e)}static fromNumber(e){return new C().fromNumber(e)}static fromString(e){return new C().fromString(e)}static fromValue(e){return new C().fromValue(e)}static fromValue_noAlloc(e){return e instanceof C?e:new C(e)}static abs(e){return p(e).abs()}static neg(e){return p(e).neg()}static negate(e){return p(e).neg()}static negated(e){return p(e).neg()}static sign(e){return p(e).sign}static sgn(e){return p(e).sign}static round(e){return p(e).round()}static floor(e){return p(e).floor()}static ceil(e){return p(e).ceil()}static trunc(e){return p(e).trunc()}static add(e,t){return p(e).add(t)}static plus(e,t){return p(e).add(t)}static sub(e,t){return p(e).sub(t)}static subtract(e,t){return p(e).sub(t)}static minus(e,t){return p(e).sub(t)}static mul(e,t){return p(e).mul(t)}static multiply(e,t){return p(e).mul(t)}static times(e,t){return p(e).mul(t)}static div(e,t){return p(e).div(t)}static divide(e,t){return p(e).div(t)}static recip(e){return p(e).recip()}static reciprocal(e){return p(e).recip()}static reciprocate(e){return p(e).reciprocate()}static cmp(e,t){return p(e).cmp(t)}static cmpabs(e,t){return p(e).cmpabs(t)}static compare(e,t){return p(e).cmp(t)}static isNaN(e){return e=p(e),isNaN(e.sign)||isNaN(e.layer)||isNaN(e.mag)}static isFinite(e){return e=p(e),isFinite(e.sign)&&isFinite(e.layer)&&isFinite(e.mag)}static eq(e,t){return p(e).eq(t)}static equals(e,t){return p(e).eq(t)}static neq(e,t){return p(e).neq(t)}static notEquals(e,t){return p(e).notEquals(t)}static lt(e,t){return p(e).lt(t)}static lte(e,t){return p(e).lte(t)}static gt(e,t){return p(e).gt(t)}static gte(e,t){return p(e).gte(t)}static max(e,t){return p(e).max(t)}static min(e,t){return p(e).min(t)}static minabs(e,t){return p(e).minabs(t)}static maxabs(e,t){return p(e).maxabs(t)}static clamp(e,t,n){return p(e).clamp(t,n)}static clampMin(e,t){return p(e).clampMin(t)}static clampMax(e,t){return p(e).clampMax(t)}static cmp_tolerance(e,t,n){return p(e).cmp_tolerance(t,n)}static compare_tolerance(e,t,n){return p(e).cmp_tolerance(t,n)}static eq_tolerance(e,t,n){return p(e).eq_tolerance(t,n)}static equals_tolerance(e,t,n){return p(e).eq_tolerance(t,n)}static neq_tolerance(e,t,n){return p(e).neq_tolerance(t,n)}static notEquals_tolerance(e,t,n){return p(e).notEquals_tolerance(t,n)}static lt_tolerance(e,t,n){return p(e).lt_tolerance(t,n)}static lte_tolerance(e,t,n){return p(e).lte_tolerance(t,n)}static gt_tolerance(e,t,n){return p(e).gt_tolerance(t,n)}static gte_tolerance(e,t,n){return p(e).gte_tolerance(t,n)}static pLog10(e){return p(e).pLog10()}static absLog10(e){return p(e).absLog10()}static log10(e){return p(e).log10()}static log(e,t){return p(e).log(t)}static log2(e){return p(e).log2()}static ln(e){return p(e).ln()}static logarithm(e,t){return p(e).logarithm(t)}static pow(e,t){return p(e).pow(t)}static pow10(e){return p(e).pow10()}static root(e,t){return p(e).root(t)}static factorial(e,t){return p(e).factorial()}static gamma(e,t){return p(e).gamma()}static lngamma(e,t){return p(e).lngamma()}static exp(e){return p(e).exp()}static sqr(e){return p(e).sqr()}static sqrt(e){return p(e).sqrt()}static cube(e){return p(e).cube()}static cbrt(e){return p(e).cbrt()}static tetrate(e,t=2,n=K(1,0,1)){return p(e).tetrate(t,n)}static iteratedexp(e,t=2,n=K(1,0,1)){return p(e).iteratedexp(t,n)}static iteratedlog(e,t=10,n=1){return p(e).iteratedlog(t,n)}static layeradd10(e,t){return p(e).layeradd10(t)}static layeradd(e,t,n=10){return p(e).layeradd(t,n)}static slog(e,t=10){return p(e).slog(t)}static lambertw(e){return p(e).lambertw()}static ssqrt(e){return p(e).ssqrt()}static pentate(e,t=2,n=K(1,0,1)){return p(e).pentate(t,n)}static affordGeometricSeries(e,t,n,s){return this.affordGeometricSeries_core(p(e),p(t),p(n),s)}static sumGeometricSeries(e,t,n,s){return this.sumGeometricSeries_core(e,p(t),p(n),s)}static affordArithmeticSeries(e,t,n,s){return this.affordArithmeticSeries_core(p(e),p(t),p(n),p(s))}static sumArithmeticSeries(e,t,n,s){return this.sumArithmeticSeries_core(p(e),p(t),p(n),p(s))}static efficiencyOfPurchase(e,t,n){return this.efficiencyOfPurchase_core(p(e),p(t),p(n))}static randomDecimalForTesting(e){if(Math.random()*20<1)return K(0,0,0);const t=Math.random()>.5?1:-1;if(Math.random()*20<1)return K(t,0,1);const n=Math.floor(Math.random()*(e+1));let s=n===0?Math.random()*616-308:Math.random()*16;Math.random()>.9&&(s=Math.trunc(s));let i=Math.pow(10,s);return Math.random()>.9&&(i=Math.trunc(i)),V(t,n,i)}static affordGeometricSeries_core(e,t,n,s){const i=t.mul(n.pow(s));return C.floor(e.div(i).mul(n.sub(1)).add(1).log10().div(n.log10()))}static sumGeometricSeries_core(e,t,n,s){return t.mul(n.pow(s)).mul(C.sub(1,n.pow(e))).div(C.sub(1,n))}static affordArithmeticSeries_core(e,t,n,s){const l=t.add(s.mul(n)).sub(n.div(2)),r=l.pow(2);return l.neg().add(r.add(n.mul(e).mul(2)).sqrt()).div(n).floor()}static sumArithmeticSeries_core(e,t,n,s){const i=t.add(s.mul(n));return e.div(2).mul(i.mul(2).plus(e.sub(1).mul(n)))}static efficiencyOfPurchase_core(e,t,n){return e.div(t).add(e.div(n))}normalize(){if(this.sign===0||this.mag===0&&this.layer===0)return this.sign=0,this.mag=0,this.layer=0,this;if(this.layer===0&&this.mag<0&&(this.mag=-this.mag,this.sign=-this.sign),this.layer===0&&this.mag<zi)return this.layer+=1,this.mag=Math.log10(this.mag),this;let e=Math.abs(this.mag),t=Math.sign(this.mag);if(e>=Hi)return this.layer+=1,this.mag=t*Math.log10(e),this;for(;e<Qi&&this.layer>0;)this.layer-=1,this.layer===0?this.mag=Math.pow(10,this.mag):(this.mag=t*Math.pow(10,e),e=Math.abs(this.mag),t=Math.sign(this.mag));return this.layer===0&&(this.mag<0?(this.mag=-this.mag,this.sign=-this.sign):this.mag===0&&(this.sign=0)),this}fromComponents(e,t,n){return this.sign=e,this.layer=t,this.mag=n,this.normalize(),this}fromComponents_noNormalize(e,t,n){return this.sign=e,this.layer=t,this.mag=n,this}fromMantissaExponent(e,t){return this.layer=1,this.sign=Math.sign(e),e=Math.abs(e),this.mag=t+Math.log10(e),this.normalize(),this}fromMantissaExponent_noNormalize(e,t){return this.fromMantissaExponent(e,t),this}fromDecimal(e){return this.sign=e.sign,this.layer=e.layer,this.mag=e.mag,this}fromNumber(e){return this.mag=Math.abs(e),this.sign=Math.sign(e),this.layer=0,this.normalize(),this}fromString(e){e=e.replace(",","");const t=e.split("^^^");if(t.length===2){const b=parseFloat(t[0]),g=parseFloat(t[1]),w=t[1].split(";");let k=1;if(w.length===2&&(k=parseFloat(w[1]),isFinite(k)||(k=1)),isFinite(b)&&isFinite(g)){const P=C.pentate(b,g,k);return this.sign=P.sign,this.layer=P.layer,this.mag=P.mag,this}}const n=e.split("^^");if(n.length===2){const b=parseFloat(n[0]),g=parseFloat(n[1]),w=n[1].split(";");let k=1;if(w.length===2&&(k=parseFloat(w[1]),isFinite(k)||(k=1)),isFinite(b)&&isFinite(g)){const P=C.tetrate(b,g,k);return this.sign=P.sign,this.layer=P.layer,this.mag=P.mag,this}}const s=e.split("^");if(s.length===2){const b=parseFloat(s[0]),g=parseFloat(s[1]);if(isFinite(b)&&isFinite(g)){const w=C.pow(b,g);return this.sign=w.sign,this.layer=w.layer,this.mag=w.mag,this}}e=e.trim().toLowerCase();let i,l,r=e.split("pt");if(r.length===2){i=10,l=parseFloat(r[0]),r[1]=r[1].replace("(",""),r[1]=r[1].replace(")","");let b=parseFloat(r[1]);if(isFinite(b)||(b=1),isFinite(i)&&isFinite(l)){const g=C.tetrate(i,l,b);return this.sign=g.sign,this.layer=g.layer,this.mag=g.mag,this}}if(r=e.split("p"),r.length===2){i=10,l=parseFloat(r[0]),r[1]=r[1].replace("(",""),r[1]=r[1].replace(")","");let b=parseFloat(r[1]);if(isFinite(b)||(b=1),isFinite(i)&&isFinite(l)){const g=C.tetrate(i,l,b);return this.sign=g.sign,this.layer=g.layer,this.mag=g.mag,this}}const c=e.split("e"),d=c.length-1;if(d===0){const b=parseFloat(e);if(isFinite(b))return this.fromNumber(b)}else if(d===1){const b=parseFloat(e);if(isFinite(b)&&b!==0)return 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isNaN(this.layer)||isNaN(this.sign)||isNaN(this.mag)?"NaN":this.mag===Number.POSITIVE_INFINITY||this.layer===Number.POSITIVE_INFINITY?this.sign===1?"Infinity":"-Infinity":this.layer===0?this.mag<1e21&&this.mag>1e-7||this.mag===0?(this.sign*this.mag).toString():this.m+"e"+this.e:this.layer===1?this.m+"e"+this.e:this.layer<=ns?(this.sign===-1?"-":"")+"e".repeat(this.layer)+this.mag:(this.sign===-1?"-":"")+"(e^"+this.layer+")"+this.mag}toExponential(e){return this.layer===0?(this.sign*this.mag).toExponential(e):this.toStringWithDecimalPlaces(e)}toFixed(e){return this.layer===0?(this.sign*this.mag).toFixed(e):this.toStringWithDecimalPlaces(e)}toPrecision(e){return this.e<=-7?this.toExponential(e-1):e>this.e?this.toFixed(e-this.exponent-1):this.toExponential(e-1)}valueOf(){return this.toString()}toJSON(){return this.toString()}toStringWithDecimalPlaces(e){return this.layer===0?this.mag<1e21&&this.mag>1e-7||this.mag===0?(this.sign*this.mag).toFixed(e):It(this.m,e)+"e"+It(this.e,e):this.layer===1?It(this.m,e)+"e"+It(this.e,e):this.layer<=ns?(this.sign===-1?"-":"")+"e".repeat(this.layer)+It(this.mag,e):(this.sign===-1?"-":"")+"(e^"+this.layer+")"+It(this.mag,e)}abs(){return K(this.sign===0?0:1,this.layer,this.mag)}neg(){return K(-this.sign,this.layer,this.mag)}negate(){return this.neg()}negated(){return this.neg()}sgn(){return this.sign}round(){return this.mag<0?C.dZero:this.layer===0?V(this.sign,0,Math.round(this.mag)):this}floor(){return this.mag<0?C.dZero:this.layer===0?V(this.sign,0,Math.floor(this.mag)):this}ceil(){return this.mag<0?C.dZero:this.layer===0?V(this.sign,0,Math.ceil(this.mag)):this}trunc(){return this.mag<0?C.dZero:this.layer===0?V(this.sign,0,Math.trunc(this.mag)):this}add(e){const t=p(e);if(!Number.isFinite(this.layer))return this;if(!Number.isFinite(t.layer)||this.sign===0)return t;if(t.sign===0)return 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this.sign<=0?C.dNaN:this.layer===0?V(this.sign,0,Math.log2(this.mag)):this.layer===1?V(Math.sign(this.mag),0,Math.abs(this.mag)*3.321928094887362):this.layer===2?V(Math.sign(this.mag),1,Math.abs(this.mag)+.5213902276543247):V(Math.sign(this.mag),this.layer-1,Math.abs(this.mag))}ln(){return this.sign<=0?C.dNaN:this.layer===0?V(this.sign,0,Math.log(this.mag)):this.layer===1?V(Math.sign(this.mag),0,Math.abs(this.mag)*2.302585092994046):this.layer===2?V(Math.sign(this.mag),1,Math.abs(this.mag)+.36221568869946325):V(Math.sign(this.mag),this.layer-1,Math.abs(this.mag))}logarithm(e){return this.log(e)}pow(e){const t=p(e),n=this,s=t;if(n.sign===0)return s.eq(0)?K(1,0,1):n;if(n.sign===1&&n.layer===0&&n.mag===1)return n;if(s.sign===0)return K(1,0,1);if(s.sign===1&&s.layer===0&&s.mag===1)return n;const i=n.absLog10().mul(s).pow10();return this.sign===-1?Math.abs(s.toNumber()%2)%2===1?i.neg():Math.abs(s.toNumber()%2)%2===0?i:C.dNaN:i}pow10(){if(!Number.isFinite(this.layer)||!Number.isFinite(this.mag))return C.dNaN;let e=this;if(e.layer===0){const t=Math.pow(10,e.sign*e.mag);if(Number.isFinite(t)&&Math.abs(t)>=.1)return V(1,0,t);if(e.sign===0)return C.dOne;e=K(e.sign,e.layer+1,Math.log10(e.mag))}return e.sign>0&&e.mag>=0?V(e.sign,e.layer+1,e.mag):e.sign<0&&e.mag>=0?V(-e.sign,e.layer+1,-e.mag):C.dOne}pow_base(e){return p(e).pow(this)}root(e){const t=p(e);return this.pow(t.recip())}factorial(){return this.mag<0?this.add(1).gamma():this.layer===0?this.add(1).gamma():this.layer===1?C.exp(C.mul(this,C.ln(this).sub(1))):C.exp(this)}gamma(){if(this.mag<0)return this.recip();if(this.layer===0){if(this.lt(K(1,0,24)))return p(Yi(this.sign*this.mag));const e=this.mag-1;let t=.9189385332046727;t=t+(e+.5)*Math.log(e),t=t-e;const n=e*e;let s=e,i=12*s,l=1/i,r=t+l;if(r===t||(t=r,s=s*n,i=360*s,l=1/i,r=t-l,r===t))return C.exp(t);t=r,s=s*n,i=1260*s;let c=1/i;return t=t+c,s=s*n,i=1680*s,c=1/i,t=t-c,C.exp(t)}else return this.layer===1?C.exp(C.mul(this,C.ln(this).sub(1))):C.exp(this)}lngamma(){return this.gamma().ln()}exp(){return this.mag<0?C.dOne:this.layer===0&&this.mag<=709.7?p(Math.exp(this.sign*this.mag)):this.layer===0?V(1,1,this.sign*Math.log10(Math.E)*this.mag):this.layer===1?V(1,2,this.sign*(Math.log10(.4342944819032518)+this.mag)):V(1,this.layer+1,this.sign*this.mag)}sqr(){return this.pow(2)}sqrt(){if(this.layer===0)return p(Math.sqrt(this.sign*this.mag));if(this.layer===1)return V(1,2,Math.log10(this.mag)-.3010299956639812);{const e=C.div(K(this.sign,this.layer-1,this.mag),K(1,0,2));return e.layer+=1,e.normalize(),e}}cube(){return this.pow(3)}cbrt(){return this.pow(1/3)}tetrate(e=2,t=K(1,0,1)){if(e===1)return C.pow(this,t);if(e===0)return new C(t);if(this.eq(C.dOne))return C.dOne;if(this.eq(-1))return C.pow(this,t);if(e===Number.POSITIVE_INFINITY){const i=this.toNumber();if(i<=1.444667861009766&&i>=.06598803584531254){if(i>1.444667861009099)return new C(Math.E);const l=C.ln(this).neg();return l.lambertw().div(l)}else return i>1.444667861009766?new C(Number.POSITIVE_INFINITY):C.dNaN}if(this.eq(C.dZero)){let i=Math.abs((e+1)%2);return i>1&&(i=2-i),new C(i)}if(e<0)return C.iteratedlog(t,this,-e);t=p(t);const n=e;e=Math.trunc(e);const s=n-e;if(this.gt(C.dZero)&&this.lte(1.444667861009766)){e=Math.min(1e4,e);for(let i=0;i<e;++i){const l=t;if(t=this.pow(t),l.eq(t))return t}if(s!=0){const i=this.pow(t);return t.mul(1-s).add(i.mul(s))}return t}s!==0&&(t.eq(C.dOne)?this.gt(10)?t=this.pow(s):(t=p(C.tetrate_critical(this.toNumber(),s)),this.lt(2)&&(t=t.sub(1).mul(this.minus(1)).plus(1))):this.eq(10)?t=t.layeradd10(s):t=t.layeradd(s,this));for(let i=0;i<e;++i){if(t=this.pow(t),!isFinite(t.layer)||!isFinite(t.mag))return t.normalize();if(t.layer-this.layer>3)return K(t.sign,t.layer+(e-i-1),t.mag);if(i>1e4)return t}return t}iteratedexp(e=2,t=K(1,0,1)){return this.tetrate(e,t)}iteratedlog(e=10,t=1){if(t<0)return C.tetrate(e,-t,this);e=p(e);let n=p(this);const s=t;t=Math.trunc(t);const i=s-t;if(n.layer-e.layer>3){const l=Math.min(t,n.layer-e.layer-3);t-=l,n.layer-=l}for(let l=0;l<t;++l){if(n=n.log(e),!isFinite(n.layer)||!isFinite(n.mag))return n.normalize();if(l>1e4)return n}return i>0&&i<1&&(e.eq(10)?n=n.layeradd10(-i):n=n.layeradd(-i,e)),n}slog(e=10){if(e=p(e),e.lte(C.dZero)||e.eq(C.dOne))return C.dNaN;if(e.lt(C.dOne))return this.eq(C.dOne)?C.dZero:this.eq(C.dZero)?C.dNegOne:C.dNaN;if(this.mag<0||this.eq(C.dZero))return C.dNegOne;let t=0,n=p(this);if(n.layer-e.layer>3){const s=n.layer-e.layer-3;t+=s,n.layer-=s}for(let s=0;s<100;++s)if(n.lt(C.dZero))n=C.pow(e,n),t-=1;else{if(n.lte(C.dOne))return p(t+C.slog_critical(e.toNumber(),n.toNumber()));t+=1,n=C.log(n,e)}return p(t)}static slog_critical(e,t){return e>10?t-1:C.critical_section(e,t,Xi)}static tetrate_critical(e,t){return 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