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i=0;i<100;++i){if(a=(e*Math.exp(-l)+l*l)/(l+1),Math.abs(a-l)<t*Math.abs(a))return a;l=a}throw Error(`Iteration failed to converge: ${e.toString()}`)};function Un(e,t=1e-10){let l,a,i,s;if(!Number.isFinite(e.mag)||e===n.dZero)return e;if(e===n.dOne)return v(la);n.abs(e),l=n.ln(e);for(let u=0;u<100;++u){if(a=n.exp(-l),i=l.sub(e.mul(a)),s=l.sub(i.div(l.add(1).sub(l.add(2).mul(i).div(n.mul(2,l).add(2))))),n.abs(s.sub(l)).lt(n.abs(s).mul(t)))return s;l=s}throw Error(`Iteration failed to converge: ${e.toString()}`)}const k=class{constructor(e){this.sign=Number.NaN,this.mag=Number.NaN,this.layer=Number.NaN,e instanceof k||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/Pi(e),this.sign*t}else if(this.layer===1){const e=this.mag-Math.floor(this.mag);return this.sign*Math.pow(10,e)}else return this.sign}set m(e){this.layer<=2?this.fromMantissaExponent(e,this.e):(this.sign=Math.sign(e),this.sign===0&&(this.layer,this.exponent))}get e(){return this.sign===0?0:this.layer===0?Math.floor(Math.log10(this.mag)):this.layer===1?Math.floor(this.mag):this.layer===2?Math.floor(Math.sign(this.mag)*Math.pow(10,Math.abs(this.mag))):this.mag*Number.POSITIVE_INFINITY}set e(e){this.fromMantissaExponent(this.m,e)}get s(){return this.sign}set s(e){e===0?(this.sign=0,this.layer=0,this.mag=0):this.sign=e}get mantissa(){return this.m}set mantissa(e){this.m=e}get exponent(){return this.e}set exponent(e){this.e=e}static fromComponents(e,t,l){return new k().fromComponents(e,t,l)}static fromComponents_noNormalize(e,t,l){return new k().fromComponents_noNormalize(e,t,l)}static fromMantissaExponent(e,t){return new k().fromMantissaExponent(e,t)}static fromMantissaExponent_noNormalize(e,t){return new k().fromMantissaExponent_noNormalize(e,t)}static fromDecimal(e){return new k().fromDecimal(e)}static fromNumber(e){return new k().fromNumber(e)}static fromString(e){return new k().fromString(e)}static fromValue(e){return new k().fromValue(e)}static fromValue_noAlloc(e){return e instanceof k?e:new k(e)}static abs(e){return v(e).abs()}static neg(e){return v(e).neg()}static negate(e){return v(e).neg()}static negated(e){return v(e).neg()}static sign(e){return v(e).sign}static sgn(e){return v(e).sign}static round(e){return v(e).round()}static floor(e){return v(e).floor()}static ceil(e){return v(e).ceil()}static trunc(e){return v(e).trunc()}static add(e,t){return v(e).add(t)}static plus(e,t){return v(e).add(t)}static sub(e,t){return v(e).sub(t)}static subtract(e,t){return v(e).sub(t)}static minus(e,t){return v(e).sub(t)}static mul(e,t){return v(e).mul(t)}static multiply(e,t){return v(e).mul(t)}static times(e,t){return v(e).mul(t)}static div(e,t){return v(e).div(t)}static divide(e,t){return v(e).div(t)}static recip(e){return v(e).recip()}static reciprocal(e){return v(e).recip()}static reciprocate(e){return v(e).reciprocate()}static cmp(e,t){return v(e).cmp(t)}static cmpabs(e,t){return v(e).cmpabs(t)}static compare(e,t){return v(e).cmp(t)}static isNaN(e){return e=v(e),isNaN(e.sign)||isNaN(e.layer)||isNaN(e.mag)}static isFinite(e){return e=v(e),isFinite(e.sign)&&isFinite(e.layer)&&isFinite(e.mag)}static eq(e,t){return v(e).eq(t)}static equals(e,t){return v(e).eq(t)}static neq(e,t){return v(e).neq(t)}static notEquals(e,t){return v(e).notEquals(t)}static lt(e,t){return v(e).lt(t)}static lte(e,t){return v(e).lte(t)}static gt(e,t){return v(e).gt(t)}static gte(e,t){return v(e).gte(t)}static max(e,t){return v(e).max(t)}static min(e,t){return v(e).min(t)}static minabs(e,t){return v(e).minabs(t)}static maxabs(e,t){return v(e).maxabs(t)}static clamp(e,t,l){return v(e).clamp(t,l)}static clampMin(e,t){return v(e).clampMin(t)}static clampMax(e,t){return v(e).clampMax(t)}static cmp_tolerance(e,t,l){return v(e).cmp_tolerance(t,l)}static compare_tolerance(e,t,l){return v(e).cmp_tolerance(t,l)}static eq_tolerance(e,t,l){return v(e).eq_tolerance(t,l)}static equals_tolerance(e,t,l){return v(e).eq_tolerance(t,l)}static neq_tolerance(e,t,l){return v(e).neq_tolerance(t,l)}static notEquals_tolerance(e,t,l){return v(e).notEquals_tolerance(t,l)}static lt_tolerance(e,t,l){return v(e).lt_tolerance(t,l)}static lte_tolerance(e,t,l){return v(e).lte_tolerance(t,l)}static gt_tolerance(e,t,l){return v(e).gt_tolerance(t,l)}static gte_tolerance(e,t,l){return v(e).gte_tolerance(t,l)}static pLog10(e){return v(e).pLog10()}static absLog10(e){return v(e).absLog10()}static log10(e){return v(e).log10()}static log(e,t){return v(e).log(t)}static log2(e){return v(e).log2()}static ln(e){return v(e).ln()}static logarithm(e,t){return v(e).logarithm(t)}static pow(e,t){return v(e).pow(t)}static pow10(e){return v(e).pow10()}static root(e,t){return v(e).root(t)}static factorial(e,t){return v(e).factorial()}static gamma(e,t){return v(e).gamma()}static lngamma(e,t){return v(e).lngamma()}static exp(e){return v(e).exp()}static sqr(e){return v(e).sqr()}static sqrt(e){return v(e).sqrt()}static cube(e){return v(e).cube()}static cbrt(e){return v(e).cbrt()}static tetrate(e,t=2,l=se(1,0,1)){return v(e).tetrate(t,l)}static iteratedexp(e,t=2,l=se(1,0,1)){return v(e).iteratedexp(t,l)}static iteratedlog(e,t=10,l=1){return v(e).iteratedlog(t,l)}static layeradd10(e,t){return v(e).layeradd10(t)}static layeradd(e,t,l=10){return v(e).layeradd(t,l)}static slog(e,t=10){return v(e).slog(t)}static lambertw(e){return v(e).lambertw()}static ssqrt(e){return v(e).ssqrt()}static pentate(e,t=2,l=se(1,0,1)){return v(e).pentate(t,l)}static affordGeometricSeries(e,t,l,a){return this.affordGeometricSeries_core(v(e),v(t),v(l),a)}static sumGeometricSeries(e,t,l,a){return this.sumGeometricSeries_core(e,v(t),v(l),a)}static affordArithmeticSeries(e,t,l,a){return 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sumArithmeticSeries_core(e,t,l,a){const i=t.add(a.mul(l));return e.div(2).mul(i.mul(2).plus(e.sub(1).mul(l)))}static efficiencyOfPurchase_core(e,t,l){return e.div(t).add(e.div(l))}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<Bi)return this.layer+=1,this.mag=Math.log10(this.mag),this;let e=Math.abs(this.mag),t=Math.sign(this.mag);if(e>=Ii)return this.layer+=1,this.mag=t*Math.log10(e),this;for(;e<Ei&&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,l){return this.sign=e,this.layer=t,this.mag=l,this.normalize(),this}fromComponents_noNormalize(e,t,l){return 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this.layer===0?this.mag<1e21&&this.mag>1e-7||this.mag===0?(this.sign*this.mag).toFixed(e):Yt(this.m,e)+"e"+Yt(this.e,e):this.layer===1?Yt(this.m,e)+"e"+Yt(this.e,e):this.layer<=Rn?(this.sign===-1?"-":"")+"e".repeat(this.layer)+Yt(this.mag,e):(this.sign===-1?"-":"")+"(e^"+this.layer+")"+Yt(this.mag,e)}abs(){return se(this.sign===0?0:1,this.layer,this.mag)}neg(){return se(-this.sign,this.layer,this.mag)}negate(){return this.neg()}negated(){return this.neg()}sgn(){return this.sign}round(){return this.mag<0?k.dZero:this.layer===0?K(this.sign,0,Math.round(this.mag)):this}floor(){return this.mag<0?k.dZero:this.layer===0?K(this.sign,0,Math.floor(this.mag)):this}ceil(){return this.mag<0?k.dZero:this.layer===0?K(this.sign,0,Math.ceil(this.mag)):this}trunc(){return this.mag<0?k.dZero:this.layer===0?K(this.sign,0,Math.trunc(this.mag)):this}add(e){const t=v(e);if(!Number.isFinite(this.layer))return this;if(!Number.isFinite(t.layer)||this.sign===0)return t;if(t.sign===0)return this;if(this.sign===-t.sign&&this.layer===t.layer&&this.mag===t.mag)return se(0,0,0);let l,a;if(this.layer>=2||t.layer>=2)return this.maxabs(t);if(k.cmpabs(this,t)>0?(l=this,a=t):(l=t,a=this),l.layer===0&&a.layer===0)return v(l.sign*l.mag+a.sign*a.mag);const i=l.layer*Math.sign(l.mag),s=a.layer*Math.sign(a.mag);if(i-s>=2)return l;if(i===0&&s===-1){if(Math.abs(a.mag-Math.log10(l.mag))>fn)return l;{const u=Math.pow(10,Math.log10(l.mag)-a.mag),d=a.sign+l.sign*u;return K(Math.sign(d),1,a.mag+Math.log10(Math.abs(d)))}}if(i===1&&s===0){if(Math.abs(l.mag-Math.log10(a.mag))>fn)return l;{const u=Math.pow(10,l.mag-Math.log10(a.mag)),d=a.sign+l.sign*u;return K(Math.sign(d),1,Math.log10(a.mag)+Math.log10(Math.abs(d)))}}if(Math.abs(l.mag-a.mag)>fn)return l;{const u=Math.pow(10,l.mag-a.mag),d=a.sign+l.sign*u;return K(Math.sign(d),1,a.mag+Math.log10(Math.abs(d)))}}plus(e){return this.add(e)}sub(e){return this.add(v(e).neg())}subtract(e){return this.sub(e)}minus(e){return this.sub(e)}mul(e){const 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this.sign<=0?k.dNaN:this.layer===0?K(this.sign,0,Math.log2(this.mag)):this.layer===1?K(Math.sign(this.mag),0,Math.abs(this.mag)*3.321928094887362):this.layer===2?K(Math.sign(this.mag),1,Math.abs(this.mag)+.5213902276543247):K(Math.sign(this.mag),this.layer-1,Math.abs(this.mag))}ln(){return this.sign<=0?k.dNaN:this.layer===0?K(this.sign,0,Math.log(this.mag)):this.layer===1?K(Math.sign(this.mag),0,Math.abs(this.mag)*2.302585092994046):this.layer===2?K(Math.sign(this.mag),1,Math.abs(this.mag)+.36221568869946325):K(Math.sign(this.mag),this.layer-1,Math.abs(this.mag))}logarithm(e){return this.log(e)}pow(e){const t=v(e),l=this,a=t;if(l.sign===0)return a.eq(0)?se(1,0,1):l;if(l.sign===1&&l.layer===0&&l.mag===1)return l;if(a.sign===0)return se(1,0,1);if(a.sign===1&&a.layer===0&&a.mag===1)return l;const i=l.absLog10().mul(a).pow10();return this.sign===-1?Math.abs(a.toNumber()%2)%2===1?i.neg():Math.abs(a.toNumber()%2)%2===0?i:k.dNaN:i}pow10(){if(!Number.isFinite(this.layer)||!Number.isFinite(this.mag))return k.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 K(1,0,t);if(e.sign===0)return k.dOne;e=se(e.sign,e.layer+1,Math.log10(e.mag))}return e.sign>0&&e.mag>=0?K(e.sign,e.layer+1,e.mag):e.sign<0&&e.mag>=0?K(-e.sign,e.layer+1,-e.mag):k.dOne}pow_base(e){return v(e).pow(this)}root(e){const t=v(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?k.exp(k.mul(this,k.ln(this).sub(1))):k.exp(this)}gamma(){if(this.mag<0)return this.recip();if(this.layer===0){if(this.lt(se(1,0,24)))return v(Ri(this.sign*this.mag));const e=this.mag-1;let t=.9189385332046727;t=t+(e+.5)*Math.log(e),t=t-e;const l=e*e;let a=e,i=12*a,s=1/i,u=t+s;if(u===t||(t=u,a=a*l,i=360*a,s=1/i,u=t-s,u===t))return k.exp(t);t=u,a=a*l,i=1260*a;let d=1/i;return t=t+d,a=a*l,i=1680*a,d=1/i,t=t-d,k.exp(t)}else return this.layer===1?k.exp(k.mul(this,k.ln(this).sub(1))):k.exp(this)}lngamma(){return this.gamma().ln()}exp(){return this.mag<0?k.dOne:this.layer===0&&this.mag<=709.7?v(Math.exp(this.sign*this.mag)):this.layer===0?K(1,1,this.sign*Math.log10(Math.E)*this.mag):this.layer===1?K(1,2,this.sign*(Math.log10(.4342944819032518)+this.mag)):K(1,this.layer+1,this.sign*this.mag)}sqr(){return this.pow(2)}sqrt(){if(this.layer===0)return v(Math.sqrt(this.sign*this.mag));if(this.layer===1)return K(1,2,Math.log10(this.mag)-.3010299956639812);{const e=k.div(se(this.sign,this.layer-1,this.mag),se(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=se(1,0,1)){if(e===1)return k.pow(this,t);if(e===0)return new k(t);if(this.eq(k.dOne))return k.dOne;if(this.eq(-1))return k.pow(this,t);if(e===Number.POSITIVE_INFINITY){const i=this.toNumber();if(i<=1.444667861009766&&i>=.06598803584531254){if(i>1.444667861009099)return new k(Math.E);const s=k.ln(this).neg();return s.lambertw().div(s)}else return i>1.444667861009766?new k(Number.POSITIVE_INFINITY):k.dNaN}if(this.eq(k.dZero)){let i=Math.abs((e+1)%2);return i>1&&(i=2-i),new k(i)}if(e<0)return k.iteratedlog(t,this,-e);t=v(t);const l=e;e=Math.trunc(e);const a=l-e;if(this.gt(k.dZero)&&this.lte(1.444667861009766)){e=Math.min(1e4,e);for(let i=0;i<e;++i){const s=t;if(t=this.pow(t),s.eq(t))return t}if(a!=0){const i=this.pow(t);return t.mul(1-a).add(i.mul(a))}return t}a!==0&&(t.eq(k.dOne)?this.gt(10)?t=this.pow(a):(t=v(k.tetrate_critical(this.toNumber(),a)),this.lt(2)&&(t=t.sub(1).mul(this.minus(1)).plus(1))):this.eq(10)?t=t.layeradd10(a):t=t.layeradd(a,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 se(t.sign,t.layer+(e-i-1),t.mag);if(i>1e4)return t}return t}iteratedexp(e=2,t=se(1,0,1)){return this.tetrate(e,t)}iteratedlog(e=10,t=1){if(t<0)return k.tetrate(e,-t,this);e=v(e);let l=v(this);const a=t;t=Math.trunc(t);const i=a-t;if(l.layer-e.layer>3){const s=Math.min(t,l.layer-e.layer-3);t-=s,l.layer-=s}for(let s=0;s<t;++s){if(l=l.log(e),!isFinite(l.layer)||!isFinite(l.mag))return l.normalize();if(s>1e4)return l}return i>0&&i<1&&(e.eq(10)?l=l.layeradd10(-i):l=l.layeradd(-i,e)),l}slog(e=10){if(e=v(e),e.lte(k.dZero)||e.eq(k.dOne))return k.dNaN;if(e.lt(k.dOne))return this.eq(k.dOne)?k.dZero:this.eq(k.dZero)?k.dNegOne:k.dNaN;if(this.mag<0||this.eq(k.dZero))return k.dNegOne;let t=0,l=v(this);if(l.layer-e.layer>3){const a=l.layer-e.layer-3;t+=a,l.layer-=a}for(let a=0;a<100;++a)if(l.lt(k.dZero))l=k.pow(e,l),t-=1;else{if(l.lte(k.dOne))return v(t+k.slog_critical(e.toNumber(),l.toNumber()));t+=1,l=k.log(l,e)}return v(t)}static slog_critical(e,t){return e>10?t-1:k.critical_section(e,t,Ti)}static tetrate_critical(e,t){return 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