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n=0;n<100;++n){if(i=(e*Math.exp(-l)+l*l)/(l+1),Math.abs(i-l)<t*Math.abs(i))return i;l=i}throw Error(`Iteration failed to converge: ${e.toString()}`)};function za(e,t=1e-10){let l,i,n,s;if(!Number.isFinite(e.mag)||e===a.dZero)return e;if(e===a.dOne)return C(ci);a.abs(e),l=a.ln(e);for(let c=0;c<100;++c){if(i=a.exp(-l),n=l.sub(e.mul(i)),s=l.sub(n.div(l.add(1).sub(l.add(2).mul(n).div(a.mul(2,l).add(2))))),a.abs(s.sub(l)).lt(a.abs(s).mul(t)))return s;l=s}throw Error(`Iteration failed to converge: ${e.toString()}`)}const I=class{constructor(e){this.sign=Number.NaN,this.mag=Number.NaN,this.layer=Number.NaN,e instanceof I||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/Wn(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 I().fromComponents(e,t,l)}static fromComponents_noNormalize(e,t,l){return new I().fromComponents_noNormalize(e,t,l)}static fromMantissaExponent(e,t){return new I().fromMantissaExponent(e,t)}static fromMantissaExponent_noNormalize(e,t){return new I().fromMantissaExponent_noNormalize(e,t)}static fromDecimal(e){return new I().fromDecimal(e)}static fromNumber(e){return new I().fromNumber(e)}static fromString(e){return new I().fromString(e)}static fromValue(e){return new I().fromValue(e)}static fromValue_noAlloc(e){return e instanceof I?e:new I(e)}static abs(e){return C(e).abs()}static neg(e){return C(e).neg()}static negate(e){return C(e).neg()}static negated(e){return C(e).neg()}static sign(e){return C(e).sign}static sgn(e){return C(e).sign}static round(e){return C(e).round()}static floor(e){return C(e).floor()}static ceil(e){return C(e).ceil()}static trunc(e){return C(e).trunc()}static add(e,t){return C(e).add(t)}static plus(e,t){return C(e).add(t)}static sub(e,t){return C(e).sub(t)}static subtract(e,t){return C(e).sub(t)}static minus(e,t){return C(e).sub(t)}static mul(e,t){return C(e).mul(t)}static multiply(e,t){return C(e).mul(t)}static times(e,t){return C(e).mul(t)}static div(e,t){return C(e).div(t)}static divide(e,t){return C(e).div(t)}static recip(e){return C(e).recip()}static reciprocal(e){return C(e).recip()}static reciprocate(e){return C(e).reciprocate()}static cmp(e,t){return C(e).cmp(t)}static cmpabs(e,t){return C(e).cmpabs(t)}static compare(e,t){return C(e).cmp(t)}static isNaN(e){return e=C(e),isNaN(e.sign)||isNaN(e.layer)||isNaN(e.mag)}static isFinite(e){return e=C(e),isFinite(e.sign)&&isFinite(e.layer)&&isFinite(e.mag)}static eq(e,t){return C(e).eq(t)}static equals(e,t){return C(e).eq(t)}static neq(e,t){return C(e).neq(t)}static notEquals(e,t){return C(e).notEquals(t)}static lt(e,t){return C(e).lt(t)}static lte(e,t){return C(e).lte(t)}static gt(e,t){return C(e).gt(t)}static gte(e,t){return C(e).gte(t)}static max(e,t){return C(e).max(t)}static min(e,t){return C(e).min(t)}static minabs(e,t){return C(e).minabs(t)}static maxabs(e,t){return C(e).maxabs(t)}static clamp(e,t,l){return C(e).clamp(t,l)}static clampMin(e,t){return C(e).clampMin(t)}static clampMax(e,t){return C(e).clampMax(t)}static cmp_tolerance(e,t,l){return C(e).cmp_tolerance(t,l)}static compare_tolerance(e,t,l){return C(e).cmp_tolerance(t,l)}static eq_tolerance(e,t,l){return C(e).eq_tolerance(t,l)}static equals_tolerance(e,t,l){return C(e).eq_tolerance(t,l)}static neq_tolerance(e,t,l){return C(e).neq_tolerance(t,l)}static notEquals_tolerance(e,t,l){return C(e).notEquals_tolerance(t,l)}static lt_tolerance(e,t,l){return C(e).lt_tolerance(t,l)}static lte_tolerance(e,t,l){return C(e).lte_tolerance(t,l)}static gt_tolerance(e,t,l){return C(e).gt_tolerance(t,l)}static gte_tolerance(e,t,l){return C(e).gte_tolerance(t,l)}static pLog10(e){return C(e).pLog10()}static absLog10(e){return C(e).absLog10()}static log10(e){return C(e).log10()}static log(e,t){return C(e).log(t)}static log2(e){return C(e).log2()}static ln(e){return C(e).ln()}static logarithm(e,t){return C(e).logarithm(t)}static pow(e,t){return C(e).pow(t)}static pow10(e){return C(e).pow10()}static root(e,t){return C(e).root(t)}static factorial(e,t){return C(e).factorial()}static gamma(e,t){return C(e).gamma()}static lngamma(e,t){return C(e).lngamma()}static exp(e){return C(e).exp()}static sqr(e){return C(e).sqr()}static sqrt(e){return C(e).sqrt()}static cube(e){return C(e).cube()}static cbrt(e){return C(e).cbrt()}static tetrate(e,t=2,l=Ne(1,0,1)){return C(e).tetrate(t,l)}static iteratedexp(e,t=2,l=Ne(1,0,1)){return C(e).iteratedexp(t,l)}static iteratedlog(e,t=10,l=1){return C(e).iteratedlog(t,l)}static layeradd10(e,t){return C(e).layeradd10(t)}static layeradd(e,t,l=10){return C(e).layeradd(t,l)}static slog(e,t=10){return C(e).slog(t)}static lambertw(e){return C(e).lambertw()}static ssqrt(e){return C(e).ssqrt()}static pentate(e,t=2,l=Ne(1,0,1)){return C(e).pentate(t,l)}static affordGeometricSeries(e,t,l,i){return this.affordGeometricSeries_core(C(e),C(t),C(l),i)}static sumGeometricSeries(e,t,l,i){return this.sumGeometricSeries_core(e,C(t),C(l),i)}static affordArithmeticSeries(e,t,l,i){return this.affordArithmeticSeries_core(C(e),C(t),C(l),C(i))}static sumArithmeticSeries(e,t,l,i){return this.sumArithmeticSeries_core(C(e),C(t),C(l),C(i))}static efficiencyOfPurchase(e,t,l){return this.efficiencyOfPurchase_core(C(e),C(t),C(l))}static randomDecimalForTesting(e){if(Math.random()*20<1)return Ne(0,0,0);const t=Math.random()>.5?1:-1;if(Math.random()*20<1)return Ne(t,0,1);const l=Math.floor(Math.random()*(e+1));let i=l===0?Math.random()*616-308:Math.random()*16;Math.random()>.9&&(i=Math.trunc(i));let n=Math.pow(10,i);return Math.random()>.9&&(n=Math.trunc(n)),ge(t,l,n)}static affordGeometricSeries_core(e,t,l,i){const n=t.mul(l.pow(i));return I.floor(e.div(n).mul(l.sub(1)).add(1).log10().div(l.log10()))}static sumGeometricSeries_core(e,t,l,i){return t.mul(l.pow(i)).mul(I.sub(1,l.pow(e))).div(I.sub(1,l))}static affordArithmeticSeries_core(e,t,l,i){const s=t.add(i.mul(l)).sub(l.div(2)),c=s.pow(2);return s.neg().add(c.add(l.mul(e).mul(2)).sqrt()).div(l).floor()}static sumArithmeticSeries_core(e,t,l,i){const n=t.add(i.mul(l));return e.div(2).mul(n.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<Vn)return this.layer+=1,this.mag=Math.log10(this.mag),this;let e=Math.abs(this.mag),t=Math.sign(this.mag);if(e>=Ln)return this.layer+=1,this.mag=t*Math.log10(e),this;for(;e<Qn&&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 this.sign=e,this.layer=t,this.mag=l,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 w=parseFloat(t[0]),v=parseFloat(t[1]),E=t[1].split(";");let S=1;if(E.length===2&&(S=parseFloat(E[1]),isFinite(S)||(S=1)),isFinite(w)&&isFinite(v)){const x=I.pentate(w,v,S);return this.sign=x.sign,this.layer=x.layer,this.mag=x.mag,this}}const l=e.split("^^");if(l.length===2){const w=parseFloat(l[0]),v=parseFloat(l[1]),E=l[1].split(";");let S=1;if(E.length===2&&(S=parseFloat(E[1]),isFinite(S)||(S=1)),isFinite(w)&&isFinite(v)){const x=I.tetrate(w,v,S);return 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this.fromNumber(w)}const m=e.split("e^");if(m.length===2){this.sign=1,m[0].charAt(0)=="-"&&(this.sign=-1);let w="";for(let v=0;v<m[1].length;++v){const E=m[1].charCodeAt(v);if(E>=43&&E<=57||E===101)w+=m[1].charAt(v);else return this.layer=parseFloat(w),this.mag=parseFloat(m[1].substr(v+1)),this.normalize(),this}}if(p<1)return this.sign=0,this.layer=0,this.mag=0,this;const h=parseFloat(d[0]);if(h===0)return this.sign=0,this.layer=0,this.mag=0,this;let y=parseFloat(d[d.length-1]);if(p>=2){const w=parseFloat(d[d.length-2]);isFinite(w)&&(y*=Math.sign(w),y+=ba(w))}if(!isFinite(h))this.sign=d[0]==="-"?-1:1,this.layer=p,this.mag=y;else if(p===1)this.sign=Math.sign(h),this.layer=1,this.mag=y+Math.log10(Math.abs(h));else if(this.sign=Math.sign(h),this.layer=p,p===2){const w=I.mul(ge(1,2,y),C(h));return this.sign=w.sign,this.layer=w.layer,this.mag=w.mag,this}else this.mag=y;return this.normalize(),this}fromValue(e){return e instanceof I||e!=null&&typeof e=="object"&&"sign"in e&&"mag"in 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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<=Wa?(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):vl(this.m,e)+"e"+vl(this.e,e):this.layer===1?vl(this.m,e)+"e"+vl(this.e,e):this.layer<=Wa?(this.sign===-1?"-":"")+"e".repeat(this.layer)+vl(this.mag,e):(this.sign===-1?"-":"")+"(e^"+this.layer+")"+vl(this.mag,e)}abs(){return Ne(this.sign===0?0:1,this.layer,this.mag)}neg(){return Ne(-this.sign,this.layer,this.mag)}negate(){return this.neg()}negated(){return this.neg()}sgn(){return this.sign}round(){return this.mag<0?I.dZero:this.layer===0?ge(this.sign,0,Math.round(this.mag)):this}floor(){return this.mag<0?I.dZero:this.layer===0?ge(this.sign,0,Math.floor(this.mag)):this}ceil(){return this.mag<0?I.dZero:this.layer===0?ge(this.sign,0,Math.ceil(this.mag)):this}trunc(){return this.mag<0?I.dZero:this.layer===0?ge(this.sign,0,Math.trunc(this.mag)):this}add(e){const t=C(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===-1?Math.abs(i.toNumber()%2)%2===1?n.neg():Math.abs(i.toNumber()%2)%2===0?n:I.dNaN:n}pow10(){if(!Number.isFinite(this.layer)||!Number.isFinite(this.mag))return I.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 ge(1,0,t);if(e.sign===0)return I.dOne;e=Ne(e.sign,e.layer+1,Math.log10(e.mag))}return e.sign>0&&e.mag>=0?ge(e.sign,e.layer+1,e.mag):e.sign<0&&e.mag>=0?ge(-e.sign,e.layer+1,-e.mag):I.dOne}pow_base(e){return C(e).pow(this)}root(e){const t=C(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?I.exp(I.mul(this,I.ln(this).sub(1))):I.exp(this)}gamma(){if(this.mag<0)return this.recip();if(this.layer===0){if(this.lt(Ne(1,0,24)))return C(Kn(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 i=e,n=12*i,s=1/n,c=t+s;if(c===t||(t=c,i=i*l,n=360*i,s=1/n,c=t-s,c===t))return I.exp(t);t=c,i=i*l,n=1260*i;let d=1/n;return t=t+d,i=i*l,n=1680*i,d=1/n,t=t-d,I.exp(t)}else return this.layer===1?I.exp(I.mul(this,I.ln(this).sub(1))):I.exp(this)}lngamma(){return this.gamma().ln()}exp(){return this.mag<0?I.dOne:this.layer===0&&this.mag<=709.7?C(Math.exp(this.sign*this.mag)):this.layer===0?ge(1,1,this.sign*Math.log10(Math.E)*this.mag):this.layer===1?ge(1,2,this.sign*(Math.log10(.4342944819032518)+this.mag)):ge(1,this.layer+1,this.sign*this.mag)}sqr(){return this.pow(2)}sqrt(){if(this.layer===0)return C(Math.sqrt(this.sign*this.mag));if(this.layer===1)return ge(1,2,Math.log10(this.mag)-.3010299956639812);{const e=I.div(Ne(this.sign,this.layer-1,this.mag),Ne(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=Ne(1,0,1)){if(e===1)return I.pow(this,t);if(e===0)return new I(t);if(this.eq(I.dOne))return I.dOne;if(this.eq(-1))return I.pow(this,t);if(e===Number.POSITIVE_INFINITY){const n=this.toNumber();if(n<=1.444667861009766&&n>=.06598803584531254){if(n>1.444667861009099)return new I(Math.E);const s=I.ln(this).neg();return s.lambertw().div(s)}else return n>1.444667861009766?new I(Number.POSITIVE_INFINITY):I.dNaN}if(this.eq(I.dZero)){let n=Math.abs((e+1)%2);return n>1&&(n=2-n),new I(n)}if(e<0)return I.iteratedlog(t,this,-e);t=C(t);const l=e;e=Math.trunc(e);const i=l-e;if(this.gt(I.dZero)&&this.lte(1.444667861009766)){e=Math.min(1e4,e);for(let n=0;n<e;++n){const s=t;if(t=this.pow(t),s.eq(t))return t}if(i!=0){const n=this.pow(t);return t.mul(1-i).add(n.mul(i))}return t}i!==0&&(t.eq(I.dOne)?this.gt(10)?t=this.pow(i):(t=C(I.tetrate_critical(this.toNumber(),i)),this.lt(2)&&(t=t.sub(1).mul(this.minus(1)).plus(1))):this.eq(10)?t=t.layeradd10(i):t=t.layeradd(i,this));for(let n=0;n<e;++n){if(t=this.pow(t),!isFinite(t.layer)||!isFinite(t.mag))return t.normalize();if(t.layer-this.layer>3)return Ne(t.sign,t.layer+(e-n-1),t.mag);if(n>1e4)return t}return t}iteratedexp(e=2,t=Ne(1,0,1)){return this.tetrate(e,t)}iteratedlog(e=10,t=1){if(t<0)return I.tetrate(e,-t,this);e=C(e);let l=C(this);const i=t;t=Math.trunc(t);const n=i-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 n>0&&n<1&&(e.eq(10)?l=l.layeradd10(-n):l=l.layeradd(-n,e)),l}slog(e=10){if(e=C(e),e.lte(I.dZero)||e.eq(I.dOne))return I.dNaN;if(e.lt(I.dOne))return this.eq(I.dOne)?I.dZero:this.eq(I.dZero)?I.dNegOne:I.dNaN;if(this.mag<0||this.eq(I.dZero))return I.dNegOne;let t=0,l=C(this);if(l.layer-e.layer>3){const i=l.layer-e.layer-3;t+=i,l.layer-=i}for(let i=0;i<100;++i)if(l.lt(I.dZero))l=I.pow(e,l),t-=1;else{if(l.lte(I.dOne))return C(t+I.slog_critical(e.toNumber(),l.toNumber()));t+=1,l=I.log(l,e)}return C(t)}static slog_critical(e,t){return e>10?t-1:I.critical_section(e,t,zn)}static tetrate_critical(e,t){return 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