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o=0;o<100;++o){if(n=(e*Math.exp(-l)+l*l)/(l+1),Math.abs(n-l)<t*Math.abs(n))return n;l=n}throw Error(`Iteration failed to converge: ${e.toString()}`)};function La(e,t=1e-10){let l,n,o,s;if(!Number.isFinite(e.mag)||e===a.dZero)return e;if(e===a.dOne)return b(sn);a.abs(e),l=a.ln(e);for(let u=0;u<100;++u){if(n=a.exp(-l),o=l.sub(e.mul(n)),s=l.sub(o.div(l.add(1).sub(l.add(2).mul(o).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 E=class{constructor(e){this.sign=Number.NaN,this.mag=Number.NaN,this.layer=Number.NaN,e instanceof E||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/qo(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 E().fromComponents(e,t,l)}static fromComponents_noNormalize(e,t,l){return new E().fromComponents_noNormalize(e,t,l)}static fromMantissaExponent(e,t){return new E().fromMantissaExponent(e,t)}static fromMantissaExponent_noNormalize(e,t){return new E().fromMantissaExponent_noNormalize(e,t)}static fromDecimal(e){return new E().fromDecimal(e)}static fromNumber(e){return new E().fromNumber(e)}static fromString(e){return new E().fromString(e)}static fromValue(e){return new E().fromValue(e)}static fromValue_noAlloc(e){return e instanceof E?e:new E(e)}static abs(e){return b(e).abs()}static neg(e){return b(e).neg()}static negate(e){return b(e).neg()}static negated(e){return b(e).neg()}static sign(e){return b(e).sign}static sgn(e){return b(e).sign}static round(e){return b(e).round()}static floor(e){return b(e).floor()}static ceil(e){return b(e).ceil()}static trunc(e){return b(e).trunc()}static add(e,t){return b(e).add(t)}static plus(e,t){return b(e).add(t)}static sub(e,t){return b(e).sub(t)}static subtract(e,t){return b(e).sub(t)}static minus(e,t){return b(e).sub(t)}static mul(e,t){return b(e).mul(t)}static multiply(e,t){return b(e).mul(t)}static times(e,t){return b(e).mul(t)}static div(e,t){return b(e).div(t)}static divide(e,t){return b(e).div(t)}static recip(e){return b(e).recip()}static reciprocal(e){return b(e).recip()}static reciprocate(e){return b(e).reciprocate()}static cmp(e,t){return b(e).cmp(t)}static cmpabs(e,t){return b(e).cmpabs(t)}static compare(e,t){return b(e).cmp(t)}static isNaN(e){return e=b(e),isNaN(e.sign)||isNaN(e.layer)||isNaN(e.mag)}static isFinite(e){return e=b(e),isFinite(e.sign)&&isFinite(e.layer)&&isFinite(e.mag)}static eq(e,t){return b(e).eq(t)}static equals(e,t){return b(e).eq(t)}static neq(e,t){return b(e).neq(t)}static notEquals(e,t){return b(e).notEquals(t)}static lt(e,t){return b(e).lt(t)}static lte(e,t){return b(e).lte(t)}static gt(e,t){return b(e).gt(t)}static gte(e,t){return b(e).gte(t)}static max(e,t){return b(e).max(t)}static min(e,t){return b(e).min(t)}static minabs(e,t){return b(e).minabs(t)}static maxabs(e,t){return b(e).maxabs(t)}static clamp(e,t,l){return b(e).clamp(t,l)}static clampMin(e,t){return b(e).clampMin(t)}static clampMax(e,t){return b(e).clampMax(t)}static cmp_tolerance(e,t,l){return b(e).cmp_tolerance(t,l)}static compare_tolerance(e,t,l){return b(e).cmp_tolerance(t,l)}static eq_tolerance(e,t,l){return b(e).eq_tolerance(t,l)}static equals_tolerance(e,t,l){return b(e).eq_tolerance(t,l)}static neq_tolerance(e,t,l){return b(e).neq_tolerance(t,l)}static notEquals_tolerance(e,t,l){return b(e).notEquals_tolerance(t,l)}static lt_tolerance(e,t,l){return b(e).lt_tolerance(t,l)}static lte_tolerance(e,t,l){return b(e).lte_tolerance(t,l)}static gt_tolerance(e,t,l){return b(e).gt_tolerance(t,l)}static gte_tolerance(e,t,l){return b(e).gte_tolerance(t,l)}static pLog10(e){return b(e).pLog10()}static absLog10(e){return b(e).absLog10()}static log10(e){return b(e).log10()}static log(e,t){return b(e).log(t)}static log2(e){return b(e).log2()}static ln(e){return b(e).ln()}static logarithm(e,t){return b(e).logarithm(t)}static pow(e,t){return b(e).pow(t)}static pow10(e){return b(e).pow10()}static root(e,t){return b(e).root(t)}static factorial(e,t){return b(e).factorial()}static gamma(e,t){return b(e).gamma()}static lngamma(e,t){return b(e).lngamma()}static exp(e){return b(e).exp()}static sqr(e){return b(e).sqr()}static sqrt(e){return b(e).sqrt()}static cube(e){return b(e).cube()}static cbrt(e){return b(e).cbrt()}static tetrate(e,t=2,l=ve(1,0,1)){return b(e).tetrate(t,l)}static iteratedexp(e,t=2,l=ve(1,0,1)){return b(e).iteratedexp(t,l)}static iteratedlog(e,t=10,l=1){return b(e).iteratedlog(t,l)}static layeradd10(e,t){return b(e).layeradd10(t)}static layeradd(e,t,l=10){return b(e).layeradd(t,l)}static slog(e,t=10){return b(e).slog(t)}static lambertw(e){return b(e).lambertw()}static ssqrt(e){return b(e).ssqrt()}static pentate(e,t=2,l=ve(1,0,1)){return b(e).pentate(t,l)}static affordGeometricSeries(e,t,l,n){return this.affordGeometricSeries_core(b(e),b(t),b(l),n)}static sumGeometricSeries(e,t,l,n){return this.sumGeometricSeries_core(e,b(t),b(l),n)}static affordArithmeticSeries(e,t,l,n){return this.affordArithmeticSeries_core(b(e),b(t),b(l),b(n))}static sumArithmeticSeries(e,t,l,n){return this.sumArithmeticSeries_core(b(e),b(t),b(l),b(n))}static efficiencyOfPurchase(e,t,l){return this.efficiencyOfPurchase_core(b(e),b(t),b(l))}static randomDecimalForTesting(e){if(Math.random()*20<1)return ve(0,0,0);const t=Math.random()>.5?1:-1;if(Math.random()*20<1)return ve(t,0,1);const l=Math.floor(Math.random()*(e+1));let n=l===0?Math.random()*616-308:Math.random()*16;Math.random()>.9&&(n=Math.trunc(n));let o=Math.pow(10,n);return Math.random()>.9&&(o=Math.trunc(o)),ie(t,l,o)}static affordGeometricSeries_core(e,t,l,n){const o=t.mul(l.pow(n));return E.floor(e.div(o).mul(l.sub(1)).add(1).log10().div(l.log10()))}static sumGeometricSeries_core(e,t,l,n){return t.mul(l.pow(n)).mul(E.sub(1,l.pow(e))).div(E.sub(1,l))}static affordArithmeticSeries_core(e,t,l,n){const s=t.add(n.mul(l)).sub(l.div(2)),u=s.pow(2);return s.neg().add(u.add(l.mul(e).mul(2)).sqrt()).div(l).floor()}static sumArithmeticSeries_core(e,t,l,n){const o=t.add(n.mul(l));return e.div(2).mul(o.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<Oo)return this.layer+=1,this.mag=Math.log10(this.mag),this;let e=Math.abs(this.mag),t=Math.sign(this.mag);if(e>=Uo)return this.layer+=1,this.mag=t*Math.log10(e),this;for(;e<Ro&&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.sign===-1?Math.abs(n.toNumber()%2)%2===1?o.neg():Math.abs(n.toNumber()%2)%2===0?o:E.dNaN:o}pow10(){if(!Number.isFinite(this.layer)||!Number.isFinite(this.mag))return E.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 ie(1,0,t);if(e.sign===0)return E.dOne;e=ve(e.sign,e.layer+1,Math.log10(e.mag))}return e.sign>0&&e.mag>=0?ie(e.sign,e.layer+1,e.mag):e.sign<0&&e.mag>=0?ie(-e.sign,e.layer+1,-e.mag):E.dOne}pow_base(e){return b(e).pow(this)}root(e){const t=b(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?E.exp(E.mul(this,E.ln(this).sub(1))):E.exp(this)}gamma(){if(this.mag<0)return this.recip();if(this.layer===0){if(this.lt(ve(1,0,24)))return b(Ho(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 n=e,o=12*n,s=1/o,u=t+s;if(u===t||(t=u,n=n*l,o=360*n,s=1/o,u=t-s,u===t))return E.exp(t);t=u,n=n*l,o=1260*n;let d=1/o;return t=t+d,n=n*l,o=1680*n,d=1/o,t=t-d,E.exp(t)}else return this.layer===1?E.exp(E.mul(this,E.ln(this).sub(1))):E.exp(this)}lngamma(){return this.gamma().ln()}exp(){return this.mag<0?E.dOne:this.layer===0&&this.mag<=709.7?b(Math.exp(this.sign*this.mag)):this.layer===0?ie(1,1,this.sign*Math.log10(Math.E)*this.mag):this.layer===1?ie(1,2,this.sign*(Math.log10(.4342944819032518)+this.mag)):ie(1,this.layer+1,this.sign*this.mag)}sqr(){return this.pow(2)}sqrt(){if(this.layer===0)return b(Math.sqrt(this.sign*this.mag));if(this.layer===1)return ie(1,2,Math.log10(this.mag)-.3010299956639812);{const e=E.div(ve(this.sign,this.layer-1,this.mag),ve(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=ve(1,0,1)){if(e===1)return E.pow(this,t);if(e===0)return new E(t);if(this.eq(E.dOne))return E.dOne;if(this.eq(-1))return E.pow(this,t);if(e===Number.POSITIVE_INFINITY){const o=this.toNumber();if(o<=1.444667861009766&&o>=.06598803584531254){if(o>1.444667861009099)return new E(Math.E);const s=E.ln(this).neg();return s.lambertw().div(s)}else return o>1.444667861009766?new E(Number.POSITIVE_INFINITY):E.dNaN}if(this.eq(E.dZero)){let o=Math.abs((e+1)%2);return o>1&&(o=2-o),new E(o)}if(e<0)return E.iteratedlog(t,this,-e);t=b(t);const l=e;e=Math.trunc(e);const n=l-e;if(this.gt(E.dZero)&&this.lte(1.444667861009766)){e=Math.min(1e4,e);for(let o=0;o<e;++o){const s=t;if(t=this.pow(t),s.eq(t))return t}if(n!=0){const o=this.pow(t);return t.mul(1-n).add(o.mul(n))}return t}n!==0&&(t.eq(E.dOne)?this.gt(10)?t=this.pow(n):(t=b(E.tetrate_critical(this.toNumber(),n)),this.lt(2)&&(t=t.sub(1).mul(this.minus(1)).plus(1))):this.eq(10)?t=t.layeradd10(n):t=t.layeradd(n,this));for(let o=0;o<e;++o){if(t=this.pow(t),!isFinite(t.layer)||!isFinite(t.mag))return t.normalize();if(t.layer-this.layer>3)return ve(t.sign,t.layer+(e-o-1),t.mag);if(o>1e4)return t}return t}iteratedexp(e=2,t=ve(1,0,1)){return this.tetrate(e,t)}iteratedlog(e=10,t=1){if(t<0)return E.tetrate(e,-t,this);e=b(e);let l=b(this);const n=t;t=Math.trunc(t);const o=n-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 o>0&&o<1&&(e.eq(10)?l=l.layeradd10(-o):l=l.layeradd(-o,e)),l}slog(e=10){if(e=b(e),e.lte(E.dZero)||e.eq(E.dOne))return E.dNaN;if(e.lt(E.dOne))return this.eq(E.dOne)?E.dZero:this.eq(E.dZero)?E.dNegOne:E.dNaN;if(this.mag<0||this.eq(E.dZero))return E.dNegOne;let t=0,l=b(this);if(l.layer-e.layer>3){const n=l.layer-e.layer-3;t+=n,l.layer-=n}for(let n=0;n<100;++n)if(l.lt(E.dZero))l=E.pow(e,l),t-=1;else{if(l.lte(E.dOne))return b(t+E.slog_critical(e.toNumber(),l.toNumber()));t+=1,l=E.log(l,e)}return b(t)}static slog_critical(e,t){return e>10?t-1:E.critical_section(e,t,Lo)}static tetrate_critical(e,t){return 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