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e=n*T((4+_)/_)/2,r=O(e),i=a(r);return[t/(2/T(_*(4+_))*(1+i)),O((r+e*(i+2))/(2+m))]},pt.invert=function(t,n){var e=T(2+_),r=n*e/2;return[e*t/(1+a(r)),r]},vt.invert=function(t,n){var e=1+m,r=T(e/2);return[2*t*r/(1+a(n*=r)),O((n+d(n))/e)]};var dt=3+2*w;function gt(t,n){var e=d(t/=2),r=a(t),o=T(a(n)),u=a(n/=2),c=d(n)/(u+w*r*o),s=T(2/(1+c*c)),l=T((w*u+(r+e)*o)/(w*u+(r-e)*o));return[dt*(s*(l-1/l)-2*f(l)),dt*(s*c*(l+1/l)-2*i(c))]}gt.invert=function(t,n){if(!(e=I.invert(t/1.2,1.065*n)))return null;var e,o=e[0],u=e[1],c=20;t/=dt,n/=dt;do{var h=o/2,p=u/2,v=d(h),g=a(h),_=d(p),x=a(p),E=a(u),M=T(E),j=_/(x+w*g*M),S=j*j,O=T(2/(1+S)),P=(w*x+(g+v)*M)/(w*x+(g-v)*M),A=T(P),k=A-1/A,C=A+1/A,N=O*k-2*f(A)-t,R=O*j*C-2*i(j)-n,D=_&&b*M*v*S/_,q=(w*g*x+M)/(2*(x+w*g*M)*(x+w*g*M)*M),L=-.5*j*O*O*O,z=L*D,B=L*q,F=(F=2*x+w*M*(g-v))*F*A,G=(w*g*x*M+E)/F,V=-w*v*_/(M*F),H=k*z-2*G/A+O*(G+G/P),U=k*B-2*V/A+O*(V+V/P),W=j*C*z-2*D/(1+S)+O*C*D+O*j*(G-G/P),Y=j*C*B-2*q/(1+S)+O*C*q+O*j*(V-V/P),$=U*W-Y*H;if(!$)break;var X=(R*U-N*Y)/$,J=(N*W-R*H)/$;o-=X,u=s(-m,l(m,u-J))}while((r(X)>y||r(J)>y)&&--c>0);return r(r(u)-m)<y?[0,u]:c&&[o,u]};var yt=a(35*S);function _t(t,n){var e=g(n/2);return[t*yt*T(1-e*e),(1+yt)*e]}function mt(t,n){var e=n/2,r=a(e);return[2*t/E*a(n)*r*r,E*g(e)]}function xt(t){return[t[0]/2,O(g(t[1]/2*S))*j]}function bt(t){return[2*t[0],2*i(d(t[1]*S))*j]}function wt(t,e){var i=2*_/e,u=t*t;function c(e,c){var f=n.geoAzimuthalEquidistantRaw(e,c),s=f[0],l=f[1],h=s*s+l*l;if(h>u){var v=T(h),g=o(l,s),x=i*p(g/i),b=g-x,w=t*a(b),E=(t*d(b)-b*d(w))/(m-w),M=Et(b,E),j=(_-t)/Mt(M,w,_);s=v;var S,O=50;do{s-=S=(t+Mt(M,w,s)*j-v)/(M(s)*j)}while(r(S)>y&&--O>0);l=b*d(s),s<m&&(l-=E*(s-m));var P=d(x),A=a(x);f[0]=s*A-l*P,f[1]=s*P+l*A}return f}return c.invert=function(e,c){var f=e*e+c*c;if(f>u){var s=T(f),l=o(c,e),h=i*p(l/i),v=l-h;e=s*a(v),c=s*d(v);for(var g=e-m,y=d(e),x=c/y,b=e<m?1/0:0,w=10;;){var E=t*d(x),M=t*a(x),j=d(M),S=m-M,O=(E-x*j)/S,P=Et(x,O);if(r(b)<1e-12||!--w)break;x-=b=(x*y-O*g-c)/(y-2*g*(S*(M+x*E*a(M)-j)-E*(E-x*j))/(S*S))}e=(s=t+Mt(P,M,e)*(_-t)/Mt(P,M,_))*a(l=h+x),c=s*d(l)}return n.geoAzimuthalEquidistantRaw.invert(e,c)},c}function Et(t,n){return function(e){var r=t*a(e);return e<m&&(r-=n),T(1+r*r)}}function Mt(t,n,e){for(var r=(e-n)/50,i=t(n)+t(e),o=1,a=n;o<50;++o)i+=2*t(a+=r);return.5*i*r}_t.invert=function(t,n){var e=n/(1+yt);return[t&&t/(yt*T(1-e*e)),2*i(e)]},mt.invert=function(t,n){var e=i(n/E),r=a(e),o=2*e;return[t*E/2/(a(o)*r*r),o]};var jt=function(t,n,e,i,o,u,c,f){function s(r,s){if(!s)return[t*r/_,0];var l=s*s,h=t+l*(n+l*(e+l*i)),p=s*(o-1+l*(u-f+l*c)),v=(h*h+p*p)/(2*p),g=r*O(h/v)/_;return[v*d(g),s*(1+l*f)+v*(1-a(g))]}return arguments.length<8&&(f=0),s.invert=function(s,l){var h,p,v=_*s/t,g=l,m=50;do{var 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n=t(m,0)[0]-t(-m,0)[0];function e(e,r){var i=e>0?-.5:.5,o=t(e+i*_,r);return o[0]-=i*n,o}return t.invert&&(e.invert=function(e,r){var i=e>0?-.5:.5,o=t.invert(e+i*n,r),a=o[0]-i*_;return a<-_?a+=2*_:a>_&&(a-=2*_),o[0]=a,o}),e};function Ct(t,n){var e=v(t),i=v(n),u=a(n),c=a(t)*u,f=d(t)*u,s=d(i*n);t=r(o(f,s)),n=O(c),r(t-m)>y&&(t%=m);var l=function(t,n){if(n===m)return[0,0];var e,i,o=d(n),u=o*o,c=u*u,f=1+c,s=1+3*c,l=1-c,h=O(1/T(f)),p=l+u*f*h,v=(1-o)/p,g=T(v),x=v*f,b=T(x),w=g*l;if(0===t)return[0,-(w+u*b)];var E,M=a(n),j=1/M,S=2*o*M,P=(-p*M-(-3*u+h*s)*S*(1-o))/(p*p),A=-j*S,k=-j*(u*f*P+v*s*S),C=-2*j*(l*(.5*P/g)-2*u*g*S),N=4*t/_;if(t>.222*_||n<_/4&&t>.175*_){if(e=(w+u*T(x*(1+c)-w*w))/(1+c),t>_/4)return[e,e];var R=e,I=.5*e;e=.5*(I+R),i=50;do{var D=T(x-e*e),q=e*(C+A*D)+k*O(e/b)-N;if(!q)break;q<0?I=e:R=e,e=.5*(I+R)}while(r(R-I)>y&&--i>0)}else{e=y,i=25;do{var L=e*e,z=T(x-L),B=C+A*z,F=e*B+k*O(e/b)-N,G=B+(k-A*L)/z;e-=E=z?F/G:0}while(r(E)>y&&--i>0)}return[e,-w-u*T(x-e*e)]}(t>_/4?m-t:t,n);return t>_/4&&(s=l[0],l[0]=-l[1],l[1]=-s),l[0]*=e,l[1]*=-i,l}function Nt(t,n){var e,o,c,f,s,l;if(n<y)return[(f=d(t))-(e=n*(t-f*(o=a(t)))/4)*o,o+e*f,1-n*f*f/2,t-e];if(n>=1-y)return e=(1-n)/4,c=1/(o=k(t)),[(f=((l=u(2*(l=t)))-1)/(l+1))+e*((s=o*A(t))-t)/(o*o),c-e*f*c*(s-t),c+e*f*c*(s+t),2*i(u(t))-m+e*(s-t)/o];var h=[1,0,0,0,0,0,0,0,0],p=[T(n),0,0,0,0,0,0,0,0],v=0;for(o=T(1-n),s=1;r(p[v]/h[v])>y&&v<8;)e=h[v++],p[v]=(e-o)/2,h[v]=(e+o)/2,o=T(e*o),s*=2;c=s*h[v]*t;do{c=(O(f=p[v]*d(o=c)/h[v])+c)/2}while(--v);return[d(c),f=a(c),f/a(c-o),c]}function Rt(t,n){if(!n)return t;if(1===n)return f(g(t/2+x));for(var e=1,o=T(1-n),a=T(n),u=0;r(a)>y;u++){if(t%_){var c=i(o*g(t)/e);c<0&&(c+=_),t+=c+~~(t/_)*_}else t+=t;a=(e+o)/2,o=T(e*o),a=((e=a)-o)/2}return t/(h(2,u)*e)}function It(t,n){var e=(w-1)/(w+1),c=T(1-e*e),s=Rt(m,c*c),l=f(g(_/4+r(n)/2)),h=u(-1*l)/T(e),p=function(t,n){var e=t*t,r=n+1,i=1-e-n*n;return[.5*((t>=0?m:-m)-o(i,2*t)),-.25*f(i*i+4*e)+.5*f(r*r+e)]}(h*a(-1*t),h*d(-1*t)),y=function(t,n,e){var o=r(t),a=A(r(n));if(o){var u=1/d(o),c=1/(g(o)*g(o)),f=-(c+e*(a*a*u*u)-1+e),s=(-f+T(f*f-(e-1)*c*4))/2;return[Rt(i(1/T(s)),e)*v(t),Rt(i(T((s/c-1)/e)),1-e)*v(n)]}return[0,Rt(i(a),1-e)*v(n)]}(p[0],p[1],c*c);return[-y[1],(n>=0?1:-1)*(.5*s-y[0])]}function Dt(t,e){if(arguments.length<2&&(e=t),1===e)return n.geoAzimuthalEqualAreaRaw;if(e===1/0)return qt;function r(r,i){var o=n.geoAzimuthalEqualAreaRaw(r/e,i);return o[0]*=t,o}return r.invert=function(r,i){var o=n.geoAzimuthalEqualAreaRaw.invert(r/t,i);return o[0]*=e,o},r}function qt(t,n){return[t*a(n)/a(n/=2),2*d(n)]}function Lt(t){var n=d(t),e=a(t),i=zt(t);function u(t,o){var u=i(t,o);t=u[0],o=u[1];var c=d(o),f=a(o),s=a(t),l=P(n*c+e*f*s),h=d(l),p=r(h)>y?l/h:1;return[p*e*d(t),(r(t)>m?p:-p)*(n*f-e*c*s)]}return i.invert=zt(-t),u.invert=function(t,e){var r=T(t*t+e*e),u=-d(r),c=a(r),f=r*c,s=-e*u,l=r*n,h=T(f*f+s*s-l*l),p=o(f*l+s*h,s*l-f*h),v=(r>m?-1:1)*o(t*u,r*a(p)*c+e*d(p)*u);return i.invert(v,p)},u}function zt(t){var n=d(t),e=a(t);return function(t,r){var i=a(r),u=a(t)*i,c=d(t)*i,f=d(r);return[o(c,u*e-f*n),O(f*e+u*n)]}}Ct.invert=function(t,n){r(t)>1&&(t=2*v(t)-t),r(n)>1&&(n=2*v(n)-n);var e=v(t),i=v(n),u=-e*t,c=-i*n,f=c/u<1,s=function(t,n){for(var e=0,i=1,o=.5,u=50;;){var c=o*o,f=T(o),s=O(1/T(1+c)),l=1-c+o*(1+c)*s,h=(1-f)/l,p=T(h),v=h*(1+c),d=p*(1-c),g=T(v-t*t),y=n+d+o*g;if(r(i-e)<1e-12||0==--u||0===y)break;y>0?e=o:i=o,o=.5*(e+i)}if(!u)return null;var m=O(f),x=a(m),b=1/x,w=2*f*x,E=(-l*x-(-3*o+s*(1+3*c))*w*(1-f))/(l*l);return[_/4*(t*(-2*b*(.5*E/p*(1-c)-2*o*p*w)+-b*w*g)+-b*(o*(1+c)*E+h*(1+3*c)*w)*O(t/T(v))),m]}(f?c:u,f?u:c),l=s[0],h=s[1],p=a(h);return f&&(l=-m-l),[e*(o(d(l)*p,-d(h))+_),i*O(a(l)*p)]},It.invert=function(t,n){var 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