source: Sophya/trunk/Cosmo/SimLSS/cmvdefsurv.cc@ 3196

Last change on this file since 3196 was 3196, checked in by cmv, 18 years ago

les AGN selon C.Jackson, une premiere approche simplifiee, recodage from Jim Rich. cmv 03/04/2007
File size: 15.4 KB
Line 
1#include "sopnamsp.h"
2#include "machdefs.h"
3#include <iostream>
4#include <stdlib.h>
5#include <stdio.h>
6#include <string.h>
7#include <math.h>
8#include <unistd.h>
9
10#include "constcosmo.h"
11#include "cosmocalc.h"
12#include "geneutils.h"
13#include "schechter.h"
14#include "planckspectra.h"
15
16/* --- Check Peterson at al. astro-ph/0606104 v1
17cmvdefsurv -z 0.0025 -x 1 -U 0.75,0.3,0.7,-1,1 -V 300 -O 400000,6000 -N 75 -M 6.156e9 -F 3 -2 1.5
18 --- */
19
20inline double rad2deg(double trad) {return trad/M_PI*180.;}
21inline double rad2min(double trad) {return trad/M_PI*180.*60.;}
22inline double rad2sec(double trad) {return trad/M_PI*180.*3600.;}
23inline double deg2rad(double tdeg) {return tdeg*M_PI/180.;}
24inline double min2rad(double tmin) {return tmin*M_PI/(180.*60.);}
25inline double sec2rad(double tsec) {return tsec*M_PI/(180.*3600.);}
26
27void usage(void);
28void usage(void) {
29 cout<<"cmvdefsurv [-r] -x adtx,atxlarg [-y adty,atylarg] -z dred,redlarg redshift"<<endl
30 <<" -x adtx,atxlarg : resolution en Theta_x (arcmin), largeur (degre)"<<endl
31 <<" -y adty,atylarg : idem selon y, si <=0 meme que x"<<endl
32 <<" -z dred,redlarg : resolution en redshift, largeur en redshift"<<endl
33 <<" -P : on donne -x -y -z en Mpc au lieu d\'angles et de redshift"<<endl
34 <<" -L lobewidth : taille du lobe d\'observation (FWHM) en arcmin (def= 1\')"<<endl
35 <<" -O surf,tobs : surface effective (m^2) et temps d\'observation (s)"<<endl
36 <<" -N Tsys : temperature du system (K)"<<endl
37 <<" -S Tsynch,indnu : temperature (K) synch a 408 Mhz, index d\'evolution"<<endl
38 <<" (indnu==0 no evolution with freq.)"<<endl
39 <<" -M : masse de HI de reference (MSol), si <=0 mean schechter in pixel"<<endl
40 <<" -F : HI flux factor to be applied for our redshift"<<endl
41 <<" -V Vrot : largeur en vitesse (km/s) pour l\'elargissement doppler (def=300km/s)"<<endl
42 <<" -U h100,om0,ol0,w0,or0,flat : cosmology"<<endl
43 <<" -2 : two polarisations measured"<<endl
44 <<" -A <log10(S_agn)> : moyenne du flux AGN en Jy dans le pixel"<<endl
45 <<" redshift : redshift moyen du survey"<<endl
46 <<endl;
47}
48
49int main(int narg,char *arg[])
50{
51 // --- Valeurs fixes
52 // WMAP
53 unsigned short flat = 0;
54 double h100=0.71, om0=0.267804, or0=7.9e-05*0., ol0=0.73,w0=-1.;
55 // Schechter
56 double h75 = h100 / 0.75;
57 double nstar = 0.006*pow(h75,3.); //
58 double mstar = pow(10.,9.8/(h75*h75)); // MSol
59 double alpha = -1.37;
60 cout<<"nstar= "<<nstar<<" mstar="<<mstar<<" alpha="<<alpha<<endl;
61
62 // --- Arguments
63 bool inmpc = false;
64 double adtx=1., atxlarg=90., adty=-1., atylarg=-1.;
65 double dx=1.,txlarg=1000., dy=-1.,tylarg=1000., dz=1.,tzlarg=100.;
66 int nx,ny,nz;
67 double redshift = 1., dred=0.01, redlarg=0.3;
68 double tobs = 6000., surfeff = 400000.;
69 double lobewidth = 1.; // taille du lobe d'observation en arcmin
70 double Tsys=75.;
71 // a 408 MHz (Haslam) + evol index a -2.6
72 double Tsynch408=60., nuhaslam=0.408, indnu = -2.6;
73 double mhiref = -1.; // reference Mass en HI (def integ schechter)
74 double hifactor = 1.;
75 double vrot = 300.; // largeur en vitesse (km/s) pour elargissement doppler
76 double facpolar = 0.5; // si on ne mesure les 2 polars -> 1.0
77 double lflux_agn = -3.;
78
79 // --- Decodage arguments
80 char c;
81 while((c = getopt(narg,arg,"hP2x:y:z:N:S:O:M:F:V:U:L:A:")) != -1) {
82 switch (c) {
83 case 'P' :
84 inmpc = true;
85 break;
86 case 'x' :
87 sscanf(optarg,"%lf,%lf",&adtx,&atxlarg);
88 break;
89 case 'y' :
90 sscanf(optarg,"%lf,%lf",&adty,&atylarg);
91 break;
92 case 'z' :
93 sscanf(optarg,"%lf,%lf",&dred,&redlarg);
94 break;
95 case 'O' :
96 sscanf(optarg,"%lf,%lf",&surfeff,&tobs);
97 break;
98 case 'L' :
99 sscanf(optarg,"%lf",&lobewidth);
100 break;
101 case 'N' :
102 sscanf(optarg,"%lf",&Tsys);
103 break;
104 case 'S' :
105 sscanf(optarg,"%lf,%lf",&Tsynch408,&indnu);
106 break;
107 case 'M' :
108 sscanf(optarg,"%lf",&mhiref);
109 break;
110 case 'F' :
111 sscanf(optarg,"%lf",&hifactor);
112 break;
113 case 'V' :
114 sscanf(optarg,"%lf",&vrot);
115 break;
116 case 'U' :
117 sscanf(optarg,"%lf,%lf,%lf,%lf,%u",&h100,&om0,&ol0,&w0,&flat);
118 break;
119 case '2' :
120 facpolar = 1.0;
121 break;
122 case 'A' :
123 sscanf(optarg,"%lf",&lflux_agn);
124 break;
125 case 'h' :
126 default :
127 usage(); return -1;
128 }
129 }
130 if(optind>=narg) {usage(); return-1;}
131 sscanf(arg[optind],"%lf",&redshift);
132 if(redshift<=0.) {cout<<"Redshift "<<redshift<<" should be >0"<<endl; return -2;}
133
134 // --- Initialisation de la Cosmologie
135 cout<<"\nh100="<<h100<<" Om0="<<om0<<" Or0="<<or0<<" Or0="
136 <<or0<<" Ol0="<<ol0<<" w0="<<w0<<" flat="<<flat<<endl;
137 cout<<"\n--- Cosmology for z = "<<redshift<<endl;
138 CosmoCalc univ(flat,true,2.*redshift);
139 double perc=0.01,dzinc=redshift/100.,dzmax=dzinc*10.; unsigned short glorder=4;
140 univ.SetInteg(perc,dzinc,dzmax,glorder);
141 univ.SetDynParam(h100,om0,or0,ol0,w0);
142 univ.Print(0.);
143 univ.Print(redshift);
144
145 double dang = univ.Dang(redshift);
146 double dtrcom = univ.Dtrcom(redshift);
147 double dlum = univ.Dlum(redshift);
148 double dloscom = univ.Dloscom(redshift);
149 double dlosdz = univ.Dhubble()/univ.E(redshift);
150 cout<<"dang="<<dang<<" dlum="<<dlum<<" dtrcom="<<dtrcom
151 <<" dloscom="<<dloscom<<" dlosdz="<<dlosdz<<" Mpc"<<endl;
152
153 cout<<"\n1\" -> "<<dang*sec2rad(1.)<<" Mpc = "<<dtrcom*sec2rad(1.)<<" Mpc com"<<endl;
154 cout<<"1\' -> "<<dang*min2rad(1.)<<" Mpc = "<<dtrcom*min2rad(1.)<<" Mpc com"<<endl;
155 cout<<"1d -> "<<dang*deg2rad(1.)<<" Mpc = "<<dtrcom*deg2rad(1.)<<" Mpc com"<<endl;
156
157 cout<<"dz=1 -> "<<dlosdz<<" Mpc com"<<endl;
158
159 cout<<"1 Mpc los com -> dz = "<<1./dlosdz<<endl;
160 cout<<"1 Mpc transv com -> "<<rad2sec(1./dtrcom)<<"\" = "
161 <<rad2min(1./dtrcom)<<" \' = "<<rad2deg(1./dtrcom)<<" d"<<endl;
162
163 // --- Mise en forme dans les unites appropriees
164 if(adty<=0.) adty=adtx;
165 if(atylarg<=0.) atylarg=atxlarg;
166 if(inmpc) {
167 dx = adtx; txlarg = atxlarg; nx = int(txlarg/dx+0.5);
168 dy = adty; txlarg = atxlarg; ny = int(tylarg/dy+0.5);
169 dz = dred; tzlarg = redlarg; nz = int(tzlarg/dz+0.5);
170 adtx = dx/dtrcom; atxlarg = adtx*nx;
171 adty = dy/dtrcom; atylarg = adty*ny;
172 dred = dz/dlosdz; redlarg = dred*nz;
173 } else {
174 adtx = min2rad(adtx); atxlarg = deg2rad(atxlarg); nx = int(atxlarg/adtx+0.5);
175 adty = min2rad(adty); atylarg = deg2rad(atylarg); ny = int(atylarg/adty+0.5);
176 nz = int(redlarg/dred+0.5);
177 dx = adtx*dtrcom; txlarg = dx*nx;
178 dy = adty*dtrcom; tylarg = dy*ny;
179 dz = dred*dlosdz; tzlarg = dz*nz;
180 }
181 double Npix = (double)nx*(double)ny*(double)nz;
182
183 double redlim[2] = {redshift-redlarg/2.,redshift+redlarg/2.};
184 if(redlim[0]<=0.)
185 {cout<<"Lower redshift limit "<<redlim[0]<<" should be >0"<<endl; return -3;}
186 double dtrlim[2] = {univ.Dtrcom(redlim[0]),univ.Dtrcom(redlim[1])};
187 double loslim[2] = {univ.Dloscom(redlim[0]), univ.Dloscom(redlim[1])};
188 double dlumlim[2] = {univ.Dlum(redlim[0]),univ.Dlum(redlim[1])};
189
190 cout<<"\n---- Type de donnees: inmpc = "<<inmpc<<endl;
191 cout<<"---- Line of Sight: Redshift = "<<redshift<<endl
192 <<"dred = "<<dred<<" redlarg = "<<redlarg<<endl
193 <<" dz = "<<dz<<" Mpc redlarg = "<<tzlarg<<" Mpc, nz = "<<nz<<" pix"<<endl;
194 cout<<"---- Transverse X:"<<endl
195 <<"adtx = "<<rad2min(adtx)<<"\', atxlarg = "<<rad2deg(atxlarg)<<" d"<<endl
196 <<" dx = "<<dx<<" Mpc, txlarg = "<<txlarg<<" Mpc, nx = "<<nx<<" pix"<<endl;
197 cout<<"---- Transverse Y:"<<endl
198 <<"adty = "<<rad2min(adty)<<"\', atylarg = "<<rad2deg(atylarg)<<" d"<<endl
199 <<" dy = "<<dy<<" Mpc, tylarg = "<<tylarg<<" Mpc, ny = "<<ny<<" pix"<<endl;
200 cout<<"---- Npix total = "<<Npix<<" -> "<<Npix*sizeof(double)/1.e6<<" Mo"<<endl;
201
202 // --- Cosmolographie Transverse
203 cout<<"\n--- Transverse"<<endl;
204 cout<<"dang comoving = "<<dtrcom<<" Mpc (com) var_in_z ["
205 <<dtrlim[0]<<","<<dtrlim[1]<<"]"<<endl;
206
207 cout<<"... dx = "<<dx<<" Mpc (com), with angle "<<adtx*dtrcom<<endl
208 <<" with angle var_in_z ["<<adtx*dtrlim[0]<<","<<adtx*dtrlim[1]<<"]"<<endl;
209 cout<<"... largx = "<<txlarg<<" Mpc (com), with angle "<<atxlarg*dtrcom<<endl
210 <<" with angle var_in_z ["<<atxlarg*dtrlim[0]<<","<<atxlarg*dtrlim[1]<<"]"<<endl;
211
212 cout<<"... dy = "<<dy<<" Mpc (com), with angle "<<adty*dtrcom<<endl
213 <<" with angle var_in_z ["<<adty*dtrlim[0]<<","<<adty*dtrlim[1]<<"]"<<endl;
214 cout<<"... largy = "<<tylarg<<" Mpc (com), with angle "<<atylarg*dtrcom<<endl
215 <<" with angle var_in_z ["<<atylarg*dtrlim[0]<<","<<atylarg*dtrlim[1]<<"]"<<endl;
216
217 // --- Cosmolographie Line of sight
218 cout<<"\n--- Line of Sight"<<endl;
219 cout<<"los comoving distance = "<<dloscom<<" Mpc (com) in ["
220 <<loslim[0]<<","<<loslim[1]<<"]"<<endl
221 <<" diff = "
222 <<loslim[1]-loslim[0]<<" Mpc"<<endl;
223
224 cout<<"...dz = "<<dz<<" Mpc (com), with redshift approx "<<dred*dlosdz<<endl;
225 cout<<"...tzlarg = "<<tzlarg<<" Mpc (com), with redshift approx "<<redlarg*dlosdz<<endl;
226
227 // --- Solid Angle & Volume
228 cout<<"\n--- Solid angle"<<endl;
229 double angsol = AngSol(adtx/2.,adty/2.,M_PI/2.);
230 cout<<"Elementary solid angle = "<<angsol<<" sr = "<<angsol/(4.*M_PI)<<" *4Pi sr"<<endl;
231 double angsoltot = AngSol(atxlarg/2.,atylarg/2.,M_PI/2.);
232 cout<<"Total solid angle = "<<angsoltot<<" sr = "<<angsoltot/(4.*M_PI)<<" *4Pi sr"<<endl;
233
234 cout<<"\n--- Volume"<<endl;
235 double dvol = dx*dy*dz;
236 cout<<"Pixel volume comoving = "<<dvol<<" Mpc^3"<<endl;
237 double vol = univ.Vol4Pi(redlim[0],redlim[1])/(4.*M_PI)*angsoltot;
238 cout<<"Volume comoving = "<<vol<<" Mpc^3 = "<<vol/1.e9<<" Gpc^3"<<endl
239 <<"Pixel volume comoving = vol/Npix = "<<vol/Npix<<" Mpc^3"<<endl;
240
241 // --- Fourier space: k = omega = 2*Pi*Nu
242 cout<<"\n--- Fourier space"<<endl;
243 cout<<"Array size: nx = "<<nx<<", ny = "<<ny<<", nz = "<<nz<<endl;
244 double dk_x = 2.*M_PI/(nx*dx), knyq_x = M_PI/dx;
245 double dk_y = 2.*M_PI/(nx*dy), knyq_y = M_PI/dy;
246 double dk_z = 2.*M_PI/(nz*dz), knyq_z = M_PI/dz;
247 cout<<"Resolution: dk_x = "<<dk_x<<" Mpc^-1 (2Pi/dk_x="<<2.*M_PI/dk_x<<" Mpc)"<<endl
248 <<" dk_y = "<<dk_y<<" Mpc^-1 (2Pi/dk_y="<<2.*M_PI/dk_y<<" Mpc)"<<endl;
249 cout<<"Nyquist: kx = "<<knyq_x<<" Mpc^-1 (2Pi/knyq_x="<<2.*M_PI/knyq_x<<" Mpc)"<<endl
250 <<" ky = "<<knyq_y<<" Mpc^-1 (2Pi/knyq_y="<<2.*M_PI/knyq_y<<" Mpc)"<<endl;
251 cout<<"Resolution: dk_z = "<<dk_z<<" Mpc^-1 (2Pi/dk_z="<<2.*M_PI/dk_z<<" Mpc)"<<endl;
252 cout<<"Nyquist: kz = "<<knyq_z<<" Mpc^-1 (2Pi/knyq_z="<<2.*M_PI/knyq_z<<" Mpc)"<<endl;
253
254 // --- Masse de HI
255 cout<<"\n--- Mass HI"<<endl;
256 Schechter sch(nstar,mstar,alpha);
257 sch.SetOutValue(1);
258 cout<<"nstar= "<<nstar<<" mstar="<<mstar<<" alpha="<<alpha<<endl;
259 cout<<"mstar*sch(mstar) = "<<sch(mstar)<<" Msol/Mpc^3/Msol"<<endl;
260 int npt = 10000;
261 double lnx1=log10(1e-6), lnx2=log10(1e+14), dlnx=(lnx2-lnx1)/npt;
262 double masshimpc3 = IntegrateFuncLog(sch,lnx1,lnx2,0.001,dlnx,10.*dlnx,6);
263 cout<<"Mass density: "<<masshimpc3<<" Msol/Mpc^3"<<endl;
264
265 double masshipix = masshimpc3*dvol;
266 double masshitot = masshimpc3*vol;
267 cout<<"Pixel mass = "<<masshipix<<" Msol"<<endl
268 <<"Total mass in survey = "<<masshitot<<" Msol"<<endl;
269 if(mhiref<=0.) mhiref = masshipix;
270
271 // --- Survey values
272 double unplusz = 1.+redshift;
273 double nuhiz = Fr_HyperFin_Par / unplusz; // GHz
274 // dnu = NuHi/(1.+z0-dz/2) - NuHi/(1.+z0+dz/2)
275 // = NuHi*dz/(1.+z0)^2 * 1/[1-(dz/(2*(1+z0)))^2]
276 double dnuhiz = Fr_HyperFin_Par *dred/(unplusz*unplusz)
277 / (1.- (dred/.2/unplusz)*(dred/.2/unplusz));
278 cout<<"\n--- Observation:"<<endl
279 <<" surf_eff="<<surfeff<<" m^2, tobs="<<tobs<<" s"<<endl
280 <<" nu="<<nuhiz<<" GHz, dnu="<<dnuhiz*1.e3<<" Mhz"<<endl;
281 cout<<"dang lumi = "<<dlum<<" in ["<<dlumlim[0]<<","<<dlumlim[1]<<"] Mpc"<<endl;
282
283 double slobe = lobewidth/2.35482; // sigma du lobe en arcmin
284 double lobecyl = sqrt(8.)*slobe; // diametre du lobe cylindrique equiv en arcmin
285 double lobearea = M_PI*lobecyl*lobecyl/4.; // en arcmin^2 (hypothese lobe gaussien)
286 double nlobes = rad2min(adtx)*rad2min(adty)/lobearea;
287 if(lobewidth<=0.) nlobes = 1.;
288 cout<<"\nBeam FWHM = "<<lobewidth<<"\' -> sigma = "<<slobe<<"\' -> "
289 <<" Dcyl = "<<lobecyl<<"\' -> area = "<<lobearea<<" arcmin^2"<<endl;
290 cout<<"Number of beams in one transversal pixel = "<<nlobes<<endl;
291
292 // --- Power emitted by HI
293 cout<<"\n--- Power from HI for M = "<<mhiref<<" Msol at "<<nuhiz<<" GHz"<<endl;
294 cout<<"flux factor = "<<hifactor<<" at redshift = "<<redshift<<endl;
295
296 double fhi = hifactor*Msol2FluxHI(mhiref,dlum);
297 cout<<"FluxHI("<<dlum<<" Mpc) all polar:"<<endl
298 <<" Flux= "<<fhi<<" W/m^2 = "<<fhi/Jansky2Watt_cst<<" Jy.Hz"<<endl
299 <<" in ["<<hifactor*Msol2FluxHI(mhiref,dlumlim[0])
300 <<","<<hifactor*Msol2FluxHI(mhiref,dlumlim[1])<<"] W/m^2"<<endl;
301 double sfhi = fhi / (dnuhiz*1e9) / Jansky2Watt_cst;
302 cout<<"If spread over "<<dnuhiz<<" GHz, flux density = "<<sfhi<<" Jy"<<endl;
303
304 // --- Signal analysis
305 cout<<"\n--- Signal analysis"<<endl;
306 cout<<"Facteur polar = "<<facpolar<<endl;
307
308 PlanckSpectra planck(T_CMB_Par);
309 planck.SetApprox(1); // Rayleigh spectra
310 planck.SetVar(0); // frequency
311 planck.SetUnitOut(0); // output en W/....
312 planck.SetTypSpectra(0); // radiance W/m^2/Sr/Hz
313
314 // Signal
315 double psig = facpolar * fhi * surfeff;
316 double tsig = psig / k_Boltzman_Cst / (dnuhiz*1e9);
317 double ssig = psig / surfeff / (dnuhiz*1e9) / Jansky2Watt_cst;
318 cout<<"Signal("<<mhiref<<" Msol): P="<<psig<<" W"<<endl;
319 cout<<" flux density = "<<ssig<<" Jy (for Dnu="<<dnuhiz<<" GHz)"<<endl;
320 cout<<" Antenna temperature: tsig="<<tsig<<" K"<<endl;
321
322 // Elargissement doppler de la raie a 21cm: dNu = vrot/C * Nu(21cm) / (1+z)
323 double doplarge = vrot / SpeedOfLight_Cst * nuhiz;
324 cout<<" Doppler width="<<doplarge*1.e3<<" MHz for rotation width of "<<vrot<<" km/s"<<endl;
325 if(doplarge>dnuhiz) {
326 cout<<"Warning: doppler width "<<doplarge<<" GHz > "<<dnuhiz<<" GHz redshift bin width"<<endl;
327 }
328
329 // Synchrotron
330 double tsynch = Tsynch408;
331 if(fabs(indnu)>1.e-50) tsynch *= pow(nuhiz/nuhaslam,indnu);
332 planck.SetTemperature(tsynch);
333 double psynch = facpolar * planck(nuhiz*1.e+9) * surfeff * angsol * (dnuhiz*1e9);
334 double ssynch = psynch / surfeff / (dnuhiz*1e9) / Jansky2Watt_cst;
335 cout<<"Synchrotron: T="<<Tsynch408<<" K ("<<nuhaslam<<" GHz), "
336 <<tsynch<<" K ("<<nuhiz<<" GHz)"<<endl
337 <<" P="<<psynch<<" W"<<endl;
338 cout<<" flux density = "<<ssynch<<" Jy"<<endl;
339
340 // CMB
341 double tcmb = T_CMB_Par;
342 planck.SetTemperature(tcmb);
343 double pcmb = facpolar * planck(nuhiz*1.e+9) * surfeff * angsol * (dnuhiz*1e9);
344 double scmb = pcmb / surfeff / (dnuhiz*1.e+9) / Jansky2Watt_cst;
345 cout<<"CMB: T="<<tcmb<<" K -> P="<<pcmb<<" W"<<endl;
346 cout<<" flux density = "<<scmb<<" Jy"<<endl;
347
348 // AGN
349 double flux_agn = pow(10.,lflux_agn);
350 cout<<"AGN: log10(S_agn)="<<lflux_agn<<" -> S_agn="<<flux_agn<<" Jy"<<endl;
351 double flux_agn_pix = flux_agn*(dnuhiz*1e9);
352 double mass_agn_pix = FluxHI2Msol(flux_agn_pix*Jansky2Watt_cst,dlum);
353 double lmass_agn_pix = log10(mass_agn_pix);
354 cout<<"...pixel: f="<<flux_agn_pix<<" 10^-26 W/m^2"
355 <<" -> "<<mass_agn_pix<<" Msol -> log10 = "<<lmass_agn_pix<<endl;
356
357 // --- Noise analysis
358 cout<<"\n--- Noise analysis"<<endl;
359 double psys = k_Boltzman_Cst * Tsys * (dnuhiz*1.e+9);
360 cout<<"Noise: T="<<Tsys<<" K, P="<<psys<<" W (for Dnu="<<dnuhiz<<" GHz)"<<endl;
361
362 double slim = 2. * k_Boltzman_Cst * Tsys / surfeff
363 / sqrt(2.*(dnuhiz*1.e+9)*tobs) /Jansky2Watt_cst;
364 cout<<"Observation flux density limit: "<<slim<<" Jy (in 1 lobe)"<<endl;
365
366 slim = slim * sqrt(nlobes);
367 cout<<"Observation flux density limit: "<<slim<<" Jy (in "<<nlobes<<" lobes)"<<endl;
368
369 double SsN = ssig/slim;
370 cout<<"\nSignal to noise ratio = "<<SsN<<endl;
371
372 double smass = mhiref/ssig*slim;
373 cout<<"\nSigma noise equivalent = "<<smass<<" Msol"<<endl;
374
375 return 0;
376}
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