47,123,518,431,753,987,304,619,414,989,870,839,333,373,283,648,159,849,892,425,783,829,511,978,540,222,360,112,588,473,386,531,352,644,713,883,067,370,116,642,148,454,726,326,166,078,509,992,620,920,917,425,621,739,981,839,782,539,923,764,794,363,631,215,686,153,514,790,629,434,424,809,140,825,012,668,570,822,474,119,116,135,486,036,723,491,427,358,844,157,958,736,845,894,293,746,475,649,516,292,661,757,665,192,288,362,873,244,351,363,255,648,431,205,329,418,671,287,661,410,261,500,481,636,840,698,676,873,191,720,162,594,534,663,970,453,362,666,201,371,400,791,859,445,820,576,351,265,980,886,600,678,294,269,247,366,329,812,645,324,984,688,854,532,855,762,043,952,595,265,729,086,061,967,514,420,235,821,329,914,599,619,215,370,112,105,542,191,064,555,590,850,041,905,772,335,638,069,835,021,818,262,511,417,913,319,224,182,598,651,894,811,164,365,234,797,554,669,152,363,932,529,615,075,832,627,452,148,819,047,613,649,435,964,611,616,959,159,067,274,154,384,310,753,816,514,194,468,546,820,194,261,194,755,035,453,203,149,990,722,849,643,090,623,040,592,951,117,851,348,226,905,274,574,777,643,439,755,825,833,848,507,641,693,171,797,586,195,137,575,422,994,770,033,392,354,786,856,674,297,817,375,296,525,275,914,213,220,562,351,315,373,255,971,132,359,039,258,942,832,844,843,185,154,961,704,647,941,451,048,907,096,577,481,449,823,876,898,739,333,741,211,801,864,196,011,397,838,272,503,891,221,002,063,675,225,669,695,828,473,508,524,791,211,544,113,388,908,165,707,154,192,105,820,222,410,868,006,990,889,567,988,782,801,033,168,723,883,022,265,490,715,283,308,826,064,380,777,827,659,884,165,762,817,967,204,796,924,400,308,329,185,559,595,098,355,489,575,558,682,369,836,293,499,245,880,453,813,634,348,663,622,655,094,524,938,165,256,665,158,249,658,802,479,230,668,416,437,298,128,597,361,806,460,062,145,935,918,999,264,046,220,182,492,873,532,480,969,579,919,132,825,151,139,596,717,105,380,688,632,013,046,859,222,168,046,212,474,143,578,977,378,785,996,372,978,542,259,098,851,191,479,491,200,284,965,465,330,234,339,335,086,003,404,856,824,707,421,540,619,684,118,200,490,658,105,358,875,550,684,363,229,773,379,757,447,994,436,459,121,453,978,807,192,002,214,748,225,226,493,674,880,076,427,086,391,000,914,560,042,751,655,895,558,425,892,522,346,171,151,964,195,069,565,998,587,806,873,151,001,905,480,823,667,942,446,773,251,681,693,291,416,965,144,801,433,305,458,380,999,627,240,648,646,672,956,325,070,477,240,661,314,986,791,033,564,956,929,590,953,020,108,046,575,766,270,104,352,248,086,924,767,001,756,703,762,277,508,854,123,816,894,044,342,586,370,651,038,582,110,590,264,308,899,969,942,248,285,426,374,935,298,973,774,673,366,796,730,920,952,921,069,662,028,951,704,341,852,594,770,664,921,170,809,653,100,666,820,346,244,153,358,919,257,430,678,629,145,835,992,560,984,130,620,591,381,193,279,054,683,117,339,381,013,742,100,670,709,620,217,139,962,997,328,923,865,258,308,281,498,064,943,704,248,952,381,763,152,395,234,859,715,705,857,572,704,411,683,508,789,728,249,625,723,804,644,703,526,015,583,108,503,085,446,945,111,600,510,132,456,101,423,940,470,639,966,408,533,058,386,159,249,194,883,759,810,825,162,733,536,421,813,961,032,258,679,154,174,314,737,413,426,784,967,362,845,345,729,333,223,859,401,986,822,935,837,597,356,356,045,414,429,845,090,166,402,438,147,373,712,171,937,296,340,535,148,759,342,775,335,351,374,767,987,056,252,771,461,205,213,138,304,592,316,236,415,039,674,432,767,873,518,883,478,620,730,056,317,563,105,676,601,493,306,432,912,393,966,900,570,965,654,415,346,813,207,082,489,069,250,861,083,197,980,751,160,750,828,000,379,266,488,928,969,939,539,874,545,930,772,496,110,832,825,181,169,131,226,625,884,382,562,920,963,740,890,293,833,491,134,952,122,931,981,301,953,433,575,051,337,976,652,429,002,478,864,430,294,250,218,046,144,267,089,164,035,904,595,201,723,104,627,833,414,616,135,482,120,039,433,359,005,081,363,402,579,138,058,225,158,591,880,308,220,250,608,048,396,259,801,895,091,003,199,795,006,625,163,729,347,433,161,121,678,006,990,116,914,998,372,972,610,376,504,903,399,493,683,893,505,789,561,742,983,775,393,055,423,759,358,616,466,696,795,159,049,039,917,409,440,279,364,169,341,644,400,168,541,838,138,335,412,497,348,817,231,679,261,861,235,899,512,557,540,851,238,403,960,273,733,734,173,088,262,229,192,804,655,202,338,704,665,947,980,257,981,212,368,053,898,932,216,255,624,170,351,324,933,487,692,426,515,836,505,779,250,422,370,302,576,231,918,691,965,399,736,662,192,766,981,377,532,390,696,939,035,923,521,240,593,246,356,216,231,061,115,913,501,860,298,067,790,919,419,547,273,186,176,435,399,854,935,243,919,562,172,556,629,030,268,021,198,964,230,122,647,836,681,394,463,235,288,472,145,758,713,201,260,072,516,825,886,494,226,691,032,698,124,147,617,953,600,306,183,816,937,478,264,738,180,880,990,763,119,196,617,168,582,122,427,768,781,583,274,852,699,154,217,310,768,457,893,673,108,582,644,159,993,466,695,972,581,359,103,386,921,034,688,076,543,017,644,757,609,582,793,550,411,796,006,494,336,685,027,963,833,816,812,905,549,249,916,739,612,857,359,760,410,976,263,495,550,846,324,522,478,649,584,221,910,386,173,112,087,455,750,685,916,841,516,592,500,384,076,134,506,837,646,061,258,624,788,263,537,124,582,447,692,242,890,484,626,721,696,536,402,352,292,655,585,947,471,255,655,111,770,323,601,321,605,322,812,039,203,232,821,637,281,453,039,811,072,452,923,156,995,642,542,163,126,166,368,627,690,995,781,750,516,960,525,735,343,510,592,376,155,225,361,354,333,379,699,624,815,928,501,859,906,124,604,079,055,588,108,671,852,831,921,023,510,423,330,767,507,168,338,080,116,564,421,596,431,780,585,099,242,495,858,240,474,086,824,452,233,587,359,510,170,959,540,760,828,685,189,909,594,635,337,909,032,010,893,749,281,776,275,706,443,164,307,596,229,617,144,475,657,415,630,269,870,492,988,256,232,251,720,095,191,694,912,454,904,124,469,168,850,809,702,865,691,694,132,991,647,067,462,903,130,707,169,414,746,873,096,026,306,873,434,015,840,352,351,284,555,723,806,469,222,610,383,205,131,284,849,533,850,463,315,911,801,709,461,569,299,040,273,084,621,785,894,084,426,427,387,802,227,991,665,691,092,738,694,085,737,238,885,376,130,336,976,263,071,766,557,336,563,432,514,330,433,389,029,354,440,482,138,041,533,675,704,996,455,163,877,484,957,492,393,702,046,216,713,005,801,883,199,250,674,264,987,080,827,854,073,979,445,583,906,352,248,433,757,634,166,124,055,245,722,061,319,876,805,539,777,666,152,180,464,141,001,960,875,859,158,606,990,139,724,613,794,667,726,307,549,459,951,365,240,939,670,160,522,251,928,942,335,502,888,129,554,335,692,663,261,386,396,955,540,607,060,150,582,948,874,510,482,513,763,180,511,924,770,179,447,244,322,862,666,482,999,788,563,516,864,821,657,983,407,478,989,068,003,545,141,066,791,381,308,241,689,803,217,715,966,380,320,298,856,925,424,063,852,956,646,383,393,560,780,685,934,319,077,879,713,609,389,273,146,581,007,649,084,067,286,731,592,256,096,209,105,310,736,295,969,521,514,094,269,215,483,225,757,683,040,218,196,373,779,666,760,208,942,132,211,295,928,045,653,382,113,563,273,632,818,979,482,140,317,634,470,585,313,158,098,261,049,615,420,946,301,168,451,642,515,488,942,287,607,113,515,945,655,867,705,070,107,151,927,847,398,783,082,071,264,318,666,462,863,541,211,954,567,819,696,520,758,317,986,652,415,424,825,984,693,214,271,804,009,192,157,028,663,796,215,504,805,616,483,690,632,408,927,461,928,449,950,875,322,282,312,449,678,018,872,689,122,526,092,781,297,622,056,417,148,682,103,156,200,307,959,544,246,769,005,638,709,086,355,146,875,409,101,401,407,906,825,525,452,125,623,132,866,209,020,948,555,928,567,904,381,572,708,107,923,879,249,932,103,488,467,397,266,537,571,232,931,846,392,277,779,788,947,568,292,846,068,219,474,274,903,340,063,959,526,876,125,890,392,572,769,937,811,604,065,579,065,748,437,932,386,690,868,337,133,040,234,217,908,116,225,049,969,069,433,028,006,477,767,193,898,742,292,463,986,194,750,949,713,818,673,963,090,045,183,073,300,783,313,675,561,363,037,128,416,441,354,256,529,490,876,998,419,370,573,735,103,389,871,814,223,266,366,470,989,541,244,818,305,395,390,023,668,568,269,582,502,576,280,088,187,853,529,016,425,349,149,663,306,685,383,963,712,063,316,842,765,705,505,653,966,021,298,795,485,390,640,818,660,916,434,271,383,654,149,871,739,791,514,266,024,259,543,952,716,500,975,624,491,697,908,319,899,187,544,052,267,814,503,230,252,193,542,413,356,386,650,055,110,442,904,546,565,094,044,545,295,984,308,135,499,128,471,457,990,948,015,982,493,504,466,048,777,307,597,478,462,291,846,764,392,887,880,487,478,444,508,219,482,812,397,417,276,389,722,867,381,567,680,974,900,373,860,499,067,385,843,579,430,775,847,925,742,383,564,044,102,924,983,458,738,700,084,211,707,520,410,404,136,056,568,922,356,124,396,474,973,301,267,764,657,805,989,947,772,404,452,992,206,485,205,679,201,756,423,922,169,717,484,615,971,433,142,937,509,193,555,408,864,769,422,321,539,400,168,894,915,373,613,451,045,728,809,506,291,207,647,494,222,058,850,007,735,860,489,832,317,904,024,521,013,224,698,152,329,522,939,897,791,301,105,305,092,552,181,218,080,532,726,190,194,530,684,905,149,538,535,461,000,932,456,950,850,181,859,603,835,153,257,601,532,969,012,788,435,793,322,875,652,902,423,190,119,480,926,582,119,036,450,570,413,979,654,518,946,605,351,166,814,564,865,345,881,242,931,487,595,651,768,648,230,772,196,339,222,215,357,006,893,344,807,257,232,050,910,176,555,859,369,799,862,165,167,536,931,633,395,192,653,366,222,676,887,147,358,548,433,054,119,116,256,037,574,454,318,642,919,166,742,309,640,013,450,254,213,737,429,776,978,012,485,671,002,093,330,403,025,843,818,311,091,966,961,553,230,449,067,170,063,915,850,965,593,750,561,330,933,000,800,707,271,833,240,606,704,212,191,802,017,675,240,152,027,466,859,406,836,852,273,863,393,109,888,602,362,919,370,047,881,369,351,925,488,447,398,861,223,987,533,904,481,291,559,344,488,353,028,725,698,549,862,050,447,976,718,609,454,193,508,275,382,418,481,249,668,275,200,407,415,271,575,480,573,796,486,482,120,999,338,742,993,736,725,067,541,312,934,711,673,505,103,081,915,034,759,610,553,509,703,265,201,712,172,884,017,369,375,893,495,120,209,613,078,775,140,139,906,870,941,847,828,854,241,288,673,356,050,052,951,582,359,513,372,016,445,055,753,015,062,415,216,171,056,284,880,244,158,530,133,469,910,174,101,838,728,647,055,492,844,806,894,763,484,972,215,643,833,961,479,406,395,627,721,388,255,550,470,471,946,144,469,624,076,746,498,180,838,739,104,242,888,703,248,904,048,982,525,827,410,116,873,940,634,640,011,355,053,533,561,885,231,746,023,681,332,245,325,370,907,233,575,032,042,140,803,227,876,962,125,661,942,662,085,663,559,203,007,461,129,581,293,932,761,375,272,379,062,124,498,624,335,630,829,055,263,998,022,026,532,078,730,887,658,924,414,570,670,404,938,343,210,473,876,159,822,159,794,702,824,558,744,711,774,558,663,610,885,827,589,191,387,452,906,692,115,051,844,326,796,786,765,277,953,603,959,687,759,434,745,115,049,708,427,914,706,388,478,886,551,959,655,477,649,373,327,501,127,495,800,719,830,683,715,215,025,906,660,960,042,087,639,114,603,928,045,638,727,040,313,326,813,333,600,178,293,405,679,537,087,681,223,203,858,941,085,841,765,772,113,930,833,836,248,375,095,140,525,999,621,177,509,741,209,194,804,002,855,712,357,216,147,377,321,168,527,590,496,235,941,256,520,094,359,004,512,269,726,079,148,787,467,647,946,749,435,093,349,346,901,492,097,335,098,143,042,479,987,579,354,154,532,934,066,238,763,130,489,214,295,273,384,236,520,067,765,474,000,543,029,936,775,797,198,087,266,924,574,522,109,992,997,873,769,264,218,370,276,674,765,419,969,963,205,731,786,775,584,795,820,238,401,349,308,985,436,831,212,373,475,834,314,794,785,198,147,079,213,002,656,813,946,273,580,891,648,127,406,339,963,277,304,578,790,179,448,240,949,379,946,043,469,015,818,258,751,978,378,639,412,896,058,308,458,594,063,710,421,030,739,339,369,424,527,270,428,350,001,029,905,360,970,761,117,351,219,988,887,863,200,489,247,786,262,890,536,633,231,348,868,369,994,652,989,580,422,627,316,983,256,686,030,454,474,265,466,258,163,295,189,848,104,595,937,918,212,645,788,899,975,128,816,797,618,137,119,507,154,028,538,760,150,644,089,804,873,972,062,223,556,911,890,988,711,701,976,112,585,197,062,447,903,056,693,156,308,980,591,822,007,114,386,846,094,762,937,933,572,674,801,517,827,581,240,033,323,427,444,278,621,063,710,184,920,952,966,380,422,233,915,659,464,247,849,028,011,227,903,298,354,140,271,836,230,102,983,281,270,372,783,123,681,062,056,768,512,498,787,923,826,678,452,401,530,706,138,110,026,863,639,521,331,829,016,604,654,158,485,998,542,566,855,038,873,258,042,665,925,558,179,730,400,959,767,689,878,866,303,779,228,139,528,810,373,848,364,156,169,228,108,259,745,030,391,176,252,733,786,670,811,203,338,779,009,411,991,404,950,143,780,971,737,325,956,024,253,483,981,360,408,986,407,425,635,651,612,323,320,628,475,406,278,793,285,354,514,856,031,254,905,259,273,831,191,965,136,571,735,920,870,116,012,368,414,322,398,251,587,930,485,690,139,850,481,830,998,946,916,601,846,247,235,477,456,178,226,379,155,814,851,240,593,871,025.490257949828841472
$ 150909293931468259530264304735674973069848282807132958671779095261923101850046590417639972601198217250681801645308245144681356304892895180785938723395234129484351519300776730531949476266094680778205897021814783878262422939604078762192838784497169179052290492924948735012242727638680878719071642118544055168110990109653512584885572349699660461628492433745477969255476782020351710983877139682141965850655555135500929838201786006937832028234894490255319198019268476514851112114898091007783028119802687486999170710429591719662619605686672406052497671806006580939538488319580480907312444762434364746526674865263481763269271429456653270040370630740147149591253836814107059929016698174154037840185495003090231645818511115987216329873778042964137906591649344767794835529773701144846233933325401202231109796447688569294990301234102273093250324508051379296464602702787982891968755350950383084600987454455860341306317299826265073638100971832141230367856826732756027642710969703470721050508269243913796970551218858270793636327556985486455531620049918712998566162049244225902471872228296889207441525130750205334530916186312216646137556683876289274567119880386150879528228207209910093116317072280060987951012795836801583100686196271090177922941415484680508562556538178215010341576509679146414057576201390895484174528076811176837221193345398268948060277631338958674370111304663826851540016156741877083703677287014810118839002399178055117253899909967647594637968434288579077866417701421197850443821909805317977912302279383743131010204909700910999830650634451226552478734796920861392338849869115648042380255893324077444202612401053486805494498577148009360314916173829781382243531032449437549317759806601640549282377991839460692637818936917084390589717027810957705241623576828190051607397775862634833476470362511255261894696997957417427069780775237857818554364178614605921768887041008414642839424239653727200045711482389965427196653771337720114764192659249783263902049649171158211282207882436882862661703459154152518587054759497818645722366871781316439463928433799821920716212455081580167751408095157875958377872172514466721161127289064870399313717314013568102430616817474972375518692600114174458922828794715838933576650682034806040373943873652683847973269888688082933510181043064611665281441830464751876151849829782487466730797260094439706068894549922605176894122974939204140991297622420787019900231616595886090665610703652130470855444683250181506528492842126972536129977305363534867404779996412025251267495221605336878231992025093710115128118433405367847696385209377250673578698539487675528481960132651903470316764766223199770927840403017233358265788099792036140968663780993894649582689071423743391979497464669283821867827168340991795890015325501951216742453876532259647673008850959291116167234786813892984448226139636874581386134646253761808039998423797210320602310291685623966713864542268851825820788731727462632729162518446321911963553940487950672462352890206400470926540050521800189089214761891423648496166097849603842756841893470612171381331094882521493417079229149153789108318198264092026643156085394185028223482191704723660654176716308671844704420025362471809065751135926381587706736301687721728968952978997000352079152755262025325147782932142358435479405502545812325584415571839610878422579992616757487614205915491387062599841693076253350711388080846583971983023895255725046455595510707348139906241578163993422962462644752464871469566062408084374250614641546057936183509745633413219755133285726090568622680609171769591258355475711240527342838624113016787596453106680384797037820782319404798770158777765103084287434518718987860705448702481971428180567835255298844340390421277850911074337757914540925648047220480772215953014759657469885927515217548937444673547286385107689713215112012251228918036396337167787650142106434902063345268384346171579392462566664446329088789246807420766505293206371873250558819670227843227723375149698888334400140796600532162929044593938169734311344130307488006221801262597307387564319549682272581181387998891400547586718147650252847501314627045042897885614140723320384050971057524041365273970385345829818322735909168923687296980575761494609771861341510261859023478467572840140805430197900433551464328349257990068920319104553498054890527892015326408779540593190598021370291348438766318211246826086317618721295669871721006754523680027371433031534206457301338848360390570343058156234053899333840175039955210596256778893641675155707492710729250807082383696125503885549907663872107035922942399096212533587894309480198683942616775644964053594403054818731667401747691439569810228143319079833038361443813269399529434881697361824698583847521819037402523678880709965445366314947882237353330102877583173100475243017531684560590964720871035629644392007824500889913470486688198650767007689609176810237209254715887482271747434563236517111352115290608944275932895026433913111560250242507231564074066657445754149586075509993457194992073811760485025004142876013168531103608404180787542019960672250164770091539924380817137405798798409754636946159120682490291146863924856341936984724711803268500618476652809849528535504774175430898236057613080768854161044676417609890811873596576523781473394906558817815046304894147116244583185396931747914574041756215617845741505387483237276672640072045216811280545241917498920216702921668749913787204507468842253818926841056245393860665509718544366607283683297929579761269670449844830933691079046558716664181503682593543040291302377856015118454914447671517458532985478470589702074716046375087081658198656830240857943900357271171269255236662417086684770255578609848030159495028362081228351653222134965221462338012434177324744832024718973187546643590167416425563204645667875071145101808981881169964332634124117879724850399778709991314780623527906743019613217062831949375340787043746576897326831215650008248643106943505261629157698840416823660016140801402980926329893328263531839595884859027507256773533898906997579245441107629434493007830229460954762570261904160679315839455758743015034020343288611366216692700894801155791194755937042481712785919346208275102731076013247085916858417905992539487666110762333708747515122645921345313001370733686014693070960481176680021550139828770292323455301510947402884147860615051855261460301626134986433172519885177910186749703360476853633058073879678624499340724494089410923455309190232870240751747202256154122328534309455256711645283960610525919732218130670719860126889861087755141216339779042928037757877900157552609545908440184552027573129071621587262539917910021723032267156410010676479058568800274137448569202771426287574262471911922607827407050467135248657823392916456921582194916313902540636613029115729271341053334435427199845535705285985387421631816571514254892851319480341607754060202148624509892040527962797792583307978515858782099699679473434521895915748965953125150323891967256132161621181069883475065403884841891291984221443077940602100972418111428203527420612836696770354976601342019383007092376672700713580579097869677684938005343432760796516251194128765937369174684443782058728922944071731059436928662426426710442056829733049902537547613981029456721779694690129785145102690283021231081676529657350970254055859979112391546828805611841401075304747156202089775268193860879578406530024337953641254831450996785504438536376252417742285184562921939862919914436212614925384877390814842504808200965387610841895945134165188155285547372861631512864153021933891724582478757444652631465995626592366157540682184438055305853361578836865913062220197217330296046362903464433607121795117700478456724126204270642232502196304866230926965714054164247075823565339162089629511715580308000149036146792150264324689678336303699890314570519162989446046646348940694006661173384323829756202636815012378873399027113362785342746314370033973311715779111345883401886660936632041658654312710450457904230864813238463088874338812239180921080203890391219525660377724309937742185550869579442545822269074782161833937763424164734427813343589697027894782027048831875159780453805819556365208112135712468836828075090981938872001561582848593368936514248770229092322812231990493902433282381624464697589174317301468808012926569775156835611596981105758165130997438004503189985187715121401192632072701599110665249992077499470099583220198170293091286386048964078487969438880656551310782142419042228374831788634587725354392271429479404182054744283869581815508595250592035869287576085322646511138195685907546870011891113987727502716160407209261473607888136014262234743265187258058878329070707640991326221169054185083720592711840524348823086924649157173395999714626082785276930179992845840083041551926753271440972694133822041205637478238838632710290637969402113208142565792201140469152514397195734473129200238470945752819073408482773186473977843843143536227997384817042624327508671273191517605889190684218799660459846668695779874535216397665316136299617429271128432152484251789370857125512988283424618950083016240361561465038350855117557925369141421811895999353282556004822335186023220503052299497325005231073148809953709246184243541529839296933131516023608883595721828796400422112412394149297490062390316142927594863950518391004517818970379543851168853182269792098911278932150372289342336286909685266500817750027282292076468178959985679232244064630420699802356688490818725710921140845022290111491206736352603804665325006017401530612157822728592610418921558538914480774972743882724658295079853695199434708872325486729046547218914614790563293582359684947934844241330480017274816362842432340482687736474079943010730210772620444426103831725880031742949443115205945988101300498475696589442066952004856873096684130527850691095595858926385962719761765979071060018630110855336756358440406827761502189046683079916433319956262448171506699631006375665126744696696907.12
