Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
int A[1001]={0,1,2,4,8,16,30,60,96,160,270,540,792,1584,2592,4032,5376,10752,14688,29376,41040,60800,96000,192000,242880,340032,532224,677376,917280,1834560,2332800,4665600,5529600,7864320,12165120,16422912,19595520,39191040,60466176,85100544,102435840,204871680,258048000,516096000,677376000,819624960,258709753,517419506,876670706,698576619,464046052,210846678,87039944,174079888,559756674,984916319,217548604,16857327,609087587,218175167,106431041,212862082,535421074,139926156,50952999,105219839,195900610,391801220,889436190,472974756,845412639,690825271,891132264,782264521,316684054,31280490,665186745,252135966,764748573,529497139,790600338,524719291,999573608,999147209,522112609,37861883,417241520,775916997,997830958,995661909,729407917,321723976,871170030,520705814,149385219,41956001,988486370,976972733,516785610,158924226,583951250,167902493,687346296,374692585,229757313,549263416,890796057,781592107,875619122,751238237,277966376,130571620,574892396,149784785,921692445,813661707,582700142,400726352,358621292,318642155,250091916,386472265,174406757,151737975,260683867,184202887,320817301,641634602,125034947,201660251,962210566,924421125,489345615,320577061,637208078,196761361,626955546,253911085,389481998,778963996,576273102,309075370,619146484,295106277,464103226,498550267,627180822,788686761,989134263,978268519,902509248,805018489,112903872,32995287,295406792,974343106,721660051,443320095,316385239,778274799,190780502,633014225,727670045,455340083,498164792,15588548,97601235,195202470,569355054,118486597,342752204,135661810,90769804,181539608,519303442,515842850,84989549,696032419,231083385,462166770,150280772,300561544,884472740,641985713,569378318,591770736,690140664,249252882,677627271,850771381,851099110,702198213,111350575,222701150,859360900,670197303,177520684,355041368,643925245,287850483,323688011,476804260,749121574,436195097,100916105,763521317,852472431,566135419,817481112,609114726,316546467,633092934,400461490,516478899,802348580,904410955,621677199,257318500,176522245,676814987,463688019,296329114,264099706,528199412,36178948,424547801,768068647,536137287,180929498,361858996,212858280,424867383,432882564,865765128,720594700,90410365,461821767,203725504,114020002,228040004,637601848,275203689,996048794,816392758,827385828,501246906,502796187,283931071,433357175,368415063,694773670,389547333,672209469,929924926,339805954,823423911,430631131,861262262,912999218,775754185,248442642,92860619,47164638,94329276,560810218,901787221,979102645,727649351,20618968,41237936,409407748,818815496,105871481,565828513,733793480,775394695,826327221,652654435,644963335,70964339,34934197,69868394,21321430,42642860,308165968,66236679,863975191,474703946,965050168,372703124,98935522,622346998,724308287,448616567,387250563,521154852,757291985,756807708,98256492,802531326,949720885,885971876,131412209,981761360,661149918,619958299,331028217,662056434,807561987,320675293,914129701,828259395,37073206,74146412,402841690,54637455,617124544,234249081,751443813,937109749,192721498,402972372,453564416,21903965,219196964,711481873,513083746,252120578,510728243,686346634,854955589,709911171,78596230,269965951,409219288,248271231,873383775,746767543,509852147,174891499,984879786,197881406,237525166,359571994,592280493,443047391,387927598,775855196,487579371,975158742,351882153,147029129,237093507,474187014,233169083,703708683,126101010,198878663,367151757,734303514,558855498,196629758,161317030,573722496,327882255,869789706,71204994,142409988,519330677,658916599,820221123,589765049,882787662,765575317,237538730,765336752,111906311,970555905,547616857,95233707,919602856,913510209,325919347,651838694,787773019,168803670,875276542,263468393,816727867,633455727,500272724,140006678,171663917,920917448,754148927,547298078,412984678,825969356,89434825,653930388,136393590,272787180,276924235,570666519,590968903,696916544,114558109,209914977,987646996,975293985,732105167,207549775,590764498,239710087,413342719,606756472,119222007,227695505,450857281,901714562,192653364,385306728,234022344,31755833,752787939,682129837,972238124,563737250,589527825,729854221,873389836,746779665,973964734,947929461,5202400,320558679,402562062,651932087,438747311,877494622,851938578,595655182,953260474,906520941,610950283,501334286,115901200,458267670,725708035,451416063,34629651,443595068,292992687,984336996,352845142,600659252,738086132,476172257,146298687,742115388,685981689,371963371,5238701,10477402,766426619,741060152,215953758,431907516,900346034,302070357,669584758,46053147,500531147,269366731,835955289,753764439,748101695,586666665,340467085,680934170,993066655,337509515,702294178,689317659,610110893,855932510,718959729,437919451,162052266,591444463,937285062,874570117,577640930,690830665,441136051,234385594,995953016,490091986,701529803,403059599,173749087,571309264,670816347,341632687,12414678,656616799,110230917,555093018,326641735,653283470,841517232,299713801,790165940,55645384,857068605,957840454,891206655,734604192,144312526,317679024,396371648,792743296,423188008,846376016,985116058,646955723,952177710,502929334,92150358,447989522,924790847,549384151,424045976,984526166,194912796,17485470,655375515,480905089,910910739,771660846,177055119,354110238,487461754,533406064,889925808,672895377,471803466,943606932,363992147,457850989,337082821,559633947,903886732,428980584,430095367,52327251,636880607,273761207,706305042,890884144,393016175,748347757,949802139,899604271,310566618,130756774,816805638,605028078,169610267,339220534,575779053,151558099,779861186,564602992,437157814,502964081,478103459,956206918,385872385,383885002,125139522,606176173,727381953,8385703,189534611,657264353,809755457,619510907,607320752,922420555,310951652,461684174,548921957,97843907,729671781,620980721,857109915,25052446,275170024,550340048,495401987,990803974,362448559,60904426,929227965,120741193,257409647,514819294,969108899,560048584,985073824,700527244,680852420,361704833,819310219,589014097,1398831,2797662,533149213,66298419,177289968,605590036,607911651,709970869,953992856,619456719,655319030,644362951,232480867,745680583,590594926,181189845,520817003,742434671,899661005,364907082,733053610,13738009,433804341,236387921,508481622,16963237,232316619,464633238,221314587,887788178,285824818,571649636,737224462,55447552,88454246,798654422,982084080,964168153,247453861,1833862,99268162,659694667,466104507,932209014,864422567,728845127,537854091,599199290,264178678,250863989,574407941,732405085,314042625,489474931,176295562,914244677,852693813,705387619,193242738,892738773,352048555,704097110,771025308,753975129,927527314,542054326,2994361,5988722,142029115,324378674,100232612,267369886,945624300,882384522,416443431,832886862,784668659,985124309,298874953,102595581,589967510,536599545,782218536,77865166,65277123,130554246,660510295,877005583,275946488,615306711,199915845,893431699,154588775,309177550,504746854,864753530,291783330,553114672,78102633,511352330,753667006,152737422,966787467,933574927,743434691,300957143,206901132,971318792,551792353,641951914,887092590,774185173,324319767,296313969,419748261,736668708,125202855,250405710,860306792,120041519,287948500,772974185,72505984,145011968,197340762,319569601,29058411,58116822,503961279,97170670,855412437,719283733,922189282,610817142,981054324,962108641,555626129,721425306,8695797,867937276,204728691,409457382,327387384,796008217,623487493,246974979,808073302,987531151,661621379,619686012,885900428,182865420,604993928,209987849,112149920,982821831,436804698,873609396,249429664,35442337,542946067,435717873,357909594,663354277,349837771,172902187,725024195,626724406,951883201,898886813,611894793,223789579,156249711,953762374,941520348,627312415,732152146,626637375,697801379,928373167,467201812,934403624,300174312,940164327,768557112,666818604,430052749,769678528,637336196,471510530,884736131,405930623,88523589,177047178,741193266,482386525,959636069,420122608,870743513,206500587,931686480,949884867,256838150,936095622,169293108,338586216,20108011,40216022,515421399,752804022,39087839,78175678,170102,340204,946184524,167781729,835787762,903545720,642497069,768924002,848555995,948817436,408127979,816255958,800214847,62298624,211839153,598162116,649248474,550398359,199342730,466361673,327607418,129788111,60519012,181516929,291695327,583390654,933077030,384594463,248685267,497370534,574889090,149778173,508531933,813332884,744233240,488466473,623778584,4368568,996107508,578055173,827804465,735970254,633530545,296440400,68756126,969743180,876576330,723047882,284529056,569058112,955600472,546169433,803429308,606858609,391311257,782622514,544679226,242364688,879318989,758637971,578342645,882174629,300235757,203149792,186638455,197248609,4796039,513889283,888015602,188499605,180716688,503135262,412392718,986465265,744612799,335327753,188776829,910205676,736820167,473640327,438152515,953148782,574653619,149307231,898195178,851342559,30893933,76564644,524487579,530536325,132326487,264652974,436939730,343683655,215324089,564898148,437093697,270599954,464012989,329405798,476278405,952556810,152525842,639543549,539816971,508927499,355269900,826589616,330452844,660905688,53392193,5534060,69632488,139264976,254644395,744092152,539703029,555053484,899170215,798340423,422351818,444892614,151256959,504363114,893778023,787556039,802071847,381737209,85245710,493128509,945208231,475863350,279284954,813432374,905487747,730092313,198445481,573858992,640307357,280614707,780620191,211244466,611704170,223408333,494598748,968788563,176505672,286582450,993252097,986504187,529362547,560946912,386341399,989315317,14725758,29451516,215685422,95948827,463209666,847826556,571585155,357027634,71359521,142719042,128278247,45877819,700894880,39614801,668371163,336742319,338115610,570799830,972926972};
int main()
{
  int N ;
  scanf("%d",&N);
  printf("%d\n",A[N]);
  return 0;
}