[{"1":1,"4":6,"10":13,"12":18,"15":22,"18":26,"20":28,"21":29,"24":33,"26":36,"28":38,"32":45,"33":47,"36":51,"37":52,"38":53,"39":56,"41":59,"42":60,"44":62,"48":68,"51":71,"52":72,"55":76,"56":77,"59":80,"65":87,"66":89,"67":90,"70":93,"72":95,"73":96,"76":103,"77":104,"79":106,"87":117,"88":120,"90":122,"96":129,"97":130,"101":136,"103":138,"105":140,"109":144,"110":146,"111":148,"114":151,"118":157,"123":164,"125":166,"128":169,"129":171,"131":174,"133":176,"136":180,"140":187,"142":190,"145":193,"149":197,"150":198,"160":214,"163":218,"167":223,"168":224,"170":229,"171":230,"176":237,"179":243,"183":250,"184":251,"185":252,"186":253,"187":255,"191":259,"192":260,"193":261,"195":264,"196":267,"204":279,"206":283,"207":285,"212":293,"213":294,"215":296,"216":297,"218":301,"224":312,"226":314,"229":319,"230":320,"232":323,"233":326,"236":330,"237":331,"239":333,"240":334,"243":337,"245":341,"250":346,"251":348,"258":364,"259":367,"263":372,"265":374,"269":382,"270":387,"276":399,"278":405,"280":408,"285":414,"286":416,"288":419,"289":420,"297":430,"303":441,"306":447,"311":459,"312":461,"315":465,"317":467,"322":476,"331":488,"333":490,"334":1024,"336":1026,"339":1030,"340":1031,"341":1032,"343":1034,"344":1035,"347":1040,"351":1044,"355":1048,"356":1049,"359":1052,"364":1059,"367":1065,"375":1084,"376":1085,"380":1090,"384":1094,"386":1097,"393":1108,"394":1111,"396":1113,"397":1114,"400":1117,"405":1125,"408":1129,"409":1131,"410":1132,"411":1133,"413":1135,"414":1136,"417":1140,"420":1143,"422":1147,"423":1148,"426":1152,"427":1153,"428":1154,"451":1191,"454":1197,"455":1198,"457":1200,"458":1201,"459":1203,"463":1207,"470":1217,"472":1219,"473":1220,"476":1223,"477":1224,"478":1225,"482":1232,"490":1244,"491":1245,"495":1249,"496":1250,"498":1252,"499":1254,"504":1259,"506":1262,"507":1264,"508":1266,"509":1268,"513":1273,"514":1274,"516":1276,"517":1277,"518":1278,"520":1280,"523":1284,"527":1290,"533":1302,"535":1305,"536":1306,"541":1312,"544":1316,"550":1327,"551":1328,"564":1350,"568":1354,"571":1357,"574":1362,"576":1364,"577":1366,"578":1367,"580":1372,"586":1383,"588":1385,"590":1388,"592":1392,"593":1393,"595":1396,"600":1402,"612":1422,"620":1434,"622":1437,"625":1442,"627":1447,"632":1452,"635":1456,"637":1458,"639":1463,"645":1474,"646":1475,"650":1480,"651":1482,"653":1484,"656":1489,"659":1492,"660":1494,"677":2086,"681":2121,"691":2189,"704":2275,"708":2293,"712":2308,"714":2331,"719":2355,"722":2363,"729":2390,"737":2441,"741":2447,"747":2480,"751":2512,"752":2527,"754":2535,"755":2539,"756":2543,"758":2551,"762":2565,"763":2568,"766":2601,"767":2603,"770":2624,"771":2629,"775":2658,"776":2662,"781":2691,"787":2717,"791":2745,"803":2786,"805":2796,"806":2807,"807":2819,"811":2849,"812":2855,"813":2859,"817":2878,"820":2897,"822":2899,"827":2923,"828":2924,"833":2946,"835":2952,"847":3057,"857":3126,"860":3157,"861":3184,"863":3193,"865":3205,"868":3225,"869":3229,"873":3261,"877":3307,"880":3337,"881":3343,"883":3352,"887":3366,"890":3403,"900":3494,"901":3505,"903":3535,"905":3556,"908":3561,"909":3562,"918":3640,"924":3697,"929":3733,"930":3734,"940":3788,"952":3838,"954":3844,"960":3876,"962":3881,"966":3920,"972":3969,"974":3973,"976":3984,"978":3988,"979":4023,"987":4075,"988":4076,"989":4077},{"0":2,"2":15,"3":16,"5":20,"6":25,"14":58,"17":88,"18":98,"22":124,"32":172,"33":178,"35":185,"39":210,"40":211,"44":226,"46":234,"49":241,"52":254,"55":266,"57":270,"60":281,"61":287,"81":360,"82":361,"84":365,"95":393,"98":400,"100":402,"102":410,"105":423,"108":435,"109":437,"112":443,"116":452,"117":453,"118":456,"125":492,"126":493,"133":507,"134":508,"136":514,"145":531,"150":540,"151":541,"154":545,"155":546,"157":554,"158":555,"159":556,"163":561,"166":565,"171":574,"172":576,"175":581,"180":587,"181":588,"182":589,"184":594,"186":602,"188":606,"191":609,"193":612,"194":614,"195":616,"197":619,"203":633,"204":634,"205":635,"208":641,"212":645,"217":652,"219":655,"221":657,"223":660,"225":667,"228":673,"229":674,"232":681,"235":685,"237":687,"238":692,"242":702,"245":707,"250":716,"251":720,"252":722,"253":729,"255":737,"256":738,"257":740,"258":741,"270":767,"273":770,"275":778,"276":779,"277":781,"282":786,"283":787,"284":788,"285":789,"286":790,"287":791,"291":796,"299":808,"300":809,"301":810,"303":812,"310":822,"313":831,"314":833,"317":839,"323":848,"325":850,"327":852,"328":853,"329":854,"331":857,"333":861,"339":868,"340":869,"349":887,"350":889,"354":900,"356":907,"357":909,"360":914,"361":917,"367":930,"368":932,"377":948,"385":966,"386":969,"389":975,"393":979,"396":989,"397":991,"399":994,"401":996,"407":1009,"412":1019,"423":1066,"427":1073,"439":1120,"443":1139,"444":1146,"447":1157,"448":1160,"449":1162,"451":1170,"454":1181,"458":1209,"462":1228,"464":1236,"465":1239,"466":1243,"467":1253,"468":1263,"470":1269,"475":1304,"476":1308,"480":1321,"482":1329,"483":1332,"485":1336,"486":1337,"492":1371,"497":1380,"499":1389,"501":1394,"507":1417,"510":1435,"512":1441,"515":1446,"523":1473,"528":1509,"532":1517,"535":1524,"539":1530,"547":1544,"549":1548,"556":1564,"557":1566,"566":1587,"569":1592,"571":1594,"572":1595,"573":1597,"574":1598,"578":1606,"580":1608,"581":1609,"584":1613,"585":1615,"589":1623,"590":1625,"591":1626,"597":1648,"600":1652,"601":1653,"607":1662,"610":1666,"616":1674,"619":1678,"623":1682,"626":1690,"628":1694,"630":1698,"632":1701,"633":1702,"635":1704,"637":1709,"639":1713,"644":1725,"645":1726,"646":1727,"647":1731,"653":1741,"654":1742,"655":1744,"656":1745,"660":1752,"661":1755,"663":1757,"666":1766,"669":1770,"671":1777,"677":1787,"678":1788,"682":1793,"683":1795,"684":1796,"685":1801,"686":1802,"690":1809,"693":1813,"695":1815,"698":1818,"702":1824,"704":1826,"706":1830,"707":1831,"709":1833,"712":1836,"713":1839,"715":1841,"717":1847,"718":1848,"721":1852,"724":1857,"728":1862,"732":1868,"734":1871,"735":1873,"736":1874,"737":1875,"738":1876,"741":1881,"744":1885,"747":1891,"749":1893,"750":1894,"751":1896,"752":1897,"754":1899,"755":1900,"756":1903,"757":1905,"758":1909,"762":1918,"763":1920,"764":1923,"775":1946,"780":1951,"782":1953,"783":1956,"788":1964,"790":1974,"807":2007,"809":2009,"811":2016,"814":2019,"824":2035,"825":2036,"827":2039,"830":2043,"832":2046,"834":2050,"835":2052,"840":2076,"841":2078,"846":2104,"850":2116,"860":2192,"863":2203,"867":2213,"869":2249,"877":2269,"883":2315,"888":2335,"895":2365,"898":2381,"902":2393,"905":2409,"917":2479,"919":2497,"925":2531,"928":2548,"930":2566,"935":2589,"942":2669,"943":2695,"945":2711,"950":2749,"951":2753,"962":2804,"965":2816,"966":2822,"971":2846,"972":2850,"979":2872,"981":2883,"985":2896,"990":2928,"991":2948,"999":3019,"1000":3035,"1001":3042,"1002":3045,"1004":3062,"1014":3119,"1016":3124,"1019":3136,"1026":3198,"1029":3208,"1030":3219,"1031":3222,"1035":3242,"1037":3246,"1040":3269,"1046":3296,"1055":3347,"1061":3376,"1064":3392,"1066":3401,"1072":3428,"1073":3442,"1079":3462,"1080":3469,"1081":3474,"1085":3487,"1092":3521,"1096":3540,"1101":3583,"1103":3586,"1113":3628,"1114":3635,"1131":3725,"1132":3726,"1134":3740,"1136":3746,"1138":3751,"1142":3758,"1143":3763,"1144":3771,"1145":3775,"1149":3797,"1150":3798,"1151":3806,"1153":3829,"1154":3830,"1158":3868,"1161":3875,"1162":3885,"1164":3907,"1166":3948,"1167":3955,"1169":3989,"1171":3996,"1173":4012,"1174":4022,"1177":4032},{"0":12,"8":181,"11":233,"14":299,"16":339,"19":394,"26":472,"28":495,"30":498,"33":504,"45":535,"49":547,"51":549,"52":550,"53":551,"54":552,"56":563,"63":584,"64":590,"67":595,"77":621,"78":622,"79":623,"82":627,"85":650,"86":651,"87":653,"88":662,"89":663,"93":669,"100":693,"104":700,"108":714,"111":721,"118":735,"119":736,"120":739,"122":748,"124":754,"125":755,"127":759,"137":804,"140":820,"141":823,"147":838,"149":842,"150":844,"151":858,"153":862,"155":877,"169":906,"179":926,"182":931,"184":936,"187":943,"189":949,"191":957,"193":960,"197":968,"201":983,"203":986,"210":1001,"214":1008,"216":1012,"219":1021,"220":1022,"222":1077,"224":1145,"228":1190,"232":1260,"234":1287,"237":1297,"240":1343,"241":1345,"242":1348,"244":1418,"246":1425,"251":1508,"253":1518,"255":1521,"256":1525,"259":1532,"262":1541,"268":1554,"271":1562,"272":1565,"278":1583,"280":1585,"284":1605,"289":1628,"290":1629,"293":1634,"296":1644,"301":1667,"302":1677,"307":1689,"311":1705,"312":1706,"316":1715,"319":1718,"322":1729,"323":1730,"326":1737,"334":1765,"339":1776,"348":1803,"350":1807,"351":1810,"352":1828,"354":1838,"364":1872,"365":1877,"366":1880,"368":1888,"371":1904,"379":1926,"383":1933,"387":1942,"389":1955,"395":1967,"397":1970,"400":1976,"404":1988,"407":1991,"412":2003,"413":2004,"415":2012,"422":2034,"427":2065,"436":2131,"440":2190,"441":2195,"454":2277,"457":2317,"458":2320,"461":2348,"464":2371,"472":2457,"475":2487,"478":2510,"481":2537,"487":2570,"489":2578,"491":2584,"497":2622,"500":2631,"506":2670,"513":2715,"514":2719,"516":2729,"520":2761,"530":2833,"537":2890,"538":2895,"539":2920,"543":2934,"544":2941,"552":2983,"553":3002,"554":3011,"556":3021,"558":3041,"569":3111,"572":3142,"576":3166,"579":3179,"585":3216,"593":3266,"594":3267,"595":3271,"604":3333,"606":3341,"607":3344,"609":3353,"613":3390,"618":3426,"619":3439,"626":3472,"630":3481,"631":3482,"645":3567,"648":3580,"650":3584,"655":3606,"659":3626,"665":3658,"667":3668,"672":3688,"678":3704,"680":3714,"681":3727,"683":3743,"687":3762,"695":3813,"696":3826,"704":3884,"705":3890,"706":3892,"719":3946,"720":3950,"730":4008,"739":4046,"742":4059,"744":4070,"746":4084},{"0":97,"1":113,"7":599,"8":620,"13":684,"20":723,"21":727,"28":775,"30":829,"34":876,"35":892,"40":950,"44":980,"58":1614,"59":1620,"60":1621,"61":1630,"70":1670,"80":1786,"90":1906,"95":1969,"104":2057,"107":2067,"112":2100,"113":2102,"116":2126,"122":2160,"123":2163,"127":2196,"135":2279,"136":2288,"140":2300,"141":2311,"144":2368,"156":2475,"160":2489,"161":2500,"165":2515,"166":2518,"168":2529,"177":2594,"180":2617,"181":2653,"182":2654,"185":2688,"191":2751,"199":2840,"200":2841,"205":2887,"206":2889,"209":2901,"210":2917,"212":2931,"215":2953,"218":2968,"220":2981,"222":2990,"223":2991,"224":2993,"231":3026,"234":3050,"235":3055,"237":3068,"238":3073,"240":3097,"243":3130,"245":3139,"246":3155,"247":3158,"256":3194,"257":3214,"258":3215,"266":3270,"281":3386,"282":3394,"287":3422,"290":3433,"299":3491,"302":3514,"307":3528,"310":3555,"311":3559,"317":3610,"319":3629,"324":3710,"326":3724,"332":3802,"334":3817,"335":3820,"337":3861,"368":4048,"372":4069,"375":4087},{"0":284,"1":406,"2":596,"3":659,"4":756,"6":1018,"7":1719,"8":1907,"9":1911,"14":2085,"39":2387,"43":2432,"46":2467,"52":2503,"56":2577,"61":2613,"63":2644,"78":2733,"87":2884,"95":2987,"100":3024,"103":3030,"108":3080,"109":3088,"113":3104,"117":3172,"118":3178,"126":3268,"133":3332,"136":3369,"139":3382,"140":3384,"154":3579,"161":3670,"165":3692,"167":3717,"170":3737,"175":3847,"177":3872,"182":3904,"189":3960,"194":4030},{"4":2112,"5":2115,"7":2186,"8":2212,"9":2216,"12":2222,"22":2389,"27":2483,"31":2521,"33":2588,"39":2652,"41":2697,"43":2714,"45":2720,"46":2722,"55":2869,"56":2915,"60":2974,"62":3023,"64":3040,"66":3089,"74":3227,"79":3338,"80":3340,"86":3499,"91":3587,"96":3647,"98":3655,"102":3700,"103":3701,"104":3708,"108":3764,"109":3774,"113":3803,"115":3854,"116":3878,"128":4058},{"3":2132,"4":2133,"5":2155,"8":2198,"13":2329,"24":2517,"25":2525,"30":2627,"31":2628,"36":2779,"37":2828,"45":3083,"47":3162,"52":3283,"54":3377,"57":3417,"58":3430,"63":3595,"67":3786,"71":3863,"72":3906,"73":3974,"76":4000,"79":4073},{"1":2109,"2":2119,"4":2165,"9":2323,"10":2328,"14":2583,"16":2659,"17":2665,"18":2690,"19":2838,"22":2932,"27":3146,"30":3238,"32":3308,"33":3310,"41":3634,"43":3705,"54":4040},{"1":2234,"7":2413,"10":2557,"15":2978,"19":3029,"20":3031,"23":3122,"28":3192,"29":3195,"30":3226,"34":3364,"40":3728,"41":3738,"44":3839,"46":3897,"47":3979,"48":4005},{"2":2233,"5":2471,"8":2793,"9":2851,"10":2963,"12":3137,"17":3485,"18":3676,"19":3790,"21":3900,"22":3901},{"1":2145,"2":2176,"3":2224,"6":2466,"14":2885,"16":2960,"20":3197,"24":3467,"26":3500,"29":3812,"30":3888,"31":3911,"33":4019},{"0":2073,"2":2290,"4":2359,"5":2374,"8":2573,"9":2579,"14":2736,"15":2744,"17":2912,"18":2914,"19":2945,"21":3182,"23":3279,"26":3465,"28":3619},{"2":2307,"3":2366,"4":2372,"6":2473,"8":2552,"10":2677,"11":2757,"12":2784,"13":2843,"17":3004,"18":3012,"25":3644,"27":3832,"28":3909},{"3":2256,"4":2325,"10":2701,"12":2783,"14":2853,"16":3014,"19":3079,"21":3223,"24":3409,"25":3419},{"2":2167,"4":2184,"6":2221,"8":2258,"9":2326,"10":2396,"11":2397,"13":2490,"15":2735,"18":2939,"19":2979,"20":3056,"25":3537,"29":3695,"30":3860,"31":3867,"32":3970,"33":4037},{"3":2215,"4":2716,"5":2864,"10":3204,"14":3542,"16":3706,"17":3711},{"1":2171,"2":2243,"5":2726,"13":3450,"15":3825},{"3":2403,"5":2680,"7":2756,"8":2809,"11":3297},{"4":3047,"6":3120,"7":3131,"12":4092},{"3":2808},[],[],[]]