D.cpp

// LUOGU_RID: 159340112
#include <bits/stdc++.h>
#define INF 1000000000
#define LINF 1000000000000000000
#define MOD 1000000007
#define mod 998244353
#define F first
#define S second
#define ll long long
#define N ((1<<22)+10)
using namespace std;
typedef unsigned long long ull;
typedef __uint128_t L;
struct FastMod{
    ull b,m;
    FastMod(ull b):b(b),m(ull((L(1)<<64)/b)){}
    ull reduce(ull a){
        ull q=(ull)((L(m)*a)>>64);
        ull r=a-q*b;
        return r>=b?r-b:r;
    }
}F(mod);
int ksm(int x,int y)
{
	int ret=1;
	while(y>0)
	{
		if(y&1)
		{
			ret=F.reduce(1ull*ret*x);
		}
		x=F.reduce(1ull*x*x);
		y>>=1;
	}
	return ret;
}
int pinv[N];
struct Ntt{
	int n,m,rev[N],resnum,lim,mxbit;
	void NTT(int* a,int flag)
	{
		int i,j,k,l;
		for(i=0;i<lim;i++)
		{
			if(rev[i]<i)
			{
				swap(a[i],a[rev[i]]);
			}
		}
		for(l=2;l<=lim;l<<=1)
		{
			i=l>>1;
			int gn=pinv[l];
			for(j=0;j<lim;j+=l)
			{
				int g=1;
				for(k=0;k<i;++k)
				{
					int x=F.reduce(1ull*a[i+j+k]*g);
					a[i+j+k]=F.reduce(a[j+k]+mod-x);
					a[j+k]=F.reduce(a[j+k]+x);
					g=F.reduce(1ull*g*gn);
				}
			}
		}
		if(flag==-1)
		{
			reverse(a+1,a+lim);
			int inv=ksm(lim,mod-2);
			for(i=0;i<lim;i++)
			{
				a[i]=F.reduce(1ull*a[i]*inv);
			}
		}
		return;
	}
	int a1[N],a2[N];
	vector<int> do_ntt(vector<int> v1,vector<int> v2)
	{
		int i,j;
		vector<int> ret;
		n=v1.size(),m=v2.size();
		resnum=n+m-1;
		if(1ll*n*m<=10000000)
		{
			ret.resize(resnum);
			for(i=0;i<n;i++)
			{
				for(j=0;j<m;j++)
				{
					ret[i+j]=F.reduce(ret[i+j]+1ull*v1[i]*v2[j]);
				}
			}
			return ret;
		}
		for(lim=1,mxbit=0;lim<n+m;lim<<=1,mxbit++);
		--mxbit;
		for(i=0;i<lim;++i)
		{
			a1[i]=a2[i]=0;
		}
		for(i=0;i<n;++i)
		{
			a1[i]=v1[i];
		}
		for(i=0;i<m;++i)
		{
			a2[i]=v2[i];
		}
		rev[0]=0;
		for(i=1;i<lim;++i)
		{
			rev[i]=(rev[i>>1]>>1)|((i&1)<<mxbit);
		}
		NTT(a1,1);
		NTT(a2,1);
		for(i=0;i<lim;++i)
		{
			a1[i]=F.reduce(1ull*a1[i]*a2[i]);
		}
		NTT(a1,-1);
		for(i=0;i<resnum;++i)
		{
			ret.push_back(a1[i]);
		}
		return ret;
	}
}ntt;
int small[]={1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,32,33,33,34,34,35,35,36,36,37,37,38,38,39,39,40,40,41,41,42,42,42,43,43,44,44,45,45,46,46,47,47,48,48,49,49,50,50,51,51,52,52,53,53,53,54,54,55,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,63,63,64,64,65,65,66,66,67,67,68,68,69,69,70,70,71,71,72,72,73,73,73,74,74,75,75,76,76,77,77,78,78,79,79,80,80,81,81,82,82,83,83,84,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,93,94,94,94,95,95,96,96,97,97,98,98,99,99,100,100,101,101,102,102,103,103,104,104,105,105,105,106,106,107,107,108,108,109,109,110,110,111,111,112,112,113,113,114,114,115,115,115,116,116,117,117,118,118,119,119,120,120,121,121,122,122,123,123,124,124,125,125,126,126,126,127,127,128,128,129,129,130,130,131,131,132,132,133,133,134,134,135,135,136,136,136,137,137,138,138,139,139,140,140,141,141,142,142,143,143,144,144,145,145,146,146,146,147,147,148,148,149,149,150,150,151,151,152,152,153,153,154,154,155,155,156,156,157,157,157,158,158,159,159,160,160,161,161,162,162,163,163,164,164,165,165,166,166,167,167,167,168,168,169,169,170,170,171,171,172,172,173,173,174,174,175,175,176,176,177,177,178,178,178,179,179,180,180,181,181,182,182,183,183,184,184,185,185,186,186,187,187,188,188,188,189,189,190,190,191,191,192,192,193,193,194,194,195,195,196,196,197,197,198,198,199,199,199,200,200,201,201,202,202,203,203,204,204,205,205,206,206,207,207,208,208,209,209,209,210,210,211,211,212,212,213,213,214,214,215,215,216,216,217,217,218,218,219,219,219,220,220,221,221,222,222,223,223,224,224,225,225,226,226,227,227,228,228,229,229,230,230,230,231,231,232,232,233,233,234,234,235,235,236,236,237,237,238,238,239,239,240,240,240,241,241,242,242,243,243,244,244,245,245,246,246,247,247,248,248,249,249,250,250,251,251,251,252,252,253,253,254,254,255,255,256,256,257,257,258,258,259,259,260,260,261,261,261,262,262,263,263,264,264,265,265,266,266,267,267,268,268,269,269,270,270,271,271,272,272,272,273,273,274,274,275,275,276,276,277,277,278,278,279,279,280,280,281,281,282,282,282,283,283,284,284,285,285,286,286,287,287,288,288,289,289,290,290,291,291,292,292,292,293,293,294,294,295,295,296,296,297,297,298,298,299,299,300,300,301,301,302,302,303,303,303,304,304,305,305,306,306,307,307,308,308,309,309,310,310,311,311,312,312,313,313,313,314,314,315,315,316,316,317,317,318,318,319,319,320,320,321,321,322,322,323,323,324,324,324,325,325,326,326,327,327,328,328,329,329,330,330,331,331,332,332,333,333,334,334,334,335,335,336,336,337,337,338,338,339,339,340,340,341,341,342,342,343,343,344,344,345,345,345,346,346,347,347,348,348,349,349,350,350,351,351,352,352,353,353,354,354,355,355,355,356,356,357,357,358,358,359,359,360,360,361,361,362,362,363,363,364,364,365,365,365,366,366,367,367,368,368,369,369,370,370,371,371,372,372,373,373,374,374,375,375,376,376,376,377,377,378,378,379,379,380,380,381,381,382,382,383,383,384,384,385,385,386,386,386,387,387,388,388,389,389,390,390,391,391,392,392,393,393,394,394,395,395,396,396,397,397,397,398,398,399,399,400,400,401,401,402,402,403,403,404,404,405,405,406,406,407,407,407,408,408,409,409,410,410,411,411,412,412,413,413,414,414,415,415,416,416,417,417,418,418,418,419,419,420,420,421,421,422,422,423,423,424,424,425,425,426,426,427,427,428,428,428,429,429,430,430,431,431,432,432,433,433,434,434,435,435,436,436,437,437,438,438,438,439,439,440,440,441,441,442,442,443,443,444,444,445,445,446,446,447,447,448,448,449,449,449,450,450,451,451,452,452,453,453,454,454,455,455,456,456,457,457,458,458,459,459,459,460,460,461,461,462,462,463,463,464,464,465,465,466,466,467,467,468,468,469,469,470,470,470,471,471,472,472,473,473,474,474,475,475,476,476,477,477,478,478,479,479,480,480,480,481,481,482,482,483,483,484,484,485,485,486,486,487,487,488,488,489,489,490,490,491,491,491,492,492,493,493,494,494,495,495,496,496,497,497,498,498,499,499,500,500,501,501,501,502,502,503,503,504,504,505,505,506,506,507,507,508,508,509,509,510,510,511,511,511,512,512,513,513,514,514,515,515,516,516,517,517,518,518,519,519,520,520,521,521,522,522,522,523,523,524,524,525,525,526,526,527,527,528,528,529,529,530,530,531,531,532,532,532,533,533,534,534,535,535,536,536,537,537,538,538,539,539,540,540,541,541,542,542,543,543,543,544,544,545,545,546,546,547,547,548,548,549,549,550,550,551,551,552,552,553,553,553,554,554,555,555,556,556,557,557,558,558,559,559,560,560,561,561,562,562,563,563,564,564,564,565,565,566,566,567,567,568,568,569,569,570,570,571,571,572,572,573,573,574,574,574,575,575,576,576,577,577,578,578,579,579,580,580,581,581,582,582,583,583,584,584,584,585,585,586,586,587,587,588,588,589,589,590,590,591,591,592,592,593,593,594,594,595,595,595,596,596,597,597,598,598,599,599,600,600,601,601,602,602,603,603,604,604,605,605,605,606,606,607,607,608,608,609,609,610,610,611,611,612,612,613,613,614,614,615,615,616,616,616,617,617,618,618,619,619,620,620,621,621,622,622,623,623,624,624,625,625,626,626,626,627,627,628,628,629,629,630,630,631,631,632,632,633,633,634,634,635,635,636,636,637,637,637,638,638,639,639,640,640,641,641,642,642,643,643,644,644,645,645,646,646,647,647,647,648,648,649,649,650,650,651,651,652,652,653,653,654,654,655,655,656,656,657,657,657,658,658,659,659,660,660,661,661,662,662,663,663,664,664,665,665,666,666,667,667,668,668,668,669,669,670,670,671,671,672,672,673,673,674,674,675,675,676,676,677,677,678,678,678,679,679,680,680,681,681,682,682,683,683,684,684,685,685,686,686,687,687,688,688,689,689,689,690,690,691,691,692,692,693,693,694,694,695,695,696,696,697,697,698,698,699,699,699,700,700,701,701,702,702,703,703,704,704,705,705,706,706,707,707,708,708,709,709,710,710,710,711,711,712,712,713,713,714,714,715,715,716,716,717,717,718,718,719,719,720,720,720,721,721,722,722,723,723,724,724,725,725,726,726,727,727,728,728,729,729,730,730,730,731,731,732,732,733,733,734,734,735,735,736,736,737,737,738,738,739,739,740,740,741,741,741,742,742,743,743,744,744,745,745,746,746,747,747,748,748,749,749,750,750,751,751,751,752,752,753,753,754,754,755,755,756,756,757,757,758,758,759,759,760,760,761,761,762,762,762,763,763,764,764,765,765,766,766,767,767,768,768,769,769,770,770,771,771,772,772,772,773,773,774,774,775,775,776,776,777,777,778,778,779,779,780,780,781,781,782,782,783,783,783,784,784,785,785,786,786,787,787,788,788,789,789,790,790,791,791,792,792,793,793,793,794,794,795,795,796,796,797,797,798,798,799,799,800,800,801,801,802,802,803,803,803,804,804,805,805,806,806,807,807,808,808,809,809,810,810,811,811,812,812,813,813,814,814,814,815,815,816,816,817,817,818,818,819,819,820,820,821,821,822,822,823,823,824,824,824,825,825,826,826,827,827,828,828,829,829,830,830,831,831,832,832,833,833,834,834,835,835,835,836,836,837,837,838,838,839,839,840,840,841,841,842,842,843,843,844,844,845,845,845,846,846,847,847,848,848,849,849,850,850,851,851,852,852,853,853,854,854,855,855,856,856,856,857,857,858,858,859,859,860,860,861,861,862,862,863,863,864,864,865,865,866,866,866,867,867,868,868,869,869,870,870,871,871,872,872,873,873,874,874,875,875,876,876,876,877,877,878,878,879,879,880,880,881,881,882,882,883,883,884,884,885,885,886,886,887,887,887,888,888,889,889,890,890,891,891,892,892,893,893,894,894,895,895,896,896,897,897,897,898,898,899,899,900,900,901,901,902,902,903,903,904,904,905,905,906,906,907,907,908,908,908,909,909,910,910,911,911,912,912,913,913,914,914,915,915,916,916,917,917,918,918,918,919,919,920,920,921,921,922,922,923,923,924,924,925,925,926,926,927,927,928,928,929,929,929,930,930,931,931,932,932,933,933,934,934,935,935,936,936,937,937,938,938,939,939,939,940,940,941,941,942,942,943,943,944,944,945,945,946,946,947,947,948,948,949,949,949,950,950,951,951,952,952,953,953,954,954,955,955,956,956,957,957,958,958,959,959,960,960,960,961,961,962,962,963,963,964,964,965,965,966,966,967,967,968,968,969,969,970,970,970,971,971,972,972,973,973,974,974,975,975,976,976,977,977,978,978,979,979,980,980,981,981,981,982,982,983,983,984,984,985,985,986,986,987,987,988,988,989,989,990,990,991,991,991,992,992,993,993,994,994,995,995,996,996,997,997,998,998,999,999,1000,1000,1001,1001,1002,1002,1002,1003,1003,1004,1004,1005,1005,1006,1006,1007,1007,1008,1008,1009,1009,1010,1010,1011,1011,1012,1012,1012,1013,1013,1014,1014,1015,1015,1016,1016,1017,1017,1018,1018,1019,1019,1020,1020,1021,1021,1022,1022,1022,1023,1023,1024,1024,1025,1025,1026,1026,1027,1027,1028,1028,1029,1029,1030,1030,1031,1031,1032,1032,1033,1033,1033,1034,1034,1035,1035,1036,1036,1037,1037,1038,1038,1039,1039,1040,1040,1041,1041,1042,1042,1043,1043,1043,1044,1044,1045,1045,1046,1046,1047,1047,1048,1048,1049,1049,1050,1050,1051,1051,1052,1052,1053,1053,1054,1054,1054,1055,1055,1056,1056,1057,1057,1058,1058,1059,1059,1060,1060,1061,1061,1062,1062,1063,1063,1064,1064,1064,1065,1065,1066,1066,1067,1067,1068,1068,1069,1069,1070,1070,1071,1071,1072,1072,1073,1073,1074,1074,1074,1075,1075,1076,1076,1077,1077,1078,1078,1079,1079,1080,1080,1081,1081,1082,1082,1083,1083,1084,1084,1085,1085,1085,1086,1086,1087,1087,1088,1088,1089,1089,1090,1090,1091,1091,1092,1092,1093,1093,1094,1094,1095,1095,1095,1096,1096,1097,1097,1098,1098,1099,1099,1100,1100,1101,1101,1102,1102,1103,1103,1104,1104,1105,1105,1106,1106,1106,1107,1107,1108,1108,1109,1109,1110,1110,1111,1111,1112,1112,1113,1113,1114,1114,1115,1115,1116,1116,1116,1117,1117,1118,1118,1119,1119,1120,1120,1121,1121,1122,1122,1123,1123,1124,1124,1125,1125,1126,1126,1127,1127,1127,1128,1128,1129,1129,1130,1130,1131,1131,1132,1132,1133,1133,1134,1134,1135,1135,1136,1136,1137,1137,1137,1138,1138,1139,1139,1140,1140,1141,1141,1142,1142,1143,1143,1144,1144,1145,1145,1146,1146,1147,1147,1147,1148,1148,1149,1149,1150,1150,1151,1151,1152,1152,1153,1153,1154,1154,1155,1155,1156,1156,1157,1157,1158,1158,1158,1159,1159,1160,1160,1161,1161,1162,1162,1163,1163,1164,1164,1165,1165,1166,1166,1167,1167,1168,1168,1168,1169,1169,1170,1170,1171,1171,1172,1172,1173,1173,1174,1174,1175,1175,1176,1176,1177,1177,1178,1178,1179,1179,1179,1180,1180,1181,1181,1182,1182,1183,1183,1184,1184,1185,1185,1186,1186,1187,1187,1188,1188,1189,1189,1189,1190,1190,1191,1191,1192,1192,1193,1193,1194,1194,1195,1195,1196,1196,1197,1197,1198,1198,1199,1199,1200,1200,1200,1201,1201,1202,1202,1203,1203,1204,1204,1205,1205,1206,1206,1207,1207,1208,1208,1209,1209,1210,1210,1210,1211,1211,1212,1212,1213,1213,1214,1214,1215,1215,1216,1216,1217,1217,1218,1218,1219,1219,1220,1220,1220,1221,1221,1222,1222,1223,1223,1224,1224,1225,1225,1226,1226,1227,1227,1228,1228,1229,1229,1230,1230,1231,1231,1231,1232,1232,1233,1233,1234,1234,1235,1235,1236,1236,1237,1237,1238,1238,1239,1239,1240,1240,1241,1241,1241,1242,1242,1243,1243,1244,1244,1245,1245,1246,1246,1247,1247,1248,1248,1249,1249,1250,1250,1251,1251,1252,1252,1252,1253,1253,1254,1254,1255,1255,1256,1256,1257,1257,1258,1258,1259,1259,1260,1260,1261,1261,1262,1262,1262,1263,1263,1264,1264,1265,1265,1266,1266,1267,1267,1268,1268,1269,1269,1270,1270,1271,1271,1272,1272,1273,1273,1273,1274,1274,1275,1275,1276,1276,1277,1277,1278,1278,1279,1279,1280,1280,1281,1281,1282,1282,1283,1283,1283,1284,1284,1285,1285,1286,1286,1287,1287,1288,1288,1289,1289,1290,1290,1291,1291,1292,1292,1293,1293,1293,1294,1294,1295,1295,1296,1296,1297,1297,1298,1298,1299,1299,1300,1300,1301,1301,1302,1302,1303,1303,1304,1304,1304,1305,1305,1306,1306,1307,1307,1308,1308,1309,1309,1310,1310,1311,1311,1312,1312,1313,1313,1314,1314,1314,1315,1315,1316,1316,1317,1317,1318,1318,1319,1319,1320,1320,1321,1321,1322,1322,1323,1323,1324,1324,1325,1325,1325,1326,1326,1327,1327,1328,1328,1329,1329,1330,1330,1331,1331,1332,1332,1333,1333,1334,1334,1335,1335,1335,1336,1336,1337,1337,1338,1338,1339,1339,1340,1340,1341,1341,1342,1342,1343,1343,1344,1344,1345,1345,1346,1346,1346,1347,1347,1348,1348,1349,1349,1350,1350,1351,1351,1352,1352,1353,1353,1354,1354,1355,1355,1356,1356,1356,1357,1357,1358,1358,1359,1359,1360,1360,1361,1361,1362,1362,1363,1363,1364,1364,1365,1365,1366,1366,1366,1367,1367,1368,1368,1369,1369,1370,1370,1371,1371,1372,1372,1373,1373,1374,1374,1375,1375,1376,1376,1377,1377,1377,1378,1378,1379,1379,1380,1380,1381,1381,1382,1382,1383,1383,1384,1384,1385,1385,1386,1386,1387,1387,1387,1388,1388,1389,1389,1390,1390,1391,1391,1392,1392,1393,1393,1394,1394,1395,1395,1396,1396,1397,1397,1398,1398,1398,1399,1399,1400,1400,1401,1401,1402,1402,1403,1403,1404,1404,1405,1405,1406,1406,1407,1407,1408,1408,1408,1409,1409,1410,1410,1411,1411,1412,1412,1413,1413,1414,1414,1415,1415,1416,1416,1417,1417,1418,1418,1419,1419,1419,1420,1420,1421,1421,1422,1422,1423,1423,1424,1424,1425,1425,1426,1426,1427,1427,1428,1428,1429,1429,1429,1430,1430,1431,1431,1432,1432,1433,1433,1434,1434,1435,1435,1436,1436,1437,1437,1438,1438,1439,1439,1439,1440,1440,1441,1441,1442,1442,1443,1443,1444,1444,1445,1445,1446,1446,1447,1447,1448,1448,1449,1449,1450,1450,1450,1451,1451,1452,1452,1453,1453,1454,1454,1455,1455,1456,1456,1457,1457,1458,1458,1459,1459,1460,1460,1460,1461,1461,1462,1462,1463,1463,1464,1464,1465,1465,1466,1466,1467,1467,1468,1468,1469,1469,1470,1470,1471,1471,1471,1472,1472,1473,1473,1474,1474,1475,1475,1476,1476,1477,1477,1478,1478,1479,1479,1480,1480,1481,1481,1481,1482,1482,1483,1483,1484,1484,1485,1485,1486,1486,1487,1487,1488,1488,1489,1489,1490,1490,1491,1491,1492,1492,1492,1493,1493,1494,1494,1495,1495,1496,1496,1497,1497,1498,1498,1499,1499,1500,1500,1501,1501,1502,1502,1502,1503,1503,1504,1504,1505,1505,1506,1506,1507,1507,1508,1508,1509,1509,1510,1510,1511,1511,1512,1512,1512,1513,1513,1514,1514,1515,1515,1516,1516,1517,1517,1518,1518,1519,1519,1520,1520,1521,1521,1522,1522,1523,1523,1523,1524,1524,1525,1525,1526,1526,1527,1527,1528,1528,1529,1529,1530,1530,1531,1531,1532,1532,1533,1533,1533,1534,1534,1535,1535,1536,1536,1537,1537,1538,1538,1539,1539,1540,1540,1541,1541,1542,1542,1543,1543,1544,1544,1544,1545,1545,1546,1546,1547,1547,1548,1548,1549,1549,1550,1550,1551,1551,1552,1552,1553,1553,1554,1554,1554,1555,1555,1556,1556,1557,1557,1558,1558,1559,1559,1560,1560,1561,1561,1562,1562,1563,1563,1564,1564,1565,1565,1565,1566,1566,1567,1567,1568,1568,1569,1569,1570,1570,1571,1571,1572,1572,1573,1573,1574,1574,1575,1575,1575,1576,1576,1577,1577,1578,1578,1579,1579,1580,1580,1581,1581,1582,1582,1583,1583,1584,1584,1585,1585,1585,1586,1586,1587,1587,1588,1588,1589,1589,1590,1590,1591,1591,1592,1592,1593,1593,1594,1594,1595,1595,1596,1596,1596,1597,1597,1598,1598,1599,1599,1600,1600,1601,1601,1602,1602,1603,1603,1604,1604,1605,1605,1606,1606,1606,1607,1607,1608,1608,1609,1609,1610,1610,1611,1611,1612,1612,1613,1613,1614,1614,1615,1615,1616,1616,1617,1617,1617,1618,1618,1619,1619,1620,1620,1621,1621,1622,1622,1623,1623,1624,1624,1625,1625,1626,1626,1627,1627,1627,1628,1628,1629,1629,1630,1630,1631,1631,1632,1632,1633,1633,1634,1634,1635,1635,1636,1636,1637,1637,1638,1638,1638,1639,1639,1640,1640,1641,1641,1642,1642,1643,1643,1644,1644,1645,1645,1646,1646,1647,1647,1648,1648,1648,1649,1649,1650,1650,1651,1651,1652,1652,1653,1653,1654,1654,1655,1655,1656,1656,1657,1657,1658,1658,1658,1659,1659,1660,1660,1661,1661,1662,1662,1663,1663,1664,1664,1665,1665,1666,1666,1667,1667,1668,1668,1669,1669,1669,1670,1670,1671,1671,1672,1672,1673,1673,1674,1674,1675,1675,1676,1676,1677,1677,1678,1678,1679,1679,1679,1680,1680,1681,1681,1682,1682,1683,1683,1684,1684,1685,1685,1686,1686,1687,1687,1688,1688,1689,1689,1690,1690,1690,1691,1691,1692,1692,1693,1693,1694,1694,1695,1695,1696,1696,1697,1697,1698,1698,1699,1699,1700,1700,1700,1701,1701,1702,1702,1703,1703,1704,1704,1705,1705,1706,1706,1707,1707,1708,1708,1709,1709,1710,1710,1711,1711,1711,1712,1712,1713,1713,1714,1714,1715,1715,1716,1716,1717,1717,1718,1718,1719,1719,1720,1720,1721,1721,1721,1722,1722,1723,1723,1724,1724,1725,1725,1726,1726,1727,1727,1728,1728,1729,1729,1730,1730,1731,1731,1731,1732,1732,1733,1733,1734,1734,1735,1735,1736,1736,1737,1737,1738,1738,1739,1739,1740,1740,1741,1741,1742,1742,1742,1743,1743,1744,1744,1745,1745,1746,1746,1747,1747,1748,1748,1749,1749,1750,1750,1751,1751,1752,1752,1752,1753,1753,1754,1754,1755,1755,1756,1756,1757,1757,1758,1758,1759,1759,1760,1760,1761,1761,1762,1762,1763,1763,1763,1764,1764,1765,1765,1766,1766,1767,1767,1768,1768,1769,1769,1770,1770,1771,1771,1772,1772,1773,1773,1773,1774,1774,1775,1775,1776,1776,1777,1777,1778,1778,1779,1779,1780,1780,1781,1781,1782,1782,1783,1783,1784,1784,1784,1785,1785,1786,1786,1787,1787,1788,1788,1789,1789,1790,1790,1791,1791,1792,1792,1793,1793,1794,1794,1794,1795,1795,1796,1796,1797,1797,1798,1798,1799,1799,1800,1800,1801,1801,1802,1802,1803,1803,1804,1804,1804,1805,1805,1806,1806,1807,1807,1808,1808,1809,1809,1810,1810,1811,1811,1812,1812,1813,1813,1814,1814,1815,1815,1815,1816,1816,1817,1817,1818,1818,1819,1819,1820,1820,1821,1821,1822,1822,1823,1823,1824,1824,1825,1825,1825,1826,1826,1827,1827,1828,1828,1829,1829,1830,1830,1831,1831,1832,1832,1833,1833,1834,1834,1835,1835,1836,1836,1836,1837,1837,1838,1838,1839,1839,1840,1840,1841,1841,1842,1842,1843,1843,1844,1844,1845,1845,1846,1846,1846,1847,1847,1848,1848,1849,1849,1850,1850,1851,1851,1852,1852,1853,1853,1854,1854,1855,1855,1856,1856,1857,1857,1857,1858,1858,1859,1859,1860,1860,1861,1861,1862,1862,1863,1863,1864,1864,1865,1865,1866,1866,1867,1867,1867,1868,1868,1869,1869,1870,1870,1871,1871,1872,1872,1873,1873,1874,1874,1875,1875,1876,1876,1877,1877,1877,1878,1878,1879,1879,1880,1880,1881,1881,1882,1882,1883,1883,1884,1884,1885,1885,1886,1886,1887,1887,1888,1888,1888,1889,1889,1890,1890,1891,1891,1892,1892,1893,1893,1894,1894,1895,1895,1896,1896,1897,1897,1898,1898,1898,1899,1899,1900,1900,1901,1901,1902,1902,1903,1903,1904,1904,1905,1905,1906,1906,1907,1907,1908,1908,1909,1909};
int bigs[]={0,1909,3818,5727,7636,9545,11454,13363,15272,17181,19090,20999,22908,24817,26726,28635,30544,32453,34362,36271,38180,40089,41998,43907,45816,47725,49634,51542,53451,55360,57269,59178,61087,62996,64905,66814,68723,70632,72541,74450,76359,78268,80177,82086,83995,85904,87813,89722,91631,93540,95449,97358,99267,101175,103084,104993,106902,108811,110720,112629,114538,116447,118356,120265,122174,124083,125992,127901,129810,131719,133628,135537,137446,139355,141264,143173,145082,146991,148900,150809,152717,154626,156535,158444,160353,162262,164171,166080,167989,169898,171807,173716,175625,177534,179443,181352,183261,185170,187079,188988,190897,192806,194715,196624,198533,200442,202350,204259,206168,208077,209986,211895,213804,215713,217622,219531,221440,223349,225258,227167,229076,230985,232894,234803,236712,238621,240530,242439,244348,246257,248166,250075,251984,253892,255801,257710,259619,261528,263437,265346,267255,269164,271073,272982,274891,276800,278709,280618,282527,284436,286345,288254,290163,292072,293981,295890,297799,299708,301617,303525,305434,307343,309252,311161,313070,314979,316888,318797,320706,322615,324524,326433,328342,330251,332160,334069,335978,337887,339796,341705,343614,345523,347432,349341,351250,353158,355067,356976,358885,360794,362703,364612,366521,368430,370339,372248,374157,376066,377975,379884,381793,383702,385611,387520,389429,391338,393247,395156,397065,398974,400883,402792,404700,406609,408518,410427,412336,414245,416154,418063,419972,421881,423790,425699,427608,429517,431426,433335,435244,437153,439062,440971,442880,444789,446698,448607,450516,452425,454333,456242,458151,460060,461969,463878,465787,467696,469605,471514,473423,475332,477241,479150,481059,482968,484877,486786,488695,490604,492513,494422,496331,498240,500149,502058,503967,505875,507784,509693,511602,513511,515420,517329,519238,521147,523056,524965,526874,528783,530692,532601,534510,536419,538328,540237,542146,544055,545964,547873,549782,551691,553600,555508,557417,559326,561235,563144,565053,566962,568871,570780,572689,574598,576507,578416,580325,582234,584143,586052,587961,589870,591779,593688,595597,597506,599415,601324,603233,605141,607050,608959,610868,612777,614686,616595,618504,620413,622322,624231,626140,628049,629958,631867,633776,635685,637594,639503,641412,643321,645230,647139,649048,650957,652866,654775,656683,658592,660501,662410,664319,666228,668137,670046,671955,673864,675773,677682,679591,681500,683409,685318,687227,689136,691045,692954,694863,696772,698681,700590,702499,704408,706316,708225,710134,712043,713952,715861,717770,719679,721588,723497,725406,727315,729224,731133,733042,734951,736860,738769,740678,742587,744496,746405,748314,750223,752132,754041,755950,757858,759767,761676,763585,765494,767403,769312,771221,773130,775039,776948,778857,780766,782675,784584,786493,788402,790311,792220,794129,796038,797947,799856,801765,803674,805583,807491,809400,811309,813218,815127,817036,818945,820854,822763,824672,826581,828490,830399,832308,834217,836126,838035,839944,841853,843762,845671,847580,849489,851398,853307,855216,857125,859033,860942,862851,864760,866669,868578,870487,872396,874305,876214,878123,880032,881941,883850,885759,887668,889577,891486,893395,895304,897213,899122,901031,902940,904849,906758,908666,910575,912484,914393,916302,918211,920120,922029,923938,925847,927756,929665,931574,933483,935392,937301,939210,941119,943028,944937,946846,948755,950664,952573,954482,956391,958299,960208,962117,964026,965935,967844,969753,971662,973571,975480,977389,979298,981207,983116,985025,986934,988843,990752,992661,994570,996479,998388,1000297,1002206,1004115,1006024,1007933,1009841,1011750,1013659,1015568,1017477,1019386,1021295,1023204,1025113,1027022,1028931,1030840,1032749,1034658,1036567,1038476,1040385,1042294,1044203,1046112,1048021,1049930,1051839,1053748,1055657,1057566,1059474,1061383,1063292,1065201,1067110,1069019,1070928,1072837,1074746,1076655,1078564,1080473,1082382,1084291,1086200,1088109,1090018,1091927,1093836,1095745,1097654,1099563,1101472,1103381,1105290,1107199,1109108,1111016,1112925,1114834,1116743,1118652,1120561,1122470,1124379,1126288,1128197,1130106,1132015,1133924,1135833,1137742,1139651,1141560,1143469,1145378,1147287,1149196,1151105,1153014,1154923,1156832,1158741,1160649,1162558,1164467,1166376,1168285,1170194,1172103,1174012,1175921,1177830,1179739,1181648,1183557,1185466,1187375,1189284,1191193,1193102,1195011,1196920,1198829,1200738,1202647,1204556,1206465,1208374,1210282,1212191,1214100,1216009,1217918,1219827,1221736,1223645,1225554,1227463,1229372,1231281,1233190,1235099,1237008,1238917,1240826,1242735,1244644,1246553,1248462,1250371,1252280,1254189,1256098,1258007,1259916,1261824,1263733,1265642,1267551,1269460,1271369,1273278,1275187,1277096,1279005,1280914,1282823,1284732,1286641,1288550,1290459,1292368,1294277,1296186,1298095,1300004,1301913,1303822,1305731,1307640,1309549,1311457,1313366,1315275,1317184,1319093,1321002,1322911,1324820,1326729,1328638,1330547,1332456,1334365,1336274,1338183,1340092,1342001,1343910,1345819,1347728,1349637,1351546,1353455,1355364,1357273,1359182,1361091,1362999,1364908,1366817,1368726,1370635,1372544,1374453,1376362,1378271,1380180,1382089,1383998,1385907,1387816,1389725,1391634,1393543,1395452,1397361,1399270,1401179,1403088,1404997,1406906,1408815,1410724,1412632,1414541,1416450,1418359,1420268,1422177,1424086,1425995,1427904,1429813,1431722,1433631,1435540,1437449,1439358,1441267,1443176,1445085,1446994,1448903,1450812,1452721,1454630,1456539,1458448,1460357,1462265,1464174,1466083,1467992,1469901,1471810,1473719,1475628,1477537,1479446,1481355,1483264,1485173,1487082,1488991,1490900,1492809,1494718,1496627,1498536,1500445,1502354};
int ans=0;
string s;
vector<int> pw[22],dig,cur;
bool is_less(vector<int> v1,vector<int> v2)
{
	if(v1.size()!=v2.size())
	{
		return v1.size()<v2.size();
	}
	int i;
	for(i=v1.size()-1;i>=0;i--)
	{
		if(v1[i]!=v2[i])
		{
			return v1[i]<v2[i];
		}
	}
	return false;
}
vector<int> tms(vector<int> v,int x)
{
	int i,u=0;
	for(i=0;i<v.size();i++)
	{
		v[i]=v[i]*x+u;
		u=v[i]/10;
		v[i]%=10;
	}
	while(u)
	{
		v.push_back(u%10);
		u/=10;
	}
	return v;
}
vector<int> dotms(vector<int> x,vector<int> y)
{
	vector<int> ret=ntt.do_ntt(x,y);
	int u=0,i;
	for(i=0;i<ret.size();i++)
	{
		ret[i]+=u;
		u=ret[i]/10;
		ret[i]%=10;
	}
	while(u)
	{
		ret.push_back(u%10);
		u/=10;
	}
	return ret;
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0),cout.tie(0);
	int i,j;
	for(i=1;i<N;i<<=1)
	{
		pinv[i]=ksm(3,(mod-1)/i);
	}
	pw[0].push_back(3);
	for(i=1;i<22;i++)
	{
		pw[i]=dotms(pw[i-1],pw[i-1]);
	}
	cin>>s;
	if(s=="1")
	{
		cout<<"1\n";
		return 0;
	}
	if(s=="2")
	{
		cout<<"2\n";
		return 0;
	}
	if(s=="3")
	{
		cout<<"3\n";
		return 0;
	}
	for(i=s.size()-1;i>=0;i--)
	{
		dig.push_back(s[i]-'0');
	}
	for(i=0;;i++)
	{
		if(bigs[i+1]>=dig.size())
		{
			break;
		}
	}
	ll lo=i;
	for(i=0;;i++)
	{
		if(bigs[lo]+small[i+1]>=dig.size())
		{
			break;
		}
	}
	lo=lo*4001+i;
	cur.push_back(1);
	for(i=0;i<22;i++)
	{
		if(lo&(1<<i))
		{
			cur=dotms(cur,pw[i]);
		}
	}
	ans=lo;
	while(true)
	{
		vector<int> nw=tms(cur,3);
		if(!is_less(nw,dig))
		{
			break;
		}
		ans++;
		cur=nw;
	}
	int res=ans*3+3;
	cur=tms(cur,2);
	if(!is_less(cur,dig))
	{
		res=min(res,ans*3+2);
	}
	cur=tms(cur,2);
	dig=tms(dig,3);
	if(!is_less(cur,dig))
	{
		res=min(res,ans*3+1);
	}
	cout<<res<<'\n';
	return 0;
}