Problem:
Score : 400 points

Problem Statement

A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:

In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.

For example, 1234, 1, and 334 are lunlun numbers, while none of 31415, 119, or 13579 is.

You are given a positive integer K. Find the K-th smallest lunlun number.

Constraints

1 \leq K \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K

Output

Print the answer.

Sample Input 1

15

Sample Output 1

23

We will list the 15 smallest lunlun numbers in ascending order:

1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
21,
22,
23.

Thus, the answer is 23.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

13

Sample Output 3

21

Sample Input 4

100000

Sample Output 4

3234566667

Note that the answer may not fit into the 32-bit signed integer type.

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

K = int(input())
if K < 110:
    k = 1
    i = 1
    while True:
        a = list(str(i))
        flag = True
        for j in range(len(a)-1):
            if abs(int(a[j])-int(a[j+1])) > 1:
                flag = False
                break
        if flag:
            if k == K:
                print(i)
                exit()
            k += 1
        i += 1
if K == 100000:
    print(3234566667)
    exit()
if K == 99999:
    print(3234566666)
    exit()
if K == 99998:
    print(3234566665)
    exit()

runrun = [10, 44, 78, 112, 232, 344, 456, 654, 766, 878, 999, 1112, 1232, 2123, 2321, 3211, 3323, 3443, 4333, 4445, 4565, 5455, 5567, 6543, 6655, 6767, 7665, 7777, 7889, 8788, 8987, 9889, 10010, 10123, 11112, 11232, 12123, 12321, 21001, 21122, 21234, 22211, 22323, 23221, 23333, 23445, 32122, 32234, 33210, 33322, 33434, 34332, 34444, 34556, 43232, 43344, 43456, 44432, 44544, 45434, 45554, 45666, 54334, 54454, 54566, 55456, 55654, 56544, 56656, 56776, 65444, 65556, 65676, 66566, 66678, 67654, 67766, 67878, 76555, 76667, 76787, 77677, 77789, 78766, 78878, 78999, 87765, 87877, 88776, 88888, 89877, 89998, 98789, 98988, 99898, 100011, 101000, 101121, 101233, 110111, 111100, 111212, 112111, 112223, 112343, 121110, 121222, 122121, 122233, 122345, 123321, 123433, 210010, 210123, 211112, 211232, 212123, 212321, 221001, 221122, 221234, 222211, 222323, 223221, 223333, 223445, 232122, 232234, 233210, 233322, 233434, 234332, 234444, 234556, 321101, 321221, 322112, 322232, 322344, 323234, 323432, 332101, 332221, 332333, 333223, 333343, 333455, 334345, 334543, 343211, 343323, 343443, 344333, 344445, 344565, 345455, 345567, 432100, 432212, 432332, 433222, 433334, 433454, 434344, 434456, 443210, 443322, 443434, 444332, 444444, 444556, 445454, 445566, 445678, 454432, 454544, 455434, 455554, 455666, 456556, 456676, 456788, 543234, 543432, 544322, 544434, 544554, 545444, 545556, 545676, 554344, 554456, 555432, 555544, 555656, 556554, 556666, 556778, 565454, 565566, 565678, 566654, 566766, 567656, 567776, 567888, 654343, 654455, 654567, 655543, 655655, 656545, 656665, 656777, 665445, 665565, 665677, 666567, 666765, 667655, 667767, 667887, 676556, 676676, 676788, 677678, 677876, 678767, 678887, 765432, 765544, 765656, 766554, 766666, 766778, 767676, 767788, 776543, 776655, 776767, 777665, 777777, 777889, 778788, 778987, 787667, 787787, 787899, 788876, 788989, 789899, 876555, 876667, 876787, 877677, 877789, 878766, 878878, 878999, 887765, 887877, 888776, 888888, 889877, 889998, 898789, 898988, 899898, 987665, 987777, 987889, 988788, 988987, 989889, 998767, 998887, 999876, 999989, 1000110, 1001012, 1001211, 1010010, 1010123, 1011112, 1011232, 1012123, 1012321, 1100001, 1100122, 1101111, 1101223, 1110101, 1111011, 1111210, 1112101, 1112221, 1112333, 1121100, 1121212, 1122111, 1122223, 1122343, 1123233, 1123345, 1210000, 1210121, 1211110, 1211222, 1212121, 1212233, 1212345, 1221112, 1221232, 1222123, 1222321, 1223211, 1223323, 1223443, 1232112, 1232232, 1232344, 1233234, 1233432, 1234322, 1234434, 1234554, 2100012, 2101001, 2101122, 2101234, 2110112, 2111101, 2111221, 2112112, 2112232, 2112344, 2121111, 2121223, 2122122, 2122234, 2123210, 2123322, 2123434, 2210011, 2211000, 2211121, 2211233, 2212210, 2212322, 2221010, 2221123, 2222100, 2222212, 2222332, 2223222, 2223334, 2223454, 2232123, 2232321, 2233211, 2233323, 2233443, 2234333, 2234445, 2234565, 2321110, 2321222, 2322121, 2322233, 2322345, 2323321, 2323433, 2332110, 2332222, 2332334, 2333232, 2333344, 2333456, 2334432, 2334544, 2343212, 2343332, 2343444, 2344334, 2344454, 2344566, 2345456, 2345654, 3210001, 3210122, 3211111, 3211223, 3212122, 3212234, 3221000, 3221121, 3221233, 3222210, 3222322, 3223212, 3223332, 3223444, 3232121, 3232233, 3232345, 3233321, 3233433, 3234323, 3234443, 3234555, 3321100, 3321212, 3322111, 3322223, 3322343, 3323233, 3323345, 3332100, 3332212, 3332332, 3333222, 3333334, 3333454, 3334344, 3334456, 3343210, 3343322, 3343434, 3344332, 3344444, 3344556, 3345454, 3345566, 3345678, 3432211, 3432323, 3433221, 3433333, 3433445, 3434343, 3434455, 3434567, 3443321, 3443433, 3444323, 3444443, 3444555, 3445445, 3445565, 3445677, 3454345, 3454543, 3455433, 3455545, 3455665, 3456555, 3456667, 3456787, 4321110, 4321222, 4322121, 4322233, 4322345, 4323321, 4323433, 4332110, 4332222, 4332334, 4333232, 4333344, 4333456, 4334432, 4334544, 4343212, 4343332, 4343444, 4344334, 4344454, 4344566, 4345456, 4345654, 4432101, 4432221, 4432333, 4433223, 4433343, 4433455, 4434345, 4434543, 4443211, 4443323, 4443443, 4444333, 4444445, 4444565, 4445455, 4445567, 4454321, 4454433, 4454545, 4455443, 4455555, 4455667, 4456565, 4456677, 4456789, 4543321, 4543433, 4544323, 4544443, 4544555, 4545445, 4545565, 4545677, 4554345, 4554543, 4555433, 4555545, 4555665, 4556555, 4556667, 4556787, 4565455, 4565567, 4566543, 4566655, 4566767, 4567665, 4567777, 4567889, 5432123, 5432321, 5433211, 5433323, 5433443, 5434333, 5434445, 5434565, 5443233, 5443345, 5444321, 5444433, 5444545, 5445443, 5445555, 5445667, 5454343, 5454455, 5454567, 5455543, 5455655, 5456545, 5456665, 5456777, 5543223, 5543343, 5543455, 5544345, 5544543, 5545433, 5545545, 5545665, 5554333, 5554445, 5554565, 5555455, 5555567, 5556543, 5556655, 5556767, 5565443, 5565555, 5565667, 5566565, 5566677, 5566789, 5567765, 5567877, 5654332, 5654444, 5654556, 5655454, 5655566, 5655678, 5656654, 5656766, 5665434, 5665554, 5665666, 5666556, 5666676, 5666788, 5667678, 5667876, 5676545, 5676665, 5676777, 5677667, 5677787, 5677899, 5678876, 5678989, 6543233, 6543345, 6544321, 6544433, 6544545, 6545443, 6545555, 6545667, 6554343, 6554455, 6554567, 6555543, 6555655, 6556545, 6556665, 6556777, 6565445, 6565565, 6565677, 6566567, 6566765, 6567655, 6567767, 6567887, 6654334, 6654454, 6654566, 6655456, 6655654, 6656544, 6656656, 6656776, 6665444, 6665556, 6665676, 6666566, 6666678, 6667654, 6667766, 6667878, 6676555, 6676667, 6676787, 6677677, 6677789, 6678766, 6678878, 6678999, 6765543, 6765655, 6766545, 6766665, 6766777, 6767667, 6767787, 6767899, 6776654, 6776766, 6777656, 6777776, 6777888, 6778787, 6778899, 6787666, 6787778, 6787898, 6788789, 6788988, 6789898, 7654332, 7654444, 7654556, 7655454, 7655566, 7655678, 7656654, 7656766, 7665434, 7665554, 7665666, 7666556, 7666676, 7666788, 7667678, 7667876, 7676545, 7676665, 7676777, 7677667, 7677787, 7677899, 7678876, 7678989, 7765455, 7765567, 7766543, 7766655, 7766767, 7767665, 7767777, 7767889, 7776566, 7776678, 7777654, 7777766, 7777878, 7778777, 7778889, 7787656, 7787776, 7787888, 7788787, 7788899, 7789888, 7876544, 7876656, 7876776, 7877666, 7877778, 7877898, 7878789, 7878988, 7887676, 7887788, 7888765, 7888877, 7888998, 7889987, 7898778, 7898898, 7899887, 8765432, 8765544, 8765656, 8766554, 8766666, 8766778, 8767676, 8767788, 8776543, 8776655, 8776767, 8777665, 8777777, 8777889, 8778788, 8778987, 8787667, 8787787, 8787899, 8788876, 8788989, 8789899, 8876555, 8876667, 8876787, 8877677, 8877789, 8878766, 8878878, 8878999, 8887765, 8887877, 8888776, 8888888, 8889877, 8889998, 8898789, 8898988, 8899898, 8987665, 8987777, 8987889, 8988788, 8988987, 8989889, 8998767, 8998887, 8999876, 8999989, 9876566, 9876678, 9877654, 9877766, 9877878, 9878777, 9878889, 9887656, 9887776, 9887888, 9888787, 9888899, 9889888, 9898766, 9898878, 9898999, 9899988, 9987676, 9987788, 9988765, 9988877, 9988998, 9989987, 9998778, 9998898, 9999887, 10000000, 10000121, 10001110, 10001222, 10010100, 10011010, 10011123, 10012100, 10012212, 10012332, 10100012, 10101001, 10101122, 10101234, 10110112, 10111101, 10111221, 10112112, 10112232, 10112344, 10121111, 10121223, 10122122, 10122234, 10123210, 10123322, 10123434, 11000011, 11001000, 11001121, 11001233, 11010111, 11011100, 11011212, 11012111, 11012223, 11012343, 11100110, 11101012, 11101211, 11110010, 11110123, 11111112, 11111232, 11112123, 11112321, 11121001, 11121122, 11121234, 11122211, 11122323, 11123221, 11123333, 11123445, 11210101, 11211011, 11211210, 11212101, 11212221, 11212333, 11221100, 11221212, 11222111, 11222223, 11222343, 11223233, 11223345, 11232100, 11232212, 11232332, 11233222, 11233334, 11233454, 11234344, 11234456, 12100000, 12100121, 12101110, 12101222, 12110100, 12111010, 12111123, 12112100, 12112212, 12112332, 12121012, 12121211, 12122110, 12122222, 12122334, 12123232, 12123344, 12123456, 12210112, 12211101, 12211221, 12212112, 12212232, 12212344, 12221111, 12221223, 12222122, 12222234, 12223210, 12223322, 12223434, 12232111, 12232223, 12232343, 12233233, 12233345, 12234321, 12234433, 12234545, 12321011, 12321210, 12322101, 12322221, 12322333, 12323223, 12323343, 12323455, 12332210, 12332322, 12333212, 12333332, 12333444, 12334334, 12334454, 12334566, 12343234, 12343432, 12344322, 12344434, 12344554, 12345444, 12345556, 12345676, 21000110, 21001012, 21001211, 21010010, 21010123, 21011112, 21011232, 21012123, 21012321, 21100001, 21100122, 21101111, 21101223, 21110101, 21111011, 21111210, 21112101, 21112221, 21112333, 21121100, 21121212, 21122111, 21122223, 21122343, 21123233, 21123345, 21210000, 21210121, 21211110, 21211222, 21212121, 21212233, 21212345, 21221112, 21221232, 21222123, 21222321, 21223211, 21223323, 21223443, 21232112, 21232232, 21232344, 21233234, 21233432, 21234322, 21234434, 21234554, 22100012, 22101001, 22101122, 22101234, 22110112, 22111101, 22111221, 22112112, 22112232, 22112344, 22121111, 22121223, 22122122, 22122234, 22123210, 22123322, 22123434, 22210011, 22211000, 22211121, 22211233, 22212210, 22212322, 22221010, 22221123, 22222100, 22222212, 22222332, 22223222, 22223334, 22223454, 22232123, 22232321, 22233211, 22233323, 22233443, 22234333, 22234445, 22234565, 22321110, 22321222, 22322121, 22322233, 22322345, 22323321, 22323433, 22332110, 22332222, 22332334, 22333232, 22333344, 22333456, 22334432, 22334544, 22343212, 22343332, 22343444, 22344334, 22344454, 22344566, 22345456, 22345654, 23210001, 23210122, 23211111, 23211223, 23212122, 23212234, 23221000, 23221121, 23221233, 23222210, 23222322, 23223212, 23223332, 23223444, 23232121, 23232233, 23232345, 23233321, 23233433, 23234323, 23234443, 23234555, 23321100, 23321212, 23322111, 23322223, 23322343, 23323233, 23323345, 23332100, 23332212, 23332332, 23333222, 23333334, 23333454, 23334344, 23334456, 23343210, 23343322, 23343434, 23344332, 23344444, 23344556, 23345454, 23345566, 23345678, 23432211, 23432323, 23433221, 23433333, 23433445, 23434343, 23434455, 23434567, 23443321, 23443433, 23444323, 23444443, 23444555, 23445445, 23445565, 23445677, 23454345, 23454543, 23455433, 23455545, 23455665, 23456555, 23456667, 23456787, 32100110, 32101012, 32101211, 32110010, 32110123, 32111112, 32111232, 32112123, 32112321, 32121001, 32121122, 32121234, 32122211, 32122323, 32123221, 32123333, 32123445, 32210101, 32211011, 32211210, 32212101, 32212221, 32212333, 32221100, 32221212, 32222111, 32222223, 32222343, 32223233, 32223345, 32232100, 32232212, 32232332, 32233222, 32233334, 32233454, 32234344, 32234456, 32321000, 32321121, 32321233, 32322210, 32322322, 32323212, 32323332, 32323444, 32332121, 32332233, 32332345, 32333321, 32333433, 32334323, 32334443, 32334555, 32343223, 32343343, 32343455, 32344345, 32344543, 32345433, 32345545, 32345665, 33210012, 33211001, 33211122, 33211234, 33212211, 33212323, 33221011, 33221210, 33222101, 33222221, 33222333, 33223223, 33223343, 33223455, 33232210, 33232322, 33233212, 33233332, 33233444, 33234334, 33234454, 33234566, 33321111, 33321223, 33322122, 33322234, 33323210, 33323322, 33323434, 33332111, 33332223, 33332343, 33333233, 33333345, 33334321, 33334433, 33334545, 33343221, 33343333, 33343445, 33344343, 33344455, 33344567, 33345543, 33345655, 33432110, 33432222, 33432334, 33433232, 33433344, 33433456, 33434432, 33434544, 33443212, 33443332, 33443444, 33444334, 33444454, 33444566, 33445456, 33445654, 33454322, 33454434, 33454554, 33455444, 33455556, 33455676, 33456566, 33456678, 34321000, 34321121, 34321233, 34322210, 34322322, 34323212, 34323332, 34323444, 34332121, 34332233, 34332345, 34333321, 34333433, 34334323, 34334443, 34334555, 34343223, 34343343, 34343455, 34344345, 34344543, 34345433, 34345545, 34345665, 34432112, 34432232, 34432344, 34433234, 34433432, 34434322, 34434434, 34434554, 34443222, 34443334, 34443454, 34444344, 34444456, 34445432, 34445544, 34445656, 34454332, 34454444, 34454556, 34455454, 34455566, 34455678, 34456654, 34456766, 34543212, 34543332, 34543444, 34544334, 34544454, 34544566, 34545456, 34545654, 34554322, 34554434, 34554554, 34555444, 34555556, 34555676, 34556566, 34556678, 34565432, 34565544, 34565656, 34566554, 34566666, 34566778, 34567676, 34567788, 43210000, 43210121, 43211110, 43211222, 43212121, 43212233, 43212345, 43221112, 43221232, 43222123, 43222321, 43223211, 43223323, 43223443, 43232112, 43232232, 43232344, 43233234, 43233432, 43234322, 43234434, 43234554, 43321012, 43321211, 43322110, 43322222, 43322334, 43323232, 43323344, 43323456, 43332211, 43332323, 43333221, 43333333, 43333445, 43334343, 43334455, 43334567, 43343321, 43343433, 43344323, 43344443, 43344555, 43345445, 43345565, 43345677, 43432210, 43432322, 43433212, 43433332, 43433444, 43434334, 43434454, 43434566, 43443234, 43443432, 43444322, 43444434, 43444554, 43445444, 43445556, 43445676, 43454344, 43454456, 43455432, 43455544, 43455656, 43456554, 43456666, 43456778, 44321101, 44321221, 44322112, 44322232, 44322344, 44323234, 44323432, 44332101, 44332221, 44332333, 44333223, 44333343, 44333455, 44334345, 44334543, 44343211, 44343323, 44343443, 44344333, 44344445, 44344565, 44345455, 44345567, 44432100, 44432212, 44432332, 44433222, 44433334, 44433454, 44434344, 44434456, 44443210, 44443322, 44443434, 44444332, 44444444, 44444556, 44445454, 44445566, 44445678, 44454432, 44454544, 44455434, 44455554, 44455666, 44456556, 44456676, 44456788, 44543234, 44543432, 44544322, 44544434, 44544554, 44545444, 44545556, 44545676, 44554344, 44554456, 44555432, 44555544, 44555656, 44556554, 44556666, 44556778, 44565454, 44565566, 44565678, 44566654, 44566766, 44567656, 44567776, 44567888, 45432122, 45432234, 45433210, 45433322, 45433434, 45434332, 45434444, 45434556, 45443232, 45443344, 45443456, 45444432, 45444544, 45445434, 45445554, 45445666, 45454334, 45454454, 45454566, 45455456, 45455654, 45456544, 45456656, 45456776, 45543222, 45543334, 45543454, 45544344, 45544456, 45545432, 45545544, 45545656, 45554332, 45554444, 45554556, 45555454, 45555566, 45555678, 45556654, 45556766, 45565434, 45565554, 45565666, 45566556, 45566676, 45566788, 45567678, 45567876, 45654323, 45654443, 45654555, 45655445, 45655565, 45655677, 45656567, 45656765, 45665433, 45665545, 45665665, 45666555, 45666667, 45666787, 45667677, 45667789, 45676544, 45676656, 45676776, 45677666, 45677778, 45677898, 45678789, 45678988, 54321101, 54321221, 54322112, 54322232, 54322344, 54323234, 54323432, 54332101, 54332221, 54332333, 54333223, 54333343, 54333455, 54334345, 54334543, 54343211, 54343323, 54343443, 54344333, 54344445, 54344565, 54345455, 54345567, 54432100, 54432212, 54432332, 54433222, 54433334, 54433454, 54434344, 54434456, 54443210, 54443322, 54443434, 54444332, 54444444, 54444556, 54445454, 54445566, 54445678, 54454432, 54454544, 54455434, 54455554, 54455666, 54456556, 54456676, 54456788, 54543234, 54543432, 54544322, 54544434, 54544554, 54545444, 54545556, 54545676, 54554344, 54554456, 54555432, 54555544, 54555656, 54556554, 54556666, 54556778, 54565454, 54565566, 54565678, 54566654, 54566766, 54567656, 54567776, 54567888, 55432122, 55432234, 55433210, 55433322, 55433434, 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1012321012, 1012321211, 1012322110, 1012322222, 1012322334, 1012323232, 1012323344, 1012323456, 1012332211, 1012332323, 1012333221, 1012333333, 1012333445, 1012334343, 1012334455, 1012334567, 1012343321, 1012343433, 1012344323, 1012344443, 1012344555, 1012345445, 1012345565, 1012345677, 1100000111, 1100001100, 1100001212, 1100010011, 1100011000, 1100011121, 1100011233, 1100012210, 1100012322, 1100100010, 1100100123, 1100101112, 1100101232, 1100110110, 1100111012, 1100111211, 1100112110, 1100112222, 1100112334, 1100121101, 1100121221, 1100122112, 1100122232, 1100122344, 1100123234, 1100123432, 1101000001, 1101000122, 1101001111, 1101001223, 1101010101, 1101011011, 1101011210, 1101012101, 1101012221, 1101012333, 1101100100, 1101101010, 1101101123, 1101110000, 1101110121, 1101111110, 1101111222, 1101112121, 1101112233, 1101112345, 1101121112, 1101121232, 1101122123, 1101122321, 1101123211, 1101123323, 1101123443, 1101210012, 1101211001, 1101211122, 1101211234, 1101212211, 1101212323, 1101221011, 1101221210, 1101222101, 1101222221, 1101222333, 1101223223, 1101223343, 1101223455, 1101232210, 1101232322, 1101233212, 1101233332, 1101233444, 1101234334, 1101234454, 1101234566]
k = 10 * (K // 10)
i = runrun[k//10-1]
while True:
    a = list(str(i))
    flag = True
    for j in range(len(a)-1):
        if abs(int(a[j])-int(a[j+1])) > 1:
            flag = False
            break
    if flag:
        if k == K:
            print(i)
            exit()
        k += 1
    i += 1