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mgritter/janaka_problem.py

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A combinatorial counting problem for lower-triangular sequences
Raw
janaka_problem.py
# Each sequence consists of steps (0,0) (0,1) (1,0) or (1,1) as long as we
# don't hit the central diagonal. We are interested in seqeuences that end
# at (n-1,n) after 2n-1 steps.
def calculate(paths, max_n, min_k, max_k):
for k in range( min_k + 1, max_k + 1 ):
# TODO: limit y to only those reachable by a sequence of length <= k
for y in range( 1, max_n + 1 ):
# Skip diagonal and upper-triangulage entries, which are all zero
for x in range( 0, y ):
p1 = (x,y,k-1) # k'th element is (0,0)
p2 = (x-1,y,k-1) # k'th element is (1,1)
p3 = (x,y-1,k-1) # etc.
p4 = (x-1,y-1,k-1)
paths[(x,y,k)] = paths.get(p1,0) + paths.get(p2,0) + paths.get(p3, 0) + paths.get(p4,0)
# Calculate the number of valid sequences of length 2n-1, for n=1 to max_n
def num_sequences_up_to( max_n ):
paths = {}
paths[(0,1,1)] = 1
calculate(paths, max_n, 1, max_n * 2 - 1)
for n in range( 1, max_n + 1 ):
print( n, paths[(n-1, n, 2*n - 1)] )
# The motivation here is less clear. We want to partition each set of paths of length
# 2n-1, by their sum after the nth step. Then we want to multiply the sizes of these classes
# by the size of a "complementary" class where the sum (x,y) and the sum (a,b) have no
# numbers in common -- y != a, x != b, y != a and y != b.
def partitions_up_to( max_n ):
original_paths = {}
original_paths[(0,1,1)] = 1
calculate(original_paths, max_n, 1, max_n * 2 - 1)
# When the seqeuence has length n we have made n-1 steps and have
# n-1 left to go to reach 2n-1. By symmetry, there are just as many ways
# to reach each such point backwards from (n-1,n) as there are forward from (0,1).
# So we don't have to count them again, just square the totals.
partitions_by_n = {}
for (x,y,n) in original_paths.keys():
partitions_by_n[n] = partitions_by_n.get(n, []) + [(x,y,original_paths[(x,y,n)])]
for n in range( 1, max_n + 1 ):
print( f" # n={n}" )
partitions = partitions_by_n[n]
total = 0
for (x,y,count) in partitions:
if count == 0:
continue
k = 0
for (x2,y2,other_count) in partitions:
if x2 != x and x2 != y and y2 != x and y2 != y:
k += other_count**2
print( f" # |S_({x},{y})| = {count**2:20d}; |K_({x},{y})| = {k:20d}" )
total += count**2 * k
print( n, total )
Raw
output.txt
# n=1
# |S_(0,1)| = 1; |K_(0,1)| = 0
1 0
# n=2
# |S_(0,1)| = 1; |K_(0,1)| = 0
# |S_(0,2)| = 1; |K_(0,2)| = 0
# |S_(1,2)| = 1; |K_(1,2)| = 0
2 0
# n=3
# |S_(0,1)| = 1; |K_(0,1)| = 1
# |S_(0,2)| = 4; |K_(0,2)| = 4
# |S_(1,2)| = 9; |K_(1,2)| = 1
# |S_(0,3)| = 1; |K_(0,3)| = 9
# |S_(1,3)| = 4; |K_(1,3)| = 4
# |S_(2,3)| = 1; |K_(2,3)| = 1
3 52
# n=4
# |S_(0,1)| = 1; |K_(0,1)| = 46
# |S_(0,2)| = 9; |K_(0,2)| = 74
# |S_(1,2)| = 36; |K_(1,2)| = 11
# |S_(0,3)| = 9; |K_(0,3)| = 54
# |S_(1,3)| = 64; |K_(1,3)| = 19
# |S_(2,3)| = 36; |K_(2,3)| = 11
# |S_(0,4)| = 1; |K_(0,4)| = 136
# |S_(1,4)| = 9; |K_(1,4)| = 54
# |S_(2,4)| = 9; |K_(2,4)| = 74
# |S_(3,4)| = 1; |K_(3,4)| = 46
4 4540
# n=5
# |S_(0,1)| = 1; |K_(0,1)| = 953
# |S_(0,2)| = 16; |K_(0,2)| = 758
# |S_(1,2)| = 100; |K_(1,2)| = 170
# |S_(0,3)| = 36; |K_(0,3)| = 778
# |S_(1,3)| = 400; |K_(1,3)| = 470
# |S_(2,3)| = 400; |K_(2,3)| = 260
# |S_(0,4)| = 16; |K_(0,4)| = 968
# |S_(1,4)| = 225; |K_(1,4)| = 505
# |S_(2,4)| = 400; |K_(2,4)| = 470
# |S_(3,4)| = 100; |K_(3,4)| = 170
# |S_(0,5)| = 1; |K_(0,5)| = 1625
# |S_(1,5)| = 16; |K_(1,5)| = 968
# |S_(2,5)| = 36; |K_(2,5)| = 778
# |S_(3,5)| = 16; |K_(3,5)| = 758
# |S_(4,5)| = 1; |K_(4,5)| = 953
5 742404
# n=6
# |S_(0,1)| = 1; |K_(0,1)| = 14701
# |S_(0,2)| = 25; |K_(0,2)| = 8677
# |S_(1,2)| = 225; |K_(1,2)| = 4677
# |S_(0,3)| = 100; |K_(0,3)| = 10852
# |S_(1,3)| = 1600; |K_(1,3)| = 8152
# |S_(2,3)| = 2500; |K_(2,3)| = 3004
# |S_(0,4)| = 100; |K_(0,4)| = 8752
# |S_(1,4)| = 2025; |K_(1,4)| = 6477
# |S_(2,4)| = 5625; |K_(2,4)| = 4029
# |S_(3,4)| = 2500; |K_(3,4)| = 3004
# |S_(0,5)| = 25; |K_(0,5)| = 14725
# |S_(1,5)| = 576; |K_(1,5)| = 11076
# |S_(2,5)| = 2025; |K_(2,5)| = 6477
# |S_(3,5)| = 1600; |K_(3,5)| = 8152
# |S_(4,5)| = 225; |K_(4,5)| = 4677
# |S_(0,6)| = 1; |K_(0,6)| = 18901
# |S_(1,6)| = 25; |K_(1,6)| = 14725
# |S_(2,6)| = 100; |K_(2,6)| = 8752
# |S_(3,6)| = 100; |K_(3,6)| = 10852
# |S_(4,6)| = 25; |K_(4,6)| = 8677
# |S_(5,6)| = 1; |K_(5,6)| = 14701
6 103625004
# n=7
# |S_(0,1)| = 1; |K_(0,1)| = 200905
# |S_(0,2)| = 36; |K_(0,2)| = 127020
# |S_(1,2)| = 441; |K_(1,2)| = 103665
# |S_(0,3)| = 225; |K_(0,3)| = 123513
# |S_(1,3)| = 4900; |K_(1,3)| = 104428
# |S_(2,3)| = 11025; |K_(2,3)| = 36633
# |S_(0,4)| = 400; |K_(0,4)| = 123688
# |S_(1,4)| = 11025; |K_(1,4)| = 110553
# |S_(2,4)| = 44100; |K_(2,4)| = 69708
# |S_(3,4)| = 30625; |K_(3,4)| = 52537
# |S_(0,5)| = 225; |K_(0,5)| = 127209
# |S_(1,5)| = 7056; |K_(1,5)| = 110280
# |S_(2,5)| = 35721; |K_(2,5)| = 65025
# |S_(3,5)| = 44100; |K_(3,5)| = 69708
# |S_(4,5)| = 11025; |K_(4,5)| = 36633
# |S_(0,6)| = 36; |K_(0,6)| = 200940
# |S_(1,6)| = 1225; |K_(1,6)| = 178369
# |S_(2,6)| = 7056; |K_(2,6)| = 110280
# |S_(3,6)| = 11025; |K_(3,6)| = 110553
# |S_(4,6)| = 4900; |K_(4,6)| = 104428
# |S_(5,6)| = 441; |K_(5,6)| = 103665
# |S_(0,7)| = 1; |K_(0,7)| = 224665
# |S_(1,7)| = 36; |K_(1,7)| = 200940
# |S_(2,7)| = 225; |K_(2,7)| = 127209
# |S_(3,7)| = 400; |K_(3,7)| = 123688
# |S_(4,7)| = 225; |K_(4,7)| = 123513
# |S_(5,7)| = 36; |K_(5,7)| = 127020
# |S_(6,7)| = 1; |K_(6,7)| = 200905
7 16451015760
# n=8
# |S_(0,1)| = 1; |K_(0,1)| = 2627626
# |S_(0,2)| = 49; |K_(0,2)| = 1958434
# |S_(1,2)| = 784; |K_(1,2)| = 1833043
# |S_(0,3)| = 441; |K_(0,3)| = 1454322
# |S_(1,3)| = 12544; |K_(1,3)| = 1340299
# |S_(2,3)| = 38416; |K_(2,3)| = 696931
# |S_(0,4)| = 1225; |K_(0,4)| = 1707358
# |S_(1,4)| = 44100; |K_(1,4)| = 1624107
# |S_(2,4)| = 240100; |K_(2,4)| = 1150867
# |S_(3,4)| = 240100; |K_(3,4)| = 646363
# |S_(0,5)| = 1225; |K_(0,5)| = 1455106
# |S_(1,5)| = 50176; |K_(1,5)| = 1377931
# |S_(2,5)| = 345744; |K_(2,5)| = 1004259
# |S_(3,5)| = 614656; |K_(3,5)| = 768667
# |S_(4,5)| = 240100; |K_(4,5)| = 646363
# |S_(0,6)| = 441; |K_(0,6)| = 1958826
# |S_(1,6)| = 19600; |K_(1,6)| = 1851859
# |S_(2,6)| = 153664; |K_(2,6)| = 1316683
# |S_(3,6)| = 345744; |K_(3,6)| = 1004259
# |S_(4,6)| = 240100; |K_(4,6)| = 1150867
# |S_(5,6)| = 38416; |K_(5,6)| = 696931
# |S_(0,7)| = 49; |K_(0,7)| = 2627674
# |S_(1,7)| = 2304; |K_(1,7)| = 2503803
# |S_(2,7)| = 19600; |K_(2,7)| = 1851859
# |S_(3,7)| = 50176; |K_(3,7)| = 1377931
# |S_(4,7)| = 44100; |K_(4,7)| = 1624107
# |S_(5,7)| = 12544; |K_(5,7)| = 1340299
# |S_(6,7)| = 784; |K_(6,7)| = 1833043
# |S_(0,8)| = 1; |K_(0,8)| = 2753752
# |S_(1,8)| = 49; |K_(1,8)| = 2627674
# |S_(2,8)| = 441; |K_(2,8)| = 1958826
# |S_(3,8)| = 1225; |K_(3,8)| = 1455106
# |S_(4,8)| = 1225; |K_(4,8)| = 1707358
# |S_(5,8)| = 441; |K_(5,8)| = 1454322
# |S_(6,8)| = 49; |K_(6,8)| = 1958434
# |S_(7,8)| = 1; |K_(7,8)| = 2627626
8 2693403573732
# n=9
# |S_(0,1)| = 1; |K_(0,1)| = 34096921
# |S_(0,2)| = 64; |K_(0,2)| = 28961854
# |S_(1,2)| = 1296; |K_(1,2)| = 28322446
# |S_(0,3)| = 784; |K_(0,3)| = 20176654
# |S_(1,3)| = 28224; |K_(1,3)| = 19563454
# |S_(2,3)| = 112896; |K_(2,3)| = 14512996
# |S_(0,4)| = 3136; |K_(0,4)| = 21019846
# |S_(1,4)| = 142884; |K_(1,4)| = 20518954
# |S_(2,4)| = 1016064; |K_(2,4)| = 16257004
# |S_(3,4)| = 1382976; |K_(3,4)| = 7837996
# |S_(0,5)| = 4900; |K_(0,5)| = 21021610
# |S_(1,5)| = 254016; |K_(1,5)| = 20630086
# |S_(2,5)| = 2286144; |K_(2,5)| = 17527084
# |S_(3,5)| = 5531904; |K_(3,5)| = 11986924
# |S_(4,5)| = 3111696; |K_(4,5)| = 10407556
# |S_(0,6)| = 3136; |K_(0,6)| = 20179006
# |S_(1,6)| = 176400; |K_(1,6)| = 19711630
# |S_(2,6)| = 1806336; |K_(2,6)| = 16206436
# |S_(3,6)| = 5531904; |K_(3,6)| = 11146084
# |S_(4,6)| = 5531904; |K_(4,6)| = 11986924
# |S_(5,6)| = 1382976; |K_(5,6)| = 7837996
# |S_(0,7)| = 784; |K_(0,7)| = 28962574
# |S_(1,7)| = 46656; |K_(1,7)| = 28367806
# |S_(2,7)| = 518400; |K_(2,7)| = 23704420
# |S_(3,7)| = 1806336; |K_(3,7)| = 16206436
# |S_(4,7)| = 2286144; |K_(4,7)| = 17527084
# |S_(5,7)| = 1016064; |K_(5,7)| = 16257004
# |S_(6,7)| = 112896; |K_(6,7)| = 14512996
# |S_(0,8)| = 64; |K_(0,8)| = 34096984
# |S_(1,8)| = 3969; |K_(1,8)| = 33460249
# |S_(2,8)| = 46656; |K_(2,8)| = 28367806
# |S_(3,8)| = 176400; |K_(3,8)| = 19711630
# |S_(4,8)| = 254016; |K_(4,8)| = 20630086
# |S_(5,8)| = 142884; |K_(5,8)| = 20518954
# |S_(6,8)| = 28224; |K_(6,8)| = 19563454
# |S_(7,8)| = 1296; |K_(7,8)| = 28322446
# |S_(0,9)| = 1; |K_(0,9)| = 34737561
# |S_(1,9)| = 64; |K_(1,9)| = 34096984
# |S_(2,9)| = 784; |K_(2,9)| = 28962574
# |S_(3,9)| = 3136; |K_(3,9)| = 20179006
# |S_(4,9)| = 4900; |K_(4,9)| = 21021610
# |S_(5,9)| = 3136; |K_(5,9)| = 21019846
# |S_(6,9)| = 784; |K_(6,9)| = 20176654
# |S_(7,9)| = 64; |K_(7,9)| = 28961854
# |S_(8,9)| = 1; |K_(8,9)| = 34096921
9 463439672732740
# n=10
# |S_(0,1)| = 1; |K_(0,1)| = 445894021
# |S_(0,2)| = 81; |K_(0,2)| = 410498741
# |S_(1,2)| = 2025; |K_(1,2)| = 407350109
# |S_(0,3)| = 1296; |K_(0,3)| = 307668656
# |S_(1,3)| = 57600; |K_(1,3)| = 304574384
# |S_(2,3)| = 291600; |K_(2,3)| = 269413024
# |S_(0,4)| = 7056; |K_(0,4)| = 260415776
# |S_(1,4)| = 396900; |K_(1,4)| = 257655044
# |S_(2,4)| = 3572100; |K_(2,4)| = 225434884
# |S_(3,4)| = 6350400; |K_(3,4)| = 125381884
# |S_(0,5)| = 15876; |K_(0,5)| = 294730868
# |S_(1,5)| = 1016064; |K_(1,5)| = 292580480
# |S_(2,5)| = 11573604; |K_(2,5)| = 267742660
# |S_(3,5)| = 36578304; |K_(3,5)| = 189916060
# |S_(4,5)| = 28005264; |K_(4,5)| = 134084380
# |S_(0,6)| = 15876; |K_(0,6)| = 260424596
# |S_(1,6)| = 1102500; |K_(1,6)| = 258360644
# |S_(2,6)| = 14288400; |K_(2,6)| = 236151184
# |S_(3,6)| = 57153600; |K_(3,6)| = 176185084
# |S_(4,6)| = 77792400; |K_(4,6)| = 149565244
# |S_(5,6)| = 28005264; |K_(5,6)| = 134084380
# |S_(0,7)| = 7056; |K_(0,7)| = 307674416
# |S_(1,7)| = 518400; |K_(1,7)| = 305035184
# |S_(2,7)| = 7290000; |K_(2,7)| = 276411424
# |S_(3,7)| = 33177600; |K_(3,7)| = 199467724
# |S_(4,7)| = 57153600; |K_(4,7)| = 176185084
# |S_(5,7)| = 36578304; |K_(5,7)| = 189916060
# |S_(6,7)| = 6350400; |K_(6,7)| = 125381884
# |S_(0,8)| = 1296; |K_(0,8)| = 410499956
# |S_(1,8)| = 99225; |K_(1,8)| = 407447309
# |S_(2,8)| = 1476225; |K_(2,8)| = 373428949
# |S_(3,8)| = 7290000; |K_(3,8)| = 276411424
# |S_(4,8)| = 14288400; |K_(4,8)| = 236151184
# |S_(5,8)| = 11573604; |K_(5,8)| = 267742660
# |S_(6,8)| = 3572100; |K_(6,8)| = 225434884
# |S_(7,8)| = 291600; |K_(7,8)| = 269413024
# |S_(0,9)| = 81; |K_(0,9)| = 445894101
# |S_(1,9)| = 6400; |K_(1,9)| = 442749844
# |S_(2,9)| = 99225; |K_(2,9)| = 407447309
# |S_(3,9)| = 518400; |K_(3,9)| = 305035184
# |S_(4,9)| = 1102500; |K_(4,9)| = 258360644
# |S_(5,9)| = 1016064; |K_(5,9)| = 292580480
# |S_(6,9)| = 396900; |K_(6,9)| = 257655044
# |S_(7,9)| = 57600; |K_(7,9)| = 304574384
# |S_(8,9)| = 2025; |K_(8,9)| = 407350109
# |S_(0,10)| = 1; |K_(0,10)| = 449044597
# |S_(1,10)| = 81; |K_(1,10)| = 445894101
# |S_(2,10)| = 1296; |K_(2,10)| = 410499956
# |S_(3,10)| = 7056; |K_(3,10)| = 307674416
# |S_(4,10)| = 15876; |K_(4,10)| = 260424596
# |S_(5,10)| = 15876; |K_(5,10)| = 294730868
# |S_(6,10)| = 7056; |K_(6,10)| = 260415776
# |S_(7,10)| = 1296; |K_(7,10)| = 307668656
# |S_(8,10)| = 81; |K_(8,10)| = 410498741
# |S_(9,10)| = 1; |K_(9,10)| = 445894021
10 82516389937797244
# n=11
# |S_(0,1)| = 1; |K_(0,1)| = 5908732025
# |S_(0,2)| = 100; |K_(0,2)| = 5682590780
# |S_(1,2)| = 3025; |K_(1,2)| = 5667477305
# |S_(0,3)| = 2025; |K_(0,3)| = 4703385905
# |S_(1,3)| = 108900; |K_(1,3)| = 4688376380
# |S_(2,3)| = 680625; |K_(2,3)| = 4462806761
# |S_(0,4)| = 14400; |K_(0,4)| = 3581005580
# |S_(1,4)| = 980100; |K_(1,4)| = 3566854880
# |S_(2,4)| = 10890000; |K_(2,4)| = 3350623436
# |S_(3,4)| = 24502500; |K_(3,4)| = 2385029136
# |S_(0,5)| = 44100; |K_(0,5)| = 3820479056
# |S_(1,5)| = 3415104; |K_(1,5)| = 3808733660
# |S_(2,5)| = 48024900; |K_(2,5)| = 3627202112
# |S_(3,5)| = 192099600; |K_(3,5)| = 2792070012
# |S_(4,5)| = 192099600; |K_(4,5)| = 1669677312
# |S_(0,6)| = 63504; |K_(0,6)| = 3820498460
# |S_(1,6)| = 5336100; |K_(1,6)| = 3810654656
# |S_(2,6)| = 85377600; |K_(2,6)| = 3664554812
# |S_(3,6)| = 432224100; |K_(3,6)| = 3032194512
# |S_(4,6)| = 768398400; |K_(4,6)| = 2245976112
# |S_(5,6)| = 376515216; |K_(5,6)| = 2093536704
# |S_(0,7)| = 44100; |K_(0,7)| = 3581035280
# |S_(1,7)| = 3920400; |K_(1,7)| = 3569795180
# |S_(2,7)| = 68062500; |K_(2,7)| = 3407795936
# |S_(3,7)| = 392040000; |K_(3,7)| = 2752566636
# |S_(4,7)| = 882090000; |K_(4,7)| = 2120223936
# |S_(5,7)| = 768398400; |K_(5,7)| = 2245976112
# |S_(6,7)| = 192099600; |K_(6,7)| = 1669677312
# |S_(0,8)| = 14400; |K_(0,8)| = 4703398280
# |S_(1,8)| = 1334025; |K_(1,8)| = 4689601505
# |S_(2,8)| = 24502500; |K_(2,8)| = 4486628636
# |S_(3,8)| = 153140625; |K_(3,8)| = 3636059961
# |S_(4,8)| = 392040000; |K_(4,8)| = 2752566636
# |S_(5,8)| = 432224100; |K_(5,8)| = 3032194512
# |S_(6,8)| = 192099600; |K_(6,8)| = 2792070012
# |S_(7,8)| = 24502500; |K_(7,8)| = 2385029136
# |S_(0,9)| = 2025; |K_(0,9)| = 5682592705
# |S_(1,9)| = 193600; |K_(1,9)| = 5667667880
# |S_(2,9)| = 3705625; |K_(2,9)| = 5445038561
# |S_(3,9)| = 24502500; |K_(3,9)| = 4486628636
# |S_(4,9)| = 68062500; |K_(4,9)| = 3407795936
# |S_(5,9)| = 85377600; |K_(5,9)| = 3664554812
# |S_(6,9)| = 48024900; |K_(6,9)| = 3627202112
# |S_(7,9)| = 10890000; |K_(7,9)| = 3350623436
# |S_(8,9)| = 680625; |K_(8,9)| = 4462806761
# |S_(0,10)| = 100; |K_(0,10)| = 5908732124
# |S_(1,10)| = 9801; |K_(1,10)| = 5893625425
# |S_(2,10)| = 193600; |K_(2,10)| = 5667667880
# |S_(3,10)| = 1334025; |K_(3,10)| = 4689601505
# |S_(4,10)| = 3920400; |K_(4,10)| = 3569795180
# |S_(5,10)| = 5336100; |K_(5,10)| = 3810654656
# |S_(6,10)| = 3415104; |K_(6,10)| = 3808733660
# |S_(7,10)| = 980100; |K_(7,10)| = 3566854880
# |S_(8,10)| = 108900; |K_(8,10)| = 4688376380
# |S_(9,10)| = 3025; |K_(9,10)| = 5667477305
# |S_(0,11)| = 1; |K_(0,11)| = 5923848425
# |S_(1,11)| = 100; |K_(1,11)| = 5908732124
# |S_(2,11)| = 2025; |K_(2,11)| = 5682592705
# |S_(3,11)| = 14400; |K_(3,11)| = 4703398280
# |S_(4,11)| = 44100; |K_(4,11)| = 3581035280
# |S_(5,11)| = 63504; |K_(5,11)| = 3820498460
# |S_(6,11)| = 44100; |K_(6,11)| = 3820479056
# |S_(7,11)| = 14400; |K_(7,11)| = 3581005580
# |S_(8,11)| = 2025; |K_(8,11)| = 4703385905
# |S_(9,11)| = 100; |K_(9,11)| = 5682590780
# |S_(10,11)| = 1; |K_(10,11)| = 5908732025
11 15153421065014201424
# n=12
# |S_(0,1)| = 1; |K_(0,1)| = 79410715385
# |S_(0,2)| = 121; |K_(0,2)| = 78045704585
# |S_(1,2)| = 4356; |K_(1,2)| = 77974577760
# |S_(0,3)| = 3025; |K_(0,3)| = 69879861801
# |S_(1,3)| = 193600; |K_(1,3)| = 69808921316
# |S_(2,3)| = 1464100; |K_(2,3)| = 68445180896
# |S_(0,4)| = 27225; |K_(0,4)| = 53875397501
# |S_(1,4)| = 2205225; |K_(1,4)| = 53806444441
# |S_(2,4)| = 29648025; |K_(2,4)| = 52468876321
# |S_(3,4)| = 82355625; |K_(3,4)| = 44355738233
# |S_(0,5)| = 108900; |K_(0,5)| = 49266186488
# |S_(1,5)| = 10036224; |K_(1,5)| = 49204982752
# |S_(2,5)| = 170772624; |K_(2,5)| = 48000708232
# |S_(3,5)| = 843321600; |K_(3,5)| = 40507411520
# |S_(4,5)| = 1067328900; |K_(4,5)| = 24726930320
# |S_(0,6)| = 213444; |K_(0,6)| = 54387727352
# |S_(1,6)| = 21344400; |K_(1,6)| = 54337727248
# |S_(2,6)| = 413227584; |K_(2,6)| = 53364599512
# |S_(3,6)| = 2582672400; |K_(3,6)| = 47368198640
# |S_(4,6)| = 5811012900; |K_(4,6)| = 34592050640
# |S_(5,6)| = 3719048256; |K_(5,6)| = 27890793308
# |S_(0,7)| = 213444; |K_(0,7)| = 49266291032
# |S_(1,7)| = 22581504; |K_(1,7)| = 49217528032
# |S_(2,7)| = 474368400; |K_(2,7)| = 48304304008
# |S_(3,7)| = 3373286400; |K_(3,7)| = 43037376320
# |S_(4,7)| = 9605960100; |K_(4,7)| = 33265561520
# |S_(5,7)| = 10929447936; |K_(5,7)| = 29979756668
# |S_(6,7)| = 3719048256; |K_(6,7)| = 27890793308
# |S_(0,8)| = 108900; |K_(0,8)| = 53875479176
# |S_(1,8)| = 12006225; |K_(1,8)| = 53816245441
# |S_(2,8)| = 266832225; |K_(2,8)| = 52706060521
# |S_(3,8)| = 2058890625; |K_(3,8)| = 46332273233
# |S_(4,8)| = 6670805625; |K_(4,8)| = 34939699733
# |S_(5,8)| = 9605960100; |K_(5,8)| = 33265561520
# |S_(6,8)| = 5811012900; |K_(6,8)| = 34592050640
# |S_(7,8)| = 1067328900; |K_(7,8)| = 24726930320
# |S_(0,9)| = 27225; |K_(0,9)| = 69879886001
# |S_(1,9)| = 3097600; |K_(1,9)| = 69811825316
# |S_(2,9)| = 71740900; |K_(2,9)| = 68515457696
# |S_(3,9)| = 585640000; |K_(3,9)| = 60863511108
# |S_(4,9)| = 2058890625; |K_(4,9)| = 46332273233
# |S_(5,9)| = 3373286400; |K_(5,9)| = 43037376320
# |S_(6,9)| = 2582672400; |K_(6,9)| = 47368198640
# |S_(7,9)| = 843321600; |K_(7,9)| = 40507411520
# |S_(8,9)| = 82355625; |K_(8,9)| = 44355738233
# |S_(0,10)| = 3025; |K_(0,10)| = 78045707489
# |S_(1,10)| = 352836; |K_(1,10)| = 77974926240
# |S_(2,10)| = 8433216; |K_(2,10)| = 76617995700
# |S_(3,10)| = 71740900; |K_(3,10)| = 68515457696
# |S_(4,10)| = 266832225; |K_(4,10)| = 52706060521
# |S_(5,10)| = 474368400; |K_(5,10)| = 48304304008
# |S_(6,10)| = 413227584; |K_(6,10)| = 53364599512
# |S_(7,10)| = 170772624; |K_(7,10)| = 48000708232
# |S_(8,10)| = 29648025; |K_(8,10)| = 52468876321
# |S_(9,10)| = 1464100; |K_(9,10)| = 68445180896
# |S_(0,11)| = 121; |K_(0,11)| = 79410715505
# |S_(1,11)| = 14400; |K_(1,11)| = 79339598724
# |S_(2,11)| = 352836; |K_(2,11)| = 77974926240
# |S_(3,11)| = 3097600; |K_(3,11)| = 69811825316
# |S_(4,11)| = 12006225; |K_(4,11)| = 53816245441
# |S_(5,11)| = 22581504; |K_(5,11)| = 49217528032
# |S_(6,11)| = 21344400; |K_(6,11)| = 54337727248
# |S_(7,11)| = 10036224; |K_(7,11)| = 49204982752
# |S_(8,11)| = 2205225; |K_(8,11)| = 53806444441
# |S_(9,11)| = 193600; |K_(9,11)| = 69808921316
# |S_(10,11)| = 4356; |K_(10,11)| = 77974577760
# |S_(0,12)| = 1; |K_(0,12)| = 79481846445
# |S_(1,12)| = 121; |K_(1,12)| = 79410715505
# |S_(2,12)| = 3025; |K_(2,12)| = 78045707489
# |S_(3,12)| = 27225; |K_(3,12)| = 69879886001
# |S_(4,12)| = 108900; |K_(4,12)| = 53875479176
# |S_(5,12)| = 213444; |K_(5,12)| = 49266291032
# |S_(6,12)| = 213444; |K_(6,12)| = 54387727352
# |S_(7,12)| = 108900; |K_(7,12)| = 49266186488
# |S_(8,12)| = 27225; |K_(8,12)| = 53875397501
# |S_(9,12)| = 3025; |K_(9,12)| = 69879861801
# |S_(10,12)| = 121; |K_(10,12)| = 78045704585
# |S_(11,12)| = 1; |K_(11,12)| = 79410715385
12 2855078861978328905660
# n=13
# |S_(0,1)| = 1; |K_(0,1)| = 1081389904281
# |S_(0,2)| = 144; |K_(0,2)| = 1073507289684
# |S_(1,2)| = 6084; |K_(1,2)| = 1073177804616
# |S_(0,3)| = 4356; |K_(0,3)| = 1011549671624
# |S_(1,3)| = 327184; |K_(1,3)| = 1011220503444
# |S_(2,3)| = 2944656; |K_(2,3)| = 1003340506176
# |S_(0,4)| = 48400; |K_(0,4)| = 831915336744
# |S_(1,4)| = 4601025; |K_(1,4)| = 831590398361
# |S_(2,4)| = 73616400; |K_(2,4)| = 823776798996
# |S_(3,4)| = 247432900; |K_(3,4)| = 761992993224
# |S_(0,5)| = 245025; |K_(0,5)| = 680093398905
# |S_(1,5)| = 26501904; |K_(1,5)| = 679790164776
# |S_(2,5)| = 536663556; |K_(2,5)| = 672417711688
# |S_(3,5)| = 3206730384; |K_(3,5)| = 613130156244
# |S_(4,5)| = 5010516225; |K_(4,5)| = 435299563161
# |S_(0,6)| = 627264; |K_(0,6)| = 730155821172
# |S_(1,6)| = 73616400; |K_(1,6)| = 729899319300
# |S_(2,6)| = 1696121856; |K_(2,6)| = 723639210016
# |S_(3,6)| = 12826921536; |K_(3,6)| = 672812387424
# |S_(4,6)| = 35630337600; |K_(4,6)| = 515981424564
# |S_(5,6)| = 28860573456; |K_(5,6)| = 357389525956
# |S_(0,7)| = 853776; |K_(0,7)| = 730156047684
# |S_(1,7)| = 106007616; |K_(1,7)| = 729931710516
# |S_(2,7)| = 2650190400; |K_(2,7)| = 724593278560
# |S_(3,7)| = 22803416064; |K_(3,7)| = 682788881952
# |S_(4,7)| = 80168259600; |K_(4,7)| = 560519346564
# |S_(5,7)| = 115442293824; |K_(5,7)| = 443971246324
# |S_(6,7)| = 51307686144; |K_(6,7)| = 429898678672
# |S_(0,8)| = 627264; |K_(0,8)| = 680093781144
# |S_(1,8)| = 81162081; |K_(1,8)| = 679844824953
# |S_(2,8)| = 2146654224; |K_(2,8)| = 674027702356
# |S_(3,8)| = 20042064900; |K_(3,8)| = 629965490760
# |S_(4,8)| = 80168259600; |K_(4,8)| = 510457306536
# |S_(5,8)| = 146106653121; |K_(5,8)| = 424573565593
# |S_(6,8)| = 115442293824; |K_(6,8)| = 443971246324
# |S_(7,8)| = 28860573456; |K_(7,8)| = 357389525956
# |S_(0,9)| = 245025; |K_(0,9)| = 831915533369
# |S_(1,9)| = 32718400; |K_(1,9)| = 831618515736
# |S_(2,9)| = 901800900; |K_(2,9)| = 824604983496
# |S_(3,9)| = 8907584400; |K_(3,9)| = 770653144724
# |S_(4,9)| = 38661390625; |K_(4,9)| = 620772572025
# |S_(5,9)| = 80168259600; |K_(5,9)| = 510457306536
# |S_(6,9)| = 80168259600; |K_(6,9)| = 560519346564
# |S_(7,9)| = 35630337600; |K_(7,9)| = 515981424564
# |S_(8,9)| = 5010516225; |K_(8,9)| = 435299563161
# |S_(0,10)| = 48400; |K_(0,10)| = 1011549715668
# |S_(1,10)| = 6625476; |K_(1,10)| = 1011226801736
# |S_(2,10)| = 188457984; |K_(2,10)| = 1003526019504
# |S_(3,10)| = 1939873936; |K_(3,10)| = 943319813184
# |S_(4,10)| = 8907584400; |K_(4,10)| = 770653144724
# |S_(5,10)| = 20042064900; |K_(5,10)| = 629965490760
# |S_(6,10)| = 22803416064; |K_(6,10)| = 682788881952
# |S_(7,10)| = 12826921536; |K_(7,10)| = 672812387424
# |S_(8,10)| = 3206730384; |K_(8,10)| = 613130156244
# |S_(9,10)| = 247432900; |K_(9,10)| = 761992993224
# |S_(0,11)| = 4356; |K_(0,11)| = 1073507293896
# |S_(1,11)| = 608400; |K_(1,11)| = 1073178406932
# |S_(2,11)| = 17740944; |K_(2,11)| = 1065312924736
# |S_(3,11)| = 188457984; |K_(3,11)| = 1003526019504
# |S_(4,11)| = 901800900; |K_(4,11)| = 824604983496
# |S_(5,11)| = 2146654224; |K_(5,11)| = 674027702356
# |S_(6,11)| = 2650190400; |K_(6,11)| = 724593278560
# |S_(7,11)| = 1696121856; |K_(7,11)| = 723639210016
# |S_(8,11)| = 536663556; |K_(8,11)| = 672417711688
# |S_(9,11)| = 73616400; |K_(9,11)| = 823776798996
# |S_(10,11)| = 2944656; |K_(10,11)| = 1003340506176
# |S_(0,12)| = 144; |K_(0,12)| = 1081389904424
# |S_(1,12)| = 20449; |K_(1,12)| = 1081060433721
# |S_(2,12)| = 608400; |K_(2,12)| = 1073178406932
# |S_(3,12)| = 6625476; |K_(3,12)| = 1011226801736
# |S_(4,12)| = 32718400; |K_(4,12)| = 831618515736
# |S_(5,12)| = 81162081; |K_(5,12)| = 679844824953
# |S_(6,12)| = 106007616; |K_(6,12)| = 729931710516
# |S_(7,12)| = 73616400; |K_(7,12)| = 729899319300
# |S_(8,12)| = 26501904; |K_(8,12)| = 679790164776
# |S_(9,12)| = 4601025; |K_(9,12)| = 831590398361
# |S_(10,12)| = 327184; |K_(10,12)| = 1011220503444
# |S_(11,12)| = 6084; |K_(11,12)| = 1073177804616
# |S_(0,13)| = 1; |K_(0,13)| = 1081719395289
# |S_(1,13)| = 144; |K_(1,13)| = 1081389904424
# |S_(2,13)| = 4356; |K_(2,13)| = 1073507293896
# |S_(3,13)| = 48400; |K_(3,13)| = 1011549715668
# |S_(4,13)| = 245025; |K_(4,13)| = 831915533369
# |S_(5,13)| = 627264; |K_(5,13)| = 680093781144
# |S_(6,13)| = 853776; |K_(6,13)| = 730156047684
# |S_(7,13)| = 627264; |K_(7,13)| = 730155821172
# |S_(8,13)| = 245025; |K_(8,13)| = 680093398905
# |S_(9,13)| = 48400; |K_(9,13)| = 831915336744
# |S_(10,13)| = 4356; |K_(10,13)| = 1011549671624
# |S_(11,13)| = 144; |K_(11,13)| = 1073507289684
# |S_(12,13)| = 1; |K_(12,13)| = 1081389904281
13 550005952989718178915472
# n=14
# |S_(0,1)| = 1; |K_(0,1)| = 14899783667601
# |S_(0,2)| = 169; |K_(0,2)| = 14855851533369
# |S_(1,2)| = 8281; |K_(1,2)| = 14854344940281
# |S_(0,3)| = 6084; |K_(0,3)| = 14418183890684
# |S_(1,3)| = 529984; |K_(1,3)| = 14416677813384
# |S_(2,3)| = 5597956; |K_(2,3)| = 14372750746956
# |S_(0,4)| = 81796; |K_(0,4)| = 12683332684596
# |S_(1,4)| = 9018009; |K_(1,4)| = 12681835019609
# |S_(2,4)| = 169338169; |K_(2,4)| = 12638063205369
# |S_(3,4)| = 677352676; |K_(3,4)| = 12200903571276
# |S_(0,5)| = 511225; |K_(0,5)| = 10131150681225
# |S_(1,5)| = 64128064; |K_(1,5)| = 10129707696864
# |S_(2,5)| = 1524043521; |K_(2,5)| = 10087235477921
# |S_(3,5)| = 10837642816; |K_(3,5)| = 9658881428616
# |S_(4,5)| = 20489918449; |K_(4,5)| = 7933682422449
# |S_(0,6)| = 1656369; |K_(0,6)| = 9705788087569
# |S_(1,6)| = 225450225; |K_(1,6)| = 9704505280225
# |S_(2,6)| = 6096174084; |K_(2,6)| = 9666443869684
# |S_(3,6)| = 54865566756; |K_(3,6)| = 9277545613756
# |S_(4,6)| = 184409266041; |K_(4,6)| = 7672238031241
# |S_(5,6)| = 184409266041; |K_(5,6)| = 5120055598441
# |S_(0,7)| = 2944656; |K_(0,7)| = 10526133729256
# |S_(1,7)| = 424030464; |K_(1,7)| = 10525048213864
# |S_(2,7)| = 12441171600; |K_(2,7)| = 10493133220600
# |S_(3,7)| = 127397597184; |K_(3,7)| = 10170421997584
# |S_(4,7)| = 541937434896; |K_(4,7)| = 8850110553496
# |S_(5,7)| = 963444328704; |K_(5,7)| = 6719435014504
# |S_(6,7)| = 541937434896; |K_(6,7)| = 5872564381896
# |S_(0,8)| = 2944656; |K_(0,8)| = 9705789375856
# |S_(1,8)| = 441882441; |K_(1,8)| = 9704721712441
# |S_(2,8)| = 13716391689; |K_(2,8)| = 9674064087289
# |S_(3,8)| = 152404352100; |K_(3,8)| = 9375084399100
# |S_(4,8)| = 737637064164; |K_(4,8)| = 8225465829364
# |S_(5,8)| = 1659683394369; |K_(5,8)| = 6595329726769
# |S_(6,8)| = 1659683394369; |K_(6,8)| = 6169965987969
# |S_(7,8)| = 541937434896; |K_(7,8)| = 5872564381896
# |S_(0,9)| = 1656369; |K_(0,9)| = 10131151826369
# |S_(1,9)| = 256512256; |K_(1,9)| = 10129900081056
# |S_(2,9)| = 8297570281; |K_(2,9)| = 10094009004681
# |S_(3,9)| = 97538785344; |K_(3,9)| = 9745582571144
# |S_(4,9)| = 512247961225; |K_(4,9)| = 8425440465225
# |S_(5,9)| = 1311354780736; |K_(5,9)| = 6672364851936
# |S_(6,9)| = 1659683394369; |K_(6,9)| = 6595329726769
# |S_(7,9)| = 963444328704; |K_(7,9)| = 6719435014504
# |S_(8,9)| = 184409266041; |K_(8,9)| = 5120055598441
# |S_(0,10)| = 511225; |K_(0,10)| = 12683333114025
# |S_(1,10)| = 81162081; |K_(1,10)| = 12681907163681
# |S_(2,10)| = 2709410704; |K_(2,10)| = 12640603277904
# |S_(3,10)| = 33190281124; |K_(3,10)| = 12233416499724
# |S_(4,10)| = 184409266041; |K_(4,10)| = 10649784202841
# |S_(5,10)| = 512247961225; |K_(5,10)| = 8425440465225
# |S_(6,10)| = 737637064164; |K_(6,10)| = 8225465829364
# |S_(7,10)| = 541937434896; |K_(7,10)| = 8850110553496
# |S_(8,10)| = 184409266041; |K_(8,10)| = 7672238031241
# |S_(9,10)| = 20489918449; |K_(9,10)| = 7933682422449
# |S_(0,11)| = 81796; |K_(0,11)| = 14418183966396
# |S_(1,11)| = 13249600; |K_(1,11)| = 14416690533000
# |S_(2,11)| = 453434436; |K_(2,11)| = 14373198583436
# |S_(3,11)| = 5732306944; |K_(3,11)| = 13940809807344
# |S_(4,11)| = 33190281124; |K_(4,11)| = 12233416499724
# |S_(5,11)| = 97538785344; |K_(5,11)| = 9745582571144
# |S_(6,11)| = 152404352100; |K_(6,11)| = 9375084399100
# |S_(7,11)| = 127397597184; |K_(7,11)| = 10170421997584
# |S_(8,11)| = 54865566756; |K_(8,11)| = 9277545613756
# |S_(9,11)| = 10837642816; |K_(9,11)| = 9658881428616
# |S_(10,11)| = 677352676; |K_(10,11)| = 12200903571276
# |S_(0,12)| = 6084; |K_(0,12)| = 14855851539284
# |S_(1,12)| = 1002001; |K_(1,12)| = 14854345934001
# |S_(2,12)| = 34987225; |K_(2,12)| = 14810447784825
# |S_(3,12)| = 453434436; |K_(3,12)| = 14373198583436
# |S_(4,12)| = 2709410704; |K_(4,12)| = 12640603277904
# |S_(5,12)| = 8297570281; |K_(5,12)| = 10094009004681
# |S_(6,12)| = 13716391689; |K_(6,12)| = 9674064087289
# |S_(7,12)| = 12441171600; |K_(7,12)| = 10493133220600
# |S_(8,12)| = 6096174084; |K_(8,12)| = 9666443869684
# |S_(9,12)| = 1524043521; |K_(9,12)| = 10087235477921
# |S_(10,12)| = 169338169; |K_(10,12)| = 12638063205369
# |S_(11,12)| = 5597956; |K_(11,12)| = 14372750746956
# |S_(0,13)| = 169; |K_(0,13)| = 14899783667769
# |S_(1,13)| = 28224; |K_(1,13)| = 14898277094624
# |S_(2,13)| = 1002001; |K_(2,13)| = 14854345934001
# |S_(3,13)| = 13249600; |K_(3,13)| = 14416690533000
# |S_(4,13)| = 81162081; |K_(4,13)| = 12681907163681
# |S_(5,13)| = 256512256; |K_(5,13)| = 10129900081056
# |S_(6,13)| = 441882441; |K_(6,13)| = 9704721712441
# |S_(7,13)| = 424030464; |K_(7,13)| = 10525048213864
# |S_(8,13)| = 225450225; |K_(8,13)| = 9704505280225
# |S_(9,13)| = 64128064; |K_(9,13)| = 10129707696864
# |S_(10,13)| = 9018009; |K_(10,13)| = 12681835019609
# |S_(11,13)| = 529984; |K_(11,13)| = 14416677813384
# |S_(12,13)| = 8281; |K_(12,13)| = 14854344940281
# |S_(0,14)| = 1; |K_(0,14)| = 14901290268801
# |S_(1,14)| = 169; |K_(1,14)| = 14899783667769
# |S_(2,14)| = 6084; |K_(2,14)| = 14855851539284
# |S_(3,14)| = 81796; |K_(3,14)| = 14418183966396
# |S_(4,14)| = 511225; |K_(4,14)| = 12683333114025
# |S_(5,14)| = 1656369; |K_(5,14)| = 10131151826369
# |S_(6,14)| = 2944656; |K_(6,14)| = 9705789375856
# |S_(7,14)| = 2944656; |K_(7,14)| = 10526133729256
# |S_(8,14)| = 1656369; |K_(8,14)| = 9705788087569
# |S_(9,14)| = 511225; |K_(9,14)| = 10131150681225
# |S_(10,14)| = 81796; |K_(10,14)| = 12683332684596
# |S_(11,14)| = 6084; |K_(11,14)| = 14418183890684
# |S_(12,14)| = 169; |K_(12,14)| = 14855851533369
# |S_(13,14)| = 1; |K_(13,14)| = 14899783667601
14 108007620360200608500699120
# n=15
# |S_(0,1)| = 1; |K_(0,1)| = 207419355388081
# |S_(0,2)| = 196; |K_(0,2)| = 207181544183476
# |S_(1,2)| = 11025; |K_(1,2)| = 207174729721185
# |S_(0,3)| = 8281; |K_(0,3)| = 204259183603561
# |S_(1,3)| = 828100; |K_(1,3)| = 204252369950260
# |S_(2,3)| = 10144225; |K_(2,3)| = 204014568061585
# |S_(0,4)| = 132496; |K_(0,4)| = 189199198132576
# |S_(1,4)| = 16769025; |K_(1,4)| = 189192400295985
# |S_(2,4)| = 365192100; |K_(2,4)| = 188954937514260
# |S_(3,4)| = 1714374025; |K_(3,4)| = 186033926108185
# |S_(0,5)| = 1002001; |K_(0,5)| = 156510171445441
# |S_(1,5)| = 144288144; |K_(1,5)| = 156503500258464
# |S_(2,5)| = 3976941969; |K_(2,5)| = 156269521707489
# |S_(3,5)| = 33190281124; |K_(3,5)| = 153376374458644
# |S_(4,5)| = 74678132529; |K_(4,5)| = 138357876714849
# |S_(0,6)| = 4008004; |K_(0,6)| = 135071842015924
# |S_(1,6)| = 626250625; |K_(1,6)| = 135065649785425
# |S_(2,6)| = 19639219600; |K_(2,6)| = 134846851549600
# |S_(3,6)| = 207439257025; |K_(3,6)| = 132112290999025
# |S_(4,6)| = 829757028100; |K_(4,6)| = 117674623174900
# |S_(5,6)| = 1004006004001; |K_(5,6)| = 85159844594161
# |S_(0,7)| = 9018009; |K_(0,7)| = 144915979266729
# |S_(1,7)| = 1490732100; |K_(1,7)| = 144910646507700
# |S_(2,7)| = 50726300625; |K_(2,7)| = 144722070871425
# |S_(3,7)| = 609617408400; |K_(3,7)| = 142358601391200
# |S_(4,7)| = 3086188130025; |K_(4,7)| = 129775186517625
# |S_(5,7)| = 6638733577476; |K_(5,7)| = 100638704408436
# |S_(6,7)| = 4610231651025; |K_(6,7)| = 77171870046465
# |S_(0,8)| = 11778624; |K_(0,8)| = 144915982027344
# |S_(1,8)| = 2029052025; |K_(1,8)| = 144911184827625
# |S_(2,8)| = 73045872900; |K_(2,8)| = 144744390443700
# |S_(3,8)| = 952527200625; |K_(3,8)| = 142701511183425
# |S_(4,8)| = 5486556675600; |K_(4,8)| = 132175555063200
# |S_(5,8)| = 14937150549321; |K_(5,8)| = 108937121380281
# |S_(6,8)| = 18440926604100; |K_(6,8)| = 91002564999540
# |S_(7,8)| = 7620995178225; |K_(7,8)| = 90026765814465
# |S_(0,9)| = 9018009; |K_(0,9)| = 135071847025929
# |S_(1,9)| = 1603201600; |K_(1,9)| = 135066626736400
# |S_(2,9)| = 60145110025; |K_(2,9)| = 134887357440025
# |S_(3,9)| = 829757028100; |K_(3,9)| = 132734608770100
# |S_(4,9)| = 5185981425625; |K_(4,9)| = 122030847572425
# |S_(5,9)| = 16064096064016; |K_(5,9)| = 100219934654176
# |S_(6,9)| = 25100150100025; |K_(6,9)| = 87817656254665
# |S_(7,9)| = 18440926604100; |K_(7,9)| = 91002564999540
# |S_(8,9)| = 4610231651025; |K_(8,9)| = 77171870046465
# |S_(0,10)| = 4008004; |K_(0,10)| = 156510174451444
# |S_(1,10)| = 730458729; |K_(1,10)| = 156504086429049
# |S_(2,10)| = 28280476224; |K_(2,10)| = 156293825241744
# |S_(3,10)| = 406580943769; |K_(3,10)| = 153749765121289
# |S_(4,10)| = 2688412771044; |K_(4,10)| = 140971611353364
# |S_(5,10)| = 9036054036009; |K_(5,10)| = 114630225061689
# |S_(6,10)| = 16064096064016; |K_(6,10)| = 100219934654176
# |S_(7,10)| = 14937150549321; |K_(7,10)| = 108937121380281
# |S_(8,10)| = 6638733577476; |K_(8,10)| = 100638704408436
# |S_(9,10)| = 1004006004001; |K_(9,10)| = 85159844594161
# |S_(0,11)| = 1002001; |K_(0,11)| = 189199199002081
# |S_(1,11)| = 186322500; |K_(1,11)| = 189192569849460
# |S_(2,11)| = 7395140025; |K_(2,11)| = 188961967462185
# |S_(3,11)| = 109719937600; |K_(3,11)| = 186141931671760
# |S_(4,11)| = 756038945025; |K_(4,11)| = 171728265083985
# |S_(5,11)| = 2688412771044; |K_(5,11)| = 140971611353364
# |S_(6,11)| = 5185981425625; |K_(6,11)| = 122030847572425
# |S_(7,11)| = 5486556675600; |K_(7,11)| = 132175555063200
# |S_(8,11)| = 3086188130025; |K_(8,11)| = 129775186517625
# |S_(9,11)| = 829757028100; |K_(9,11)| = 117674623174900
# |S_(10,11)| = 74678132529; |K_(10,11)| = 138357876714849
# |S_(0,12)| = 132496; |K_(0,12)| = 204259183727776
# |S_(1,12)| = 25050025; |K_(1,12)| = 204252394172185
# |S_(2,12)| = 1014422500; |K_(2,12)| = 204015572339860
# |S_(3,12)| = 15429366225; |K_(3,12)| = 201107626695585
# |S_(4,12)| = 109719937600; |K_(4,12)| = 186141931671760
# |S_(5,12)| = 406580943769; |K_(5,12)| = 153749765121289
# |S_(6,12)| = 829757028100; |K_(6,12)| = 132734608770100
# |S_(7,12)| = 952527200625; |K_(7,12)| = 142701511183425
# |S_(8,12)| = 609617408400; |K_(8,12)| = 142358601391200
# |S_(9,12)| = 207439257025; |K_(9,12)| = 132112290999025
# |S_(10,12)| = 33190281124; |K_(10,12)| = 153376374458644
# |S_(11,12)| = 1714374025; |K_(11,12)| = 186033926108185
# |S_(0,13)| = 8281; |K_(0,13)| = 207181544191561
# |S_(1,13)| = 1587600; |K_(1,13)| = 207174731297760
# |S_(2,13)| = 65367225; |K_(2,13)| = 206936983872585
# |S_(3,13)| = 1014422500; |K_(3,13)| = 204015572339860
# |S_(4,13)| = 7395140025; |K_(4,13)| = 188961967462185
# |S_(5,13)| = 28280476224; |K_(5,13)| = 156293825241744
# |S_(6,13)| = 60145110025; |K_(6,13)| = 134887357440025
# |S_(7,13)| = 73045872900; |K_(7,13)| = 144744390443700
# |S_(8,13)| = 50726300625; |K_(8,13)| = 144722070871425
# |S_(9,13)| = 19639219600; |K_(9,13)| = 134846851549600
# |S_(10,13)| = 3976941969; |K_(10,13)| = 156269521707489
# |S_(11,13)| = 365192100; |K_(11,13)| = 188954937514260
# |S_(12,13)| = 10144225; |K_(12,13)| = 204014568061585
# |S_(0,14)| = 196; |K_(0,14)| = 207419355388276
# |S_(1,14)| = 38025; |K_(1,14)| = 207412540952985
# |S_(2,14)| = 1587600; |K_(2,14)| = 207174731297760
# |S_(3,14)| = 25050025; |K_(3,14)| = 204252394172185
# |S_(4,14)| = 186322500; |K_(4,14)| = 189192569849460
# |S_(5,14)| = 730458729; |K_(5,14)| = 156504086429049
# |S_(6,14)| = 1603201600; |K_(6,14)| = 135066626736400
# |S_(7,14)| = 2029052025; |K_(7,14)| = 144911184827625
# |S_(8,14)| = 1490732100; |K_(8,14)| = 144910646507700
# |S_(9,14)| = 626250625; |K_(9,14)| = 135065649785425
# |S_(10,14)| = 144288144; |K_(10,14)| = 156503500258464
# |S_(11,14)| = 16769025; |K_(11,14)| = 189192400295985
# |S_(12,14)| = 828100; |K_(12,14)| = 204252369950260
# |S_(13,14)| = 11025; |K_(13,14)| = 207174729721185
# |S_(0,15)| = 1; |K_(0,15)| = 207426169861201
# |S_(1,15)| = 196; |K_(1,15)| = 207419355388276
# |S_(2,15)| = 8281; |K_(2,15)| = 207181544191561
# |S_(3,15)| = 132496; |K_(3,15)| = 204259183727776
# |S_(4,15)| = 1002001; |K_(4,15)| = 189199199002081
# |S_(5,15)| = 4008004; |K_(5,15)| = 156510174451444
# |S_(6,15)| = 9018009; |K_(6,15)| = 135071847025929
# |S_(7,15)| = 11778624; |K_(7,15)| = 144915982027344
# |S_(8,15)| = 9018009; |K_(8,15)| = 144915979266729
# |S_(9,15)| = 4008004; |K_(9,15)| = 135071842015924
# |S_(10,15)| = 1002001; |K_(10,15)| = 156510171445441
# |S_(11,15)| = 132496; |K_(11,15)| = 189199198132576
# |S_(12,15)| = 8281; |K_(12,15)| = 204259183603561
# |S_(13,15)| = 196; |K_(13,15)| = 207181544183476
# |S_(14,15)| = 1; |K_(14,15)| = 207419355388081
15 21569526154939330279935568704
# n=16
# |S_(0,1)| = 1; |K_(0,1)| = 2913659757797986
# |S_(0,2)| = 225; |K_(0,2)| = 2912403461003730
# |S_(1,2)| = 14400; |K_(1,2)| = 2912372922256155
# |S_(0,3)| = 11025; |K_(0,3)| = 2893762213048530
# |S_(1,3)| = 1254400; |K_(1,3)| = 2893731675530155
# |S_(2,3)| = 17640000; |K_(2,3)| = 2892475395121275
# |S_(0,4)| = 207025; |K_(0,4)| = 2773195181855530
# |S_(1,4)| = 29811600; |K_(1,4)| = 2773164672698355
# |S_(2,4)| = 745290000; |K_(2,4)| = 2771909091382275
# |S_(3,4)| = 4057690000; |K_(3,4)| = 2753271155816275
# |S_(0,5)| = 1863225; |K_(0,5)| = 2418023140879050
# |S_(1,5)| = 305270784; |K_(1,5)| = 2417992905524859
# |S_(2,5)| = 9658958400; |K_(2,5)| = 2416745962417995
# |S_(3,5)| = 93489177600; |K_(3,5)| = 2398188544671195
# |S_(4,5)| = 246869859600; |K_(4,5)| = 2277774893964195
# |S_(0,6)| = 9018009; |K_(0,6)| = 2000551488519834
# |S_(1,6)| = 1603201600; |K_(1,6)| = 2000522543941675
# |S_(2,6)| = 57715257600; |K_(2,6)| = 1999322359203195
# |S_(3,6)| = 707011905600; |K_(3,6)| = 1981330407885195
# |S_(4,6)| = 3319028112400; |K_(4,6)| = 1863375392702995
# |S_(5,6)| = 4779400481856; |K_(5,6)| = 1509663722439771
# |S_(0,7)| = 25050025; |K_(0,7)| = 1972003521053530
# |S_(1,7)| = 4711449600; |K_(1,7)| = 1971977668691355
# |S_(2,7)| = 184041000000; |K_(2,7)| = 1970900701447275
# |S_(3,7)| = 2565122560000; |K_(3,7)| = 1954640535041275
# |S_(4,7)| = 15240435210000; |K_(4,7)| = 1846748816302275
# |S_(5,7)| = 39015514137600; |K_(5,7)| = 1515351852597195
# |S_(6,7)| = 32783869518400; |K_(6,7)| = 1091648548463995
# |S_(0,8)| = 41409225; |K_(0,8)| = 2110778457196230
# |S_(1,8)| = 8116208100; |K_(1,8)| = 2110755993233355
# |S_(2,8)| = 335414722500; |K_(2,8)| = 2109826994953275
# |S_(3,8)| = 5072630062500; |K_(3,8)| = 2095922962327275
# |S_(4,8)| = 34290979222500; |K_(4,8)| = 2004574280098275
# |S_(5,8)| = 111102772680900; |K_(5,8)| = 1726214030923995
# |S_(6,8)| = 165968339436900; |K_(6,8)| = 1363607938165995
# |S_(7,8)| = 84677724202500; |K_(7,8)| = 1253769339433275
# |S_(0,9)| = 41409225; |K_(0,9)| = 1972003537412730
# |S_(1,9)| = 8375910400; |K_(1,9)| = 1971981333152155
# |S_(2,9)| = 360720360000; |K_(2,9)| = 1971077380807275
# |S_(3,9)| = 5771525760000; |K_(3,9)| = 1957846938241275
# |S_(4,9)| = 42334542250000; |K_(4,9)| = 1873842923342275
# |S_(5,9)| = 156062056550400; |K_(5,9)| = 1632398395009995
# |S_(6,9)| = 295054825665600; |K_(6,9)| = 1353919504611195
# |S_(7,9)| = 267623424640000; |K_(7,9)| = 1297940120087275
# |S_(8,9)| = 84677724202500; |K_(8,9)| = 1253769339433275
# |S_(0,10)| = 25050025; |K_(0,10)| = 2000551504551850
# |S_(1,10)| = 5194373184; |K_(1,10)| = 2000526135113259
# |S_(2,10)| = 230861030400; |K_(2,10)| = 1999495504975995
# |S_(3,10)| = 3849287041600; |K_(3,10)| = 1984472683021195
# |S_(4,10)| = 29871253011600; |K_(4,10)| = 1889927617602195
# |S_(5,10)| = 119485012046400; |K_(5,10)| = 1624369334004315
# |S_(6,10)| = 257025537024256; |K_(6,10)| = 1344438199468171
# |S_(7,10)| = 295054825665600; |K_(7,10)| = 1353919504611195
# |S_(8,10)| = 165968339436900; |K_(8,10)| = 1363607938165995
# |S_(9,10)| = 32783869518400; |K_(9,10)| = 1091648548463995
# |S_(0,11)| = 9018009; |K_(0,11)| = 2418023148033834
# |S_(1,11)| = 1907942400; |K_(1,11)| = 2417994508196475
# |S_(2,11)| = 86930625600; |K_(2,11)| = 2416823234085195
# |S_(3,11)| = 1495826841600; |K_(3,11)| = 2399590882335195
# |S_(4,11)| = 12096623120400; |K_(4,11)| = 2289624647224995
# |S_(5,11)| = 51190934086656; |K_(5,11)| = 1973546915558571
# |S_(6,11)| = 119485012046400; |K_(6,11)| = 1624369334004315
# |S_(7,11)| = 156062056550400; |K_(7,11)| = 1632398395009995
# |S_(8,11)| = 111102772680900; |K_(8,11)| = 1726214030923995
# |S_(9,11)| = 39015514137600; |K_(9,11)| = 1515351852597195
# |S_(10,11)| = 4779400481856; |K_(10,11)| = 1509663722439771
# |S_(0,12)| = 1863225; |K_(0,12)| = 2773195183511730
# |S_(1,12)| = 400800400; |K_(1,12)| = 2773165043687155
# |S_(2,12)| = 18632250000; |K_(2,12)| = 2771926978342275
# |S_(3,12)| = 328672890000; |K_(3,12)| = 2753595771016275
# |S_(4,12)| = 2742998440000; |K_(4,12)| = 2635443065177275
# |S_(5,12)| = 12096623120400; |K_(5,12)| = 2289624647224995
# |S_(6,12)| = 29871253011600; |K_(6,12)| = 1889927617602195
# |S_(7,12)| = 42334542250000; |K_(7,12)| = 1873842923342275
# |S_(8,12)| = 34290979222500; |K_(8,12)| = 2004574280098275
# |S_(9,12)| = 15240435210000; |K_(9,12)| = 1846748816302275
# |S_(10,12)| = 3319028112400; |K_(10,12)| = 1863375392702995
# |S_(11,12)| = 246869859600; |K_(11,12)| = 2277774893964195
# |S_(0,13)| = 207025; |K_(0,13)| = 2893762213244530
# |S_(1,13)| = 45158400; |K_(1,13)| = 2893731719434155
# |S_(2,13)| = 2134440000; |K_(2,13)| = 2892477511921275
# |S_(3,13)| = 38416000000; |K_(3,13)| = 2873872545515275
# |S_(4,13)| = 328672890000; |K_(4,13)| = 2753595771016275
# |S_(5,13)| = 1495826841600; |K_(5,13)| = 2399590882335195
# |S_(6,13)| = 3849287041600; |K_(6,13)| = 1984472683021195
# |S_(7,13)| = 5771525760000; |K_(7,13)| = 1957846938241275
# |S_(8,13)| = 5072630062500; |K_(8,13)| = 2095922962327275
# |S_(9,13)| = 2565122560000; |K_(9,13)| = 1954640535041275
# |S_(10,13)| = 707011905600; |K_(10,13)| = 1981330407885195
# |S_(11,13)| = 93489177600; |K_(11,13)| = 2398188544671195
# |S_(12,13)| = 4057690000; |K_(12,13)| = 2753271155816275
# |S_(0,14)| = 11025; |K_(0,14)| = 2912403461014530
# |S_(1,14)| = 2433600; |K_(1,14)| = 2912372924675355
# |S_(2,14)| = 116640000; |K_(2,14)| = 2911116742087275
# |S_(3,14)| = 2134440000; |K_(3,14)| = 2892477511921275
# |S_(4,14)| = 18632250000; |K_(4,14)| = 2771926978342275
# |S_(5,14)| = 86930625600; |K_(5,14)| = 2416823234085195
# |S_(6,14)| = 230861030400; |K_(6,14)| = 1999495504975995
# |S_(7,14)| = 360720360000; |K_(7,14)| = 1971077380807275
# |S_(8,14)| = 335414722500; |K_(8,14)| = 2109826994953275
# |S_(9,14)| = 184041000000; |K_(9,14)| = 1970900701447275
# |S_(10,14)| = 57715257600; |K_(10,14)| = 1999322359203195
# |S_(11,14)| = 9658958400; |K_(11,14)| = 2416745962417995
# |S_(12,14)| = 745290000; |K_(12,14)| = 2771909091382275
# |S_(13,14)| = 17640000; |K_(13,14)| = 2892475395121275
# |S_(0,15)| = 225; |K_(0,15)| = 2913659757798210
# |S_(1,15)| = 50176; |K_(1,15)| = 2913629219086411
# |S_(2,15)| = 2433600; |K_(2,15)| = 2912372924675355
# |S_(3,15)| = 45158400; |K_(3,15)| = 2893731719434155
# |S_(4,15)| = 400800400; |K_(4,15)| = 2773165043687155
# |S_(5,15)| = 1907942400; |K_(5,15)| = 2417994508196475
# |S_(6,15)| = 5194373184; |K_(6,15)| = 2000526135113259
# |S_(7,15)| = 8375910400; |K_(7,15)| = 1971981333152155
# |S_(8,15)| = 8116208100; |K_(8,15)| = 2110755993233355
# |S_(9,15)| = 4711449600; |K_(9,15)| = 1971977668691355
# |S_(10,15)| = 1603201600; |K_(10,15)| = 2000522543941675
# |S_(11,15)| = 305270784; |K_(11,15)| = 2417992905524859
# |S_(12,15)| = 29811600; |K_(12,15)| = 2773164672698355
# |S_(13,15)| = 1254400; |K_(13,15)| = 2893731675530155
# |S_(14,15)| = 14400; |K_(14,15)| = 2912372922256155
# |S_(0,16)| = 1; |K_(0,16)| = 2913690296559736
# |S_(1,16)| = 225; |K_(1,16)| = 2913659757798210
# |S_(2,16)| = 11025; |K_(2,16)| = 2912403461014530
# |S_(3,16)| = 207025; |K_(3,16)| = 2893762213244530
# |S_(4,16)| = 1863225; |K_(4,16)| = 2773195183511730
# |S_(5,16)| = 9018009; |K_(5,16)| = 2418023148033834
# |S_(6,16)| = 25050025; |K_(6,16)| = 2000551504551850
# |S_(7,16)| = 41409225; |K_(7,16)| = 1972003537412730
# |S_(8,16)| = 41409225; |K_(8,16)| = 2110778457196230
# |S_(9,16)| = 25050025; |K_(9,16)| = 1972003521053530
# |S_(10,16)| = 9018009; |K_(10,16)| = 2000551488519834
# |S_(11,16)| = 1863225; |K_(11,16)| = 2418023140879050
# |S_(12,16)| = 207025; |K_(12,16)| = 2773195181855530
# |S_(13,16)| = 11025; |K_(13,16)| = 2893762213048530
# |S_(14,16)| = 225; |K_(14,16)| = 2912403461003730
# |S_(15,16)| = 1; |K_(15,16)| = 2913659757797986
16 4371800947801400957074108324596
# n=17
# |S_(0,1)| = 1; |K_(0,1)| = 41255302342740121
# |S_(0,2)| = 256; |K_(0,2)| = 41248801658322526
# |S_(1,2)| = 18496; |K_(1,2)| = 41248665884887966
# |S_(0,3)| = 14400; |K_(0,3)| = 41134317482935710
# |S_(1,3)| = 1849600; |K_(1,3)| = 41134181711318110
# |S_(2,3)| = 29593600; |K_(2,3)| = 41127681054644260
# |S_(0,4)| = 313600; |K_(0,4)| = 40229090415894910
# |S_(1,4)| = 50979600; |K_(1,4)| = 40228954693108110
# |S_(2,4)| = 1450086400; |K_(2,4)| = 40222455407797060
# |S_(3,4)| = 9063040000; |K_(3,4)| = 40107978845349700
# |S_(0,5)| = 3312400; |K_(0,5)| = 36790872118948750
# |S_(1,5)| = 612661504; |K_(1,5)| = 36790736954845054
# |S_(2,5)| = 22055814144; |K_(2,5)| = 36784257713579844
# |S_(3,5)| = 245064601600; |K_(3,5)| = 36669996546966340
# |S_(4,5)| = 750510342400; |K_(4,5)| = 35765274925367140
# |S_(0,6)| = 19079424; |K_(0,6)| = 30817816083207774
# |S_(1,6)| = 3829134400; |K_(1,6)| = 30817684119809950
# |S_(2,6)| = 156841345024; |K_(2,6)| = 30811336447602724
# |S_(3,6)| = 2205581414400; |K_(3,6)| = 30698901012271140
# |S_(4,6)| = 12008165478400; |K_(4,6)| = 29803476528995140
# |S_(5,6)| = 20293799658496; |K_(5,6)| = 26373543863230276
# |S_(0,7)| = 64128064; |K_(0,7)| = 27697199089101214
# |S_(1,7)| = 13616089344; |K_(1,7)| = 27697076867609694
# |S_(2,7)| = 605159526400; |K_(2,7)| = 27691167726628900
# |S_(3,7)| = 9682552422400; |K_(3,7)| = 27585760944123940
# |S_(4,7)| = 66718837785600; |K_(4,7)| = 26737570162147140
# |S_(5,7)| = 200453041524736; |K_(5,7)| = 23433086065941316
# |S_(6,7)| = 200453041524736; |K_(6,7)| = 17460030014433316
# |S_(0,8)| = 130873600; |K_(0,8)| = 29614672047483910
# |S_(1,8)| = 28957828900; |K_(1,8)| = 29614565100986410
# |S_(2,8)| = 1361608934400; |K_(2,8)| = 29609397067674060
# |S_(3,8)| = 23639044000000; |K_(3,8)| = 29517190327338700
# |S_(4,8)| = 185330104960000; |K_(4,8)| = 28773654320958700
# |S_(5,8)| = 704717724110400; |K_(5,8)| = 25854823640164140
# |S_(6,8)| = 1252831509529600; |K_(6,8)| = 20429881374075340
# |S_(7,8)| = 773431697209600; |K_(7,8)| = 16829864522600140
# |S_(0,9)| = 165636900; |K_(0,9)| = 29614672082247210
# |S_(1,9)| = 37822470400; |K_(1,9)| = 29614573965627910
# |S_(2,9)| = 1853301049600; |K_(2,9)| = 29609888759789260
# |S_(3,9)| = 34040223360000; |K_(3,9)| = 29527591506698700
# |S_(4,9)| = 289578289000000; |K_(4,9)| = 28877902504998700
# |S_(5,9)| = 1252831509529600; |K_(5,9)| = 26402937425583340
# |S_(6,9)| = 2818870896441600; |K_(6,9)| = 21995920760987340
# |S_(7,9)| = 3093726788838400; |K_(7,9)| = 19150159614228940
# |S_(8,9)| = 1208487026890000; |K_(8,9)| = 19182392743917700
# |S_(0,10)| = 130873600; |K_(0,10)| = 27697199155846750
# |S_(1,10)| = 30636201024; |K_(1,10)| = 27697093887721374
# |S_(2,10)| = 1549208387584; |K_(2,10)| = 27692111775490084
# |S_(3,10)| = 29652816793600; |K_(3,10)| = 27605731208495140
# |S_(4,10)| = 266875351142400; |K_(4,10)| = 26937726675503940
# |S_(5,10)| = 1252831509529600; |K_(5,10)| = 24485464533946180
# |S_(6,10)| = 3207248664395776; |K_(6,10)| = 20466825637304356
# |S_(7,10)| = 4454966575927296; |K_(7,10)| = 18593926509680676
# |S_(8,10)| = 3093726788838400; |K_(8,10)| = 19150159614228940
# |S_(9,10)| = 773431697209600; |K_(9,10)| = 16829864522600140
# |S_(0,11)| = 64128064; |K_(0,11)| = 30817816128256414
# |S_(1,11)| = 15316537600; |K_(1,11)| = 30817695607213150
# |S_(2,11)| = 794009309184; |K_(2,11)| = 30811973615566884
# |S_(3,11)| = 15684134502400; |K_(3,11)| = 30712379565359140
# |S_(4,11)| = 147100027110400; |K_(4,11)| = 29938568390627140
# |S_(5,11)| = 730576787705856; |K_(5,11)| = 27083826851277636
# |S_(6,11)| = 2029379965849600; |K_(6,11)| = 22409573977913380
# |S_(7,11)| = 3207248664395776; |K_(7,11)| = 20466825637304356
# |S_(8,11)| = 2818870896441600; |K_(8,11)| = 21995920760987340
# |S_(9,11)| = 1252831509529600; |K_(9,11)| = 20429881374075340
# |S_(10,11)| = 200453041524736; |K_(10,11)| = 17460030014433316
# |S_(0,12)| = 19079424; |K_(0,12)| = 36790872134715774
# |S_(1,12)| = 4633252624; |K_(1,12)| = 36790740975436174
# |S_(2,12)| = 245064601600; |K_(2,12)| = 36784480722367300
# |S_(3,12)| = 4962558182400; |K_(3,12)| = 36674714040547140
# |S_(4,12)| = 48032661913600; |K_(4,12)| = 35812557076938340
# |S_(5,12)| = 248599045816576; |K_(5,12)| = 32574905160896356
# |S_(6,12)| = 730576787705856; |K_(6,12)| = 27083826851277636
# |S_(7,12)| = 1252831509529600; |K_(7,12)| = 24485464533946180
# |S_(8,12)| = 1252831509529600; |K_(8,12)| = 26402937425583340
# |S_(9,12)| = 704717724110400; |K_(9,12)| = 25854823640164140
# |S_(10,12)| = 200453041524736; |K_(10,12)| = 23433086065941316
# |S_(11,12)| = 20293799658496; |K_(11,12)| = 26373543863230276
# |S_(0,13)| = 3312400; |K_(0,13)| = 40229090418893710
# |S_(1,13)| = 815673600; |K_(1,13)| = 40228955457802110
# |S_(2,13)| = 43865113600; |K_(2,13)| = 40222497822824260
# |S_(3,13)| = 906304000000; |K_(3,13)| = 40108876086309700
# |S_(4,13)| = 8992801440000; |K_(4,13)| = 39211735516409700
# |S_(5,13)| = 48032661913600; |K_(5,13)| = 35812557076938340
# |S_(6,13)| = 147100027110400; |K_(6,13)| = 29938568390627140
# |S_(7,13)| = 266875351142400; |K_(7,13)| = 26937726675503940
# |S_(8,13)| = 289578289000000; |K_(8,13)| = 28877902504998700
# |S_(9,13)| = 185330104960000; |K_(9,13)| = 28773654320958700
# |S_(10,13)| = 66718837785600; |K_(10,13)| = 26737570162147140
# |S_(11,13)| = 12008165478400; |K_(11,13)| = 29803476528995140
# |S_(12,13)| = 750510342400; |K_(12,13)| = 35765274925367140
# |S_(0,14)| = 313600; |K_(0,14)| = 41134317483234910
# |S_(1,14)| = 78145600; |K_(1,14)| = 41134181787614110
# |S_(2,14)| = 4261478400; |K_(2,14)| = 41127685286529060
# |S_(3,14)| = 89520640000; |K_(3,14)| = 41013286370289700
# |S_(4,14)| = 906304000000; |K_(4,14)| = 40108876086309700
# |S_(5,14)| = 4962558182400; |K_(5,14)| = 36674714040547140
# |S_(6,14)| = 15684134502400; |K_(6,14)| = 30712379565359140
# |S_(7,14)| = 29652816793600; |K_(7,14)| = 27605731208495140
# |S_(8,14)| = 34040223360000; |K_(8,14)| = 29527591506698700
# |S_(9,14)| = 23639044000000; |K_(9,14)| = 29517190327338700
# |S_(10,14)| = 9682552422400; |K_(10,14)| = 27585760944123940
# |S_(11,14)| = 2205581414400; |K_(11,14)| = 30698901012271140
# |S_(12,14)| = 245064601600; |K_(12,14)| = 36669996546966340
# |S_(13,14)| = 9063040000; |K_(13,14)| = 40107978845349700
# |S_(0,15)| = 14400; |K_(0,15)| = 41248801658336670
# |S_(1,15)| = 3625216; |K_(1,15)| = 41248665888494686
# |S_(2,15)| = 200052736; |K_(2,15)| = 41242165400504356
# |S_(3,15)| = 4261478400; |K_(3,15)| = 41127685286529060
# |S_(4,15)| = 43865113600; |K_(4,15)| = 40222497822824260
# |S_(5,15)| = 245064601600; |K_(5,15)| = 36784480722367300
# |S_(6,15)| = 794009309184; |K_(6,15)| = 30811973615566884
# |S_(7,15)| = 1549208387584; |K_(7,15)| = 27692111775490084
# |S_(8,15)| = 1853301049600; |K_(8,15)| = 29609888759789260
# |S_(9,15)| = 1361608934400; |K_(9,15)| = 29609397067674060
# |S_(10,15)| = 605159526400; |K_(10,15)| = 27691167726628900
# |S_(11,15)| = 156841345024; |K_(11,15)| = 30811336447602724
# |S_(12,15)| = 22055814144; |K_(12,15)| = 36784257713579844
# |S_(13,15)| = 1450086400; |K_(13,15)| = 40222455407797060
# |S_(14,15)| = 29593600; |K_(14,15)| = 41127681054644260
# |S_(0,16)| = 256; |K_(0,16)| = 41255302342740376
# |S_(1,16)| = 65025; |K_(1,16)| = 41255166569352345
# |S_(2,16)| = 3625216; |K_(2,16)| = 41248665888494686
# |S_(3,16)| = 78145600; |K_(3,16)| = 41134181787614110
# |S_(4,16)| = 815673600; |K_(4,16)| = 40228955457802110
# |S_(5,16)| = 4633252624; |K_(5,16)| = 36790740975436174
# |S_(6,16)| = 15316537600; |K_(6,16)| = 30817695607213150
# |S_(7,16)| = 30636201024; |K_(7,16)| = 27697093887721374
# |S_(8,16)| = 37822470400; |K_(8,16)| = 29614573965627910
# |S_(9,16)| = 28957828900; |K_(9,16)| = 29614565100986410
# |S_(10,16)| = 13616089344; |K_(10,16)| = 27697076867609694
# |S_(11,16)| = 3829134400; |K_(11,16)| = 30817684119809950
# |S_(12,16)| = 612661504; |K_(12,16)| = 36790736954845054
# |S_(13,16)| = 50979600; |K_(13,16)| = 40228954693108110
# |S_(14,16)| = 1849600; |K_(14,16)| = 41134181711318110
# |S_(15,16)| = 18496; |K_(15,16)| = 41248665884887966
# |S_(0,17)| = 1; |K_(0,17)| = 41255438116192921
# |S_(1,17)| = 256; |K_(1,17)| = 41255302342740376
# |S_(2,17)| = 14400; |K_(2,17)| = 41248801658336670
# |S_(3,17)| = 313600; |K_(3,17)| = 41134317483234910
# |S_(4,17)| = 3312400; |K_(4,17)| = 40229090418893710
# |S_(5,17)| = 19079424; |K_(5,17)| = 36790872134715774
# |S_(6,17)| = 64128064; |K_(6,17)| = 30817816128256414
# |S_(7,17)| = 130873600; |K_(7,17)| = 27697199155846750
# |S_(8,17)| = 165636900; |K_(8,17)| = 29614672082247210
# |S_(9,17)| = 130873600; |K_(9,17)| = 29614672047483910
# |S_(10,17)| = 64128064; |K_(10,17)| = 27697199089101214
# |S_(11,17)| = 19079424; |K_(11,17)| = 30817816083207774
# |S_(12,17)| = 3312400; |K_(12,17)| = 36790872118948750
# |S_(13,17)| = 313600; |K_(13,17)| = 40229090415894910
# |S_(14,17)| = 14400; |K_(14,17)| = 41134317482935710
# |S_(15,17)| = 256; |K_(15,17)| = 41248801658322526
# |S_(16,17)| = 1; |K_(16,17)| = 41255302342740121
17 897828555540713658594160811941188
# n=18
# |S_(0,1)| = 1; |K_(0,1)| = 588271400950322101
# |S_(0,2)| = 289; |K_(0,2)| = 588238357086247189
# |S_(1,2)| = 23409; |K_(1,2)| = 588237757608761349
# |S_(0,3)| = 18496; |K_(0,3)| = 587557425570775456
# |S_(1,3)| = 2663424; |K_(1,3)| = 587556826095911424
# |S_(2,3)| = 48108096; |K_(2,3)| = 587523782277280896
# |S_(0,4)| = 462400; |K_(0,4)| = 581108246529827680
# |S_(1,4)| = 84272400; |K_(1,4)| = 581107647136128720
# |S_(2,4)| = 2706080400; |K_(2,4)| = 581074605893861520
# |S_(3,4)| = 19243238400; |K_(3,4)| = 580393690915529580
# |S_(0,5)| = 5664400; |K_(0,5)| = 550614024609252400
# |S_(1,5)| = 1174569984; |K_(1,5)| = 550613426300649024
# |S_(2,5)| = 47735258256; |K_(2,5)| = 550580428997262096
# |S_(3,5)| = 603467956224; |K_(3,5)| = 549900053214470124
# |S_(4,5)| = 2121567033600; |K_(4,5)| = 543452392272155820
# |S_(0,6)| = 38291344; |K_(0,6)| = 479057991262377904
# |S_(1,6)| = 8615552400; |K_(1,6)| = 479057400362130000
# |S_(2,6)| = 398383142976; |K_(2,6)| = 479024746265645376
# |S_(3,6)| = 6374130287616; |K_(3,6)| = 478349790497300076
# |S_(4,6)| = 39838314297600; |K_(4,6)| = 471934075639918380
# |S_(5,6)| = 78083096023296; |K_(5,6)| = 441478098495866796
# |S_(0,7)| = 153165376; |K_(0,7)| = 409152919057426336
# |S_(1,7)| = 36459611136; |K_(1,7)| = 409152355886363136
# |S_(2,7)| = 1829310350400; |K_(2,7)| = 409121104873027200
# |S_(3,7)| = 33301578645504; |K_(3,7)| = 408471645625832364
# |S_(4,7)| = 263420690457600; |K_(4,7)| = 402252585696252780
# |S_(5,7)| = 917874761416704; |K_(5,7)| = 372412817841434604
# |S_(6,7)| = 1077228018607104; |K_(6,7)| = 301016137719123564
# |S_(0,8)| = 378224704; |K_(0,8)| = 410520627219177904
# |S_(1,8)| = 93823365636; |K_(1,8)| = 410520121186809876
# |S_(2,8)| = 4980297428964; |K_(2,8)| = 410491963796798004
# |S_(3,8)| = 98376245510400; |K_(3,8)| = 409904428229389500
# |S_(4,8)| = 885386209593600; |K_(4,8)| = 404242259152081020
# |S_(5,8)| = 3904553184307776; |K_(5,8)| = 376767204201017916
# |S_(6,8)| = 8146536890716224; |K_(6,8)| = 309453154527924924
# |S_(7,8)| = 5985210776852736; |K_(7,8)| = 237386756094235836
# |S_(0,9)| = 590976100; |K_(0,9)| = 435038058593375380
# |S_(1,9)| = 151289881600; |K_(1,9)| = 435037609814771920
# |S_(2,9)| = 8368812552100; |K_(2,9)| = 435012783473367220
# |S_(3,9)| = 174891103129600; |K_(3,9)| = 434498374248454780
# |S_(4,9)| = 1707920929000000; |K_(4,9)| = 429582225032933500
# |S_(5,9)| = 8569664053350400; |K_(5,9)| = 405949746231506620
# |S_(6,9)| = 22629269140878400; |K_(6,9)| = 348453317939533180
# |S_(7,9)| = 29556596428902400; |K_(7,9)| = 285475572907731580
# |S_(8,9)| = 13970110030848400; |K_(8,9)| = 271256794446369820
# |S_(0,10)| = 590976100; |K_(0,10)| = 410520627431929300
# |S_(1,10)| = 155095767684; |K_(1,10)| = 410520182459211924
# |S_(2,10)| = 8853862095936; |K_(2,10)| = 410495837361464976
# |S_(3,10)| = 192817441200384; |K_(3,10)| = 409998869425079484
# |S_(4,10)| = 1992118971585600; |K_(4,10)| = 405348991914073020
# |S_(5,10)| = 10845981067521600; |K_(5,10)| = 383708632084231740
# |S_(6,10)| = 32586147562864896; |K_(6,10)| = 333892765200073596
# |S_(7,10)| = 53866896991674624; |K_(7,10)| = 285268442309057724
# |S_(8,10)| = 45263156499948816; |K_(8,10)| = 278032409754024156
# |S_(9,10)| = 13970110030848400; |K_(9,10)| = 271256794446369820
# |S_(0,11)| = 378224704; |K_(0,11)| = 409152919282485664
# |S_(1,11)| = 101276697600; |K_(1,11)| = 409152420703449600
# |S_(2,11)| = 5926965535296; |K_(2,11)| = 409125202528212096
# |S_(3,11)| = 133206314582016; |K_(3,11)| = 408571550361768876
# |S_(4,11)| = 1434179314713600; |K_(4,11)| = 403423344320508780
# |S_(5,11)| = 8260872852750336; |K_(5,11)| = 379755815932768236
# |S_(6,11)| = 26930700465177600; |K_(6,11)| = 326869610165694060
# |S_(7,11)| = 50651701119811584; |K_(7,11)| = 280685538500502444
# |S_(8,11)| = 53866896991674624; |K_(8,11)| = 285268442309057724
# |S_(9,11)| = 29556596428902400; |K_(9,11)| = 285475572907731580
# |S_(10,11)| = 5985210776852736; |K_(10,11)| = 237386756094235836
# |S_(0,12)| = 153165376; |K_(0,12)| = 479057991377251936
# |S_(1,12)| = 41699273616; |K_(1,12)| = 479057433445851216
# |S_(2,12)| = 2489894643600; |K_(2,12)| = 479026837777146000
# |S_(3,12)| = 57367172588544; |K_(3,12)| = 478400783539601004
# |S_(4,12)| = 637413028761600; |K_(4,12)| = 472531650354382380
# |S_(5,12)| = 3826071705141504; |K_(5,12)| = 445226087104985004
# |S_(6,12)| = 13196043227937024; |K_(6,12)| = 383040025248279084
# |S_(7,12)| = 26930700465177600; |K_(7,12)| = 326869610165694060
# |S_(8,12)| = 32586147562864896; |K_(8,12)| = 333892765200073596
# |S_(9,12)| = 22629269140878400; |K_(9,12)| = 348453317939533180
# |S_(10,12)| = 8146536890716224; |K_(10,12)| = 309453154527924924
# |S_(11,12)| = 1077228018607104; |K_(11,12)| = 301016137719123564
# |S_(0,13)| = 38291344; |K_(0,13)| = 550614024641879344
# |S_(1,13)| = 10571129856; |K_(1,13)| = 550613435697208896
# |S_(2,13)| = 641774027664; |K_(2,13)| = 550581023036031504
# |S_(3,13)| = 15086698905600; |K_(3,13)| = 549914536445419500
# |S_(4,13)| = 171846929721600; |K_(4,13)| = 543622117634843820
# |S_(5,13)| = 1064517474779136; |K_(5,13)| = 514020566254124076
# |S_(6,13)| = 3826071705141504; |K_(6,13)| = 445226087104985004
# |S_(7,13)| = 8260872852750336; |K_(7,13)| = 379755815932768236
# |S_(8,13)| = 10845981067521600; |K_(8,13)| = 383708632084231740
# |S_(9,13)| = 8569664053350400; |K_(9,13)| = 405949746231506620
# |S_(10,13)| = 3904553184307776; |K_(10,13)| = 376767204201017916
# |S_(11,13)| = 917874761416704; |K_(11,13)| = 372412817841434604
# |S_(12,13)| = 78083096023296; |K_(12,13)| = 441478098495866796
# |S_(0,14)| = 5664400; |K_(0,14)| = 581108246535029680
# |S_(1,14)| = 1582448400; |K_(1,14)| = 581107648634304720
# |S_(2,14)| = 97418894400; |K_(2,14)| = 581074700606675520
# |S_(3,14)| = 2328431846400; |K_(3,14)| = 580396000104137580
# |S_(4,14)| = 27060804000000; |K_(4,14)| = 573971553434899500
# |S_(5,14)| = 171846929721600; |K_(5,14)| = 543622117634843820
# |S_(6,14)| = 637413028761600; |K_(6,14)| = 472531650354382380
# |S_(7,14)| = 1434179314713600; |K_(7,14)| = 403423344320508780
# |S_(8,14)| = 1992118971585600; |K_(8,14)| = 405348991914073020
# |S_(9,14)| = 1707920929000000; |K_(9,14)| = 429582225032933500
# |S_(10,14)| = 885386209593600; |K_(10,14)| = 404242259152081020
# |S_(11,14)| = 263420690457600; |K_(11,14)| = 402252585696252780
# |S_(12,14)| = 39838314297600; |K_(12,14)| = 471934075639918380
# |S_(13,14)| = 2121567033600; |K_(13,14)| = 543452392272155820
# |S_(0,15)| = 462400; |K_(0,15)| = 587557425571219360
# |S_(1,15)| = 130507776; |K_(1,15)| = 587556826223755776
# |S_(2,15)| = 8130268224; |K_(2,15)| = 587523790359441024
# |S_(3,15)| = 197050761216; |K_(3,15)| = 586843047764444076
# |S_(4,15)| = 2328431846400; |K_(4,15)| = 580396000104137580
# |S_(5,15)| = 15086698905600; |K_(5,15)| = 549914536445419500
# |S_(6,15)| = 57367172588544; |K_(6,15)| = 478400783539601004
# |S_(7,15)| = 133206314582016; |K_(7,15)| = 408571550361768876
# |S_(8,15)| = 192817441200384; |K_(8,15)| = 409998869425079484
# |S_(9,15)| = 174891103129600; |K_(9,15)| = 434498374248454780
# |S_(10,15)| = 98376245510400; |K_(10,15)| = 409904428229389500
# |S_(11,15)| = 33301578645504; |K_(11,15)| = 408471645625832364
# |S_(12,15)| = 6374130287616; |K_(12,15)| = 478349790497300076
# |S_(13,15)| = 603467956224; |K_(13,15)| = 549900053214470124
# |S_(14,15)| = 19243238400; |K_(14,15)| = 580393690915529580
# |S_(0,16)| = 18496; |K_(0,16)| = 588238357086265396
# |S_(1,16)| = 5267025; |K_(1,16)| = 588237757614004965
# |S_(2,16)| = 331494849; |K_(2,16)| = 588204714076157589
# |S_(3,16)| = 8130268224; |K_(3,16)| = 587523790359441024
# |S_(4,16)| = 97418894400; |K_(4,16)| = 581074700606675520
# |S_(5,16)| = 641774027664; |K_(5,16)| = 550581023036031504
# |S_(6,16)| = 2489894643600; |K_(6,16)| = 479026837777146000
# |S_(7,16)| = 5926965535296; |K_(7,16)| = 409125202528212096
# |S_(8,16)| = 8853862095936; |K_(8,16)| = 410495837361464976
# |S_(9,16)| = 8368812552100; |K_(9,16)| = 435012783473367220
# |S_(10,16)| = 4980297428964; |K_(10,16)| = 410491963796798004
# |S_(11,16)| = 1829310350400; |K_(11,16)| = 409121104873027200
# |S_(12,16)| = 398383142976; |K_(12,16)| = 479024746265645376
# |S_(13,16)| = 47735258256; |K_(13,16)| = 550580428997262096
# |S_(14,16)| = 2706080400; |K_(14,16)| = 581074605893861520
# |S_(15,16)| = 48108096; |K_(15,16)| = 587523782277280896
# |S_(0,17)| = 289; |K_(0,17)| = 588271400950322389
# |S_(1,17)| = 82944; |K_(1,17)| = 588270801472896084
# |S_(2,17)| = 5267025; |K_(2,17)| = 588237757614004965
# |S_(3,17)| = 130507776; |K_(3,17)| = 587556826223755776
# |S_(4,17)| = 1582448400; |K_(4,17)| = 581107648634304720
# |S_(5,17)| = 10571129856; |K_(5,17)| = 550613435697208896
# |S_(6,17)| = 41699273616; |K_(6,17)| = 479057433445851216
# |S_(7,17)| = 101276697600; |K_(7,17)| = 409152420703449600
# |S_(8,17)| = 155095767684; |K_(8,17)| = 410520182459211924
# |S_(9,17)| = 151289881600; |K_(9,17)| = 435037609814771920
# |S_(10,17)| = 93823365636; |K_(10,17)| = 410520121186809876
# |S_(11,17)| = 36459611136; |K_(11,17)| = 409152355886363136
# |S_(12,17)| = 8615552400; |K_(12,17)| = 479057400362130000
# |S_(13,17)| = 1174569984; |K_(13,17)| = 550613426300649024
# |S_(14,17)| = 84272400; |K_(14,17)| = 581107647136128720
# |S_(15,17)| = 2663424; |K_(15,17)| = 587556826095911424
# |S_(16,17)| = 23409; |K_(16,17)| = 588237757608761349
# |S_(0,18)| = 1; |K_(0,18)| = 588272000427831061
# |S_(1,18)| = 289; |K_(1,18)| = 588271400950322389
# |S_(2,18)| = 18496; |K_(2,18)| = 588238357086265396
# |S_(3,18)| = 462400; |K_(3,18)| = 587557425571219360
# |S_(4,18)| = 5664400; |K_(4,18)| = 581108246535029680
# |S_(5,18)| = 38291344; |K_(5,18)| = 550614024641879344
# |S_(6,18)| = 153165376; |K_(6,18)| = 479057991377251936
# |S_(7,18)| = 378224704; |K_(7,18)| = 409152919282485664
# |S_(8,18)| = 590976100; |K_(8,18)| = 410520627431929300
# |S_(9,18)| = 590976100; |K_(9,18)| = 435038058593375380
# |S_(10,18)| = 378224704; |K_(10,18)| = 410520627219177904
# |S_(11,18)| = 153165376; |K_(11,18)| = 409152919057426336
# |S_(12,18)| = 38291344; |K_(12,18)| = 479057991262377904
# |S_(13,18)| = 5664400; |K_(13,18)| = 550614024609252400
# |S_(14,18)| = 462400; |K_(14,18)| = 581108246529827680
# |S_(15,18)| = 18496; |K_(15,18)| = 587557425570775456
# |S_(16,18)| = 289; |K_(16,18)| = 588238357086247189
# |S_(17,18)| = 1; |K_(17,18)| = 588271400950322101
18 186565891073214765905088787601733756
# n=19
# |S_(0,1)| = 1; |K_(0,1)| = 8441130277310299801
# |S_(0,2)| = 324; |K_(0,2)| = 8440964892044592924
# |S_(1,2)| = 29241; |K_(1,2)| = 8440962261210662241
# |S_(0,3)| = 23409; |K_(0,3)| = 8437024504597897209
# |S_(1,3)| = 3755844; |K_(1,3)| = 8437021873767670044
# |S_(2,3)| = 76055841; |K_(2,3)| = 8436856488574262841
# |S_(0,4)| = 665856; |K_(0,4)| = 8393049457255335756
# |S_(1,4)| = 135210384; |K_(1,4)| = 8393046826555920684
# |S_(2,4)| = 4867573824; |K_(2,4)| = 8392881446022576924
# |S_(3,4)| = 39075800976; |K_(3,4)| = 8388941092784085276
# |S_(0,5)| = 9363600; |K_(0,5)| = 8140765342393307100
# |S_(1,5)| = 2163366144; |K_(1,5)| = 8140762713713350044
# |S_(2,5)| = 98568369936; |K_(2,5)| = 8140597424852646636
# |S_(3,5)| = 1406728835136; |K_(3,5)| = 8136658345566393036
# |S_(4,5)| = 5626915340544; |K_(4,5)| = 8092687518409694544
# |S_(0,6)| = 73410624; |K_(0,6)| = 7382402314522595724
# |S_(1,6)| = 18403635600; |K_(1,6)| = 7382399702018861100
# |S_(2,6)| = 954044469504; |K_(2,6)| = 7382235252393987804
# |S_(3,6)| = 17232428230416; |K_(3,6)| = 7378311143331029916
# |S_(4,6)| = 122541711860736; |K_(4,6)| = 7334441405271456336
# |S_(5,6)| = 275718851686656; |K_(5,6)| = 7082310467540555856
# |S_(0,7)| = 344622096; |K_(0,7)| = 6281114172633570396
# |S_(1,7)| = 91402219584; |K_(1,7)| = 6281111632857208284
# |S_(2,7)| = 5141374851600; |K_(2,7)| = 6280951297564133100
# |S_(3,7)| = 105660965839104; |K_(3,7)| = 6277111429708401804
# |S_(4,7)| = 950948692551936; |K_(4,7)| = 6233981670091910736
# |S_(5,7)| = 3803794770207744; |K_(5,7)| = 5984550401298840144
# |S_(6,7)| = 5177387326116096; |K_(6,7)| = 5227560965919990096
# |S_(0,8)| = 1012766976; |K_(0,8)| = 5818372988054174076
# |S_(1,8)| = 279919297476; |K_(1,8)| = 5818370636126744976
# |S_(2,8)| = 16658054519184; |K_(2,8)| = 5818221628996259484
# |S_(3,8)| = 371464333028100; |K_(3,8)| = 5814636047828049600
# |S_(4,8)| = 3803794770207744; |K_(4,8)| = 5774093330922025344
# |S_(5,8)| = 19256711024176704; |K_(5,8)| = 5537262132305267904
# |S_(6,8)| = 46596485935044864; |K_(6,8)| = 4806238879281377664
# |S_(7,8)| = 40177582260319296; |K_(7,8)| = 3698531833446415296
# |S_(0,9)| = 1914762564; |K_(0,9)| = 6194239392299000064
# |S_(1,9)| = 546156472576; |K_(1,9)| = 6194237305706750476
# |S_(2,9)| = 33870234994596; |K_(2,9)| = 6194105244519565296
# |S_(3,9)| = 799061054158224; |K_(3,9)| = 6190930047892010124
# |S_(4,9)| = 8878456157313600; |K_(4,9)| = 6155034395651961600
# |S_(5,9)| = 51139907466126336; |K_(5,9)| = 5945011732090047936
# |S_(6,9)| = 156615966615011904; |K_(6,9)| = 5292124763304175104
# |S_(7,9)| = 240073454493759744; |K_(7,9)| = 4274294109022686144
# |S_(8,9)| = 135041318152739856; |K_(8,9)| = 3706520787434125056
# |S_(0,10)| = 2363904400; |K_(0,10)| = 6194239392748141900
# |S_(1,10)| = 691229285604; |K_(1,10)| = 6194237450779563504
# |S_(2,10)| = 44238674278656; |K_(2,10)| = 6194115612958849356
# |S_(3,10)| = 1087610879270916; |K_(3,10)| = 6191218597717122816
# |S_(4,10)| = 12784976866531584; |K_(4,10)| = 6158940916361179584
# |S_(5,10)| = 79906105415822400; |K_(5,10)| = 5973777930039744000
# |S_(6,10)| = 278428385093354496; |K_(6,10)| = 5413937181782517696
# |S_(7,10)| = 540165272610959424; |K_(7,10)| = 4574385927139885824
# |S_(8,10)| = 540165272610959424; |K_(8,10)| = 4111644741892344624
# |S_(9,10)| = 201728388845450896; |K_(9,10)| = 4149074261469666496
# |S_(0,11)| = 1914762564; |K_(0,11)| = 5818372988956169664
# |S_(1,11)| = 571263872400; |K_(1,11)| = 5818370927471319900
# |S_(2,11)| = 37480622668164; |K_(2,11)| = 5818242451564408464
# |S_(3,11)| = 950948692551936; |K_(3,11)| = 5815215532187573436
# |S_(4,11)| = 11649121483761216; |K_(4,11)| = 5781938657635578816
# |S_(5,11)| = 77026844096706816; |K_(5,11)| = 5595032265377798016
# |S_(6,11)| = 291228037094030400; |K_(6,11)| = 5050870430440363200
# |S_(7,11)| = 642841316165108736; |K_(7,11)| = 4301195567351204736
# |S_(8,11)| = 813596040771465744; |K_(8,11)| = 4009209106710020544
# |S_(9,11)| = 540165272610959424; |K_(9,11)| = 4111644741892344624
# |S_(10,11)| = 135041318152739856; |K_(10,11)| = 3706520787434125056
# |S_(0,12)| = 1012766976; |K_(0,12)| = 6281114173301715276
# |S_(1,12)| = 307213015824; |K_(1,12)| = 6281111848668004524
# |S_(2,12)| = 20565499406400; |K_(2,12)| = 6280966721688687900
# |S_(3,12)| = 534908639560464; |K_(3,12)| = 6277540677382123164
# |S_(4,12)| = 6762301813702656; |K_(4,12)| = 6239793023213061456
# |S_(5,12)| = 46596485935044864; |K_(5,12)| = 6027343092463677264
# |S_(6,12)| = 186385943740179456; |K_(6,12)| = 5408769522334053456
# |S_(7,12)| = 446417580670214400; |K_(7,12)| = 4567513017103851600
# |S_(8,12)| = 642841316165108736; |K_(8,12)| = 4301195567351204736
# |S_(9,12)| = 540165272610959424; |K_(9,12)| = 4574385927139885824
# |S_(10,12)| = 240073454493759744; |K_(10,12)| = 4274294109022686144
# |S_(11,12)| = 40177582260319296; |K_(11,12)| = 3698531833446415296
# |S_(0,13)| = 344622096; |K_(0,13)| = 7382402314793807196
# |S_(1,13)| = 106004941056; |K_(1,13)| = 7382399789620166556
# |S_(2,13)| = 7214961300624; |K_(2,13)| = 7382241513310818924
# |S_(3,13)| = 191471424782400; |K_(3,13)| = 7378485382327581900
# |S_(4,13)| = 2481469665179904; |K_(4,13)| = 7336800333224775504
# |S_(5,13)| = 17646006507945984; |K_(5,13)| = 7099680755196815184
# |S_(6,13)| = 73555662544406784; |K_(6,13)| = 6397227383298517584
# |S_(7,13)| = 186385943740179456; |K_(7,13)| = 5408769522334053456
# |S_(8,13)| = 291228037094030400; |K_(8,13)| = 5050870430440363200
# |S_(9,13)| = 278428385093354496; |K_(9,13)| = 5413937181782517696
# |S_(10,13)| = 156615966615011904; |K_(10,13)| = 5292124763304175104
# |S_(11,13)| = 46596485935044864; |K_(11,13)| = 4806238879281377664
# |S_(12,13)| = 5177387326116096; |K_(12,13)| = 5227560965919990096
# |S_(0,14)| = 73410624; |K_(0,14)| = 8140765342457354124
# |S_(1,14)| = 22850554896; |K_(1,14)| = 8140762734400538796
# |S_(2,14)| = 1577093918976; |K_(2,14)| = 8140598903378195676
# |S_(3,14)| = 42553547262864; |K_(3,14)| = 8136699492384820764
# |S_(4,14)| = 562691534054400; |K_(4,14)| = 8093244583028408400
# |S_(5,14)| = 4102021283256576; |K_(5,14)| = 7844499797906884176
# |S_(6,14)| = 17646006507945984; |K_(6,14)| = 7099680755196815184
# |S_(7,14)| = 46596485935044864; |K_(7,14)| = 6027343092463677264
# |S_(8,14)| = 77026844096706816; |K_(8,14)| = 5595032265377798016
# |S_(9,14)| = 79906105415822400; |K_(9,14)| = 5973777930039744000
# |S_(10,14)| = 51139907466126336; |K_(10,14)| = 5945011732090047936
# |S_(11,14)| = 19256711024176704; |K_(11,14)| = 5537262132305267904
# |S_(12,14)| = 3803794770207744; |K_(12,14)| = 5984550401298840144
# |S_(13,14)| = 275718851686656; |K_(13,14)| = 7082310467540555856
# |S_(0,15)| = 9363600; |K_(0,15)| = 8393049457264033500
# |S_(1,15)| = 2944581696; |K_(1,15)| = 8393046829365291996
# |S_(2,15)| = 205654994064; |K_(2,15)| = 8392881646809997164
# |S_(3,15)| = 5626915340544; |K_(3,15)| = 8388946680623624844
# |S_(4,15)| = 75650750689536; |K_(4,15)| = 8345041657115769936
# |S_(5,15)| = 562691534054400; |K_(5,15)| = 8093244583028408400
# |S_(6,15)| = 2481469665179904; |K_(6,15)| = 7336800333224775504
# |S_(7,15)| = 6762301813702656; |K_(7,15)| = 6239793023213061456
# |S_(8,15)| = 11649121483761216; |K_(8,15)| = 5781938657635578816
# |S_(9,15)| = 12784976866531584; |K_(9,15)| = 6158940916361179584
# |S_(10,15)| = 8878456157313600; |K_(10,15)| = 6155034395651961600
# |S_(11,15)| = 3803794770207744; |K_(11,15)| = 5774093330922025344
# |S_(12,15)| = 950948692551936; |K_(12,15)| = 6233981670091910736
# |S_(13,15)| = 122541711860736; |K_(13,15)| = 7334441405271456336
# |S_(14,15)| = 5626915340544; |K_(14,15)| = 8092687518409694544
# |S_(0,16)| = 665856; |K_(0,16)| = 8437024504598539656
# |S_(1,16)| = 211266225; |K_(1,16)| = 8437021873975180425
# |S_(2,16)| = 14906944836; |K_(2,16)| = 8436856503405151836
# |S_(3,16)| = 412738147809; |K_(3,16)| = 8432916513789636009
# |S_(4,16)| = 5626915340544; |K_(4,16)| = 8388946680623624844
# |S_(5,16)| = 42553547262864; |K_(5,16)| = 8136699492384820764
# |S_(6,16)| = 191471424782400; |K_(6,16)| = 7378485382327581900
# |S_(7,16)| = 534908639560464; |K_(7,16)| = 6277540677382123164
# |S_(8,16)| = 950948692551936; |K_(8,16)| = 5815215532187573436
# |S_(9,16)| = 1087610879270916; |K_(9,16)| = 6191218597717122816
# |S_(10,16)| = 799061054158224; |K_(10,16)| = 6190930047892010124
# |S_(11,16)| = 371464333028100; |K_(11,16)| = 5814636047828049600
# |S_(12,16)| = 105660965839104; |K_(12,16)| = 6277111429708401804
# |S_(13,16)| = 17232428230416; |K_(13,16)| = 7378311143331029916
# |S_(14,16)| = 1406728835136; |K_(14,16)| = 8136658345566393036
# |S_(15,16)| = 39075800976; |K_(15,16)| = 8388941092784085276
# |S_(0,17)| = 23409; |K_(0,17)| = 8440964892044616009
# |S_(1,17)| = 7485696; |K_(1,17)| = 8440962261218118696
# |S_(2,17)| = 532917225; |K_(2,17)| = 8440796876477843025
# |S_(3,17)| = 14906944836; |K_(3,17)| = 8436856503405151836
# |S_(4,17)| = 205654994064; |K_(4,17)| = 8392881646809997164
# |S_(5,17)| = 1577093918976; |K_(5,17)| = 8140598903378195676
# |S_(6,17)| = 7214961300624; |K_(6,17)| = 7382241513310818924
# |S_(7,17)| = 20565499406400; |K_(7,17)| = 6280966721688687900
# |S_(8,17)| = 37480622668164; |K_(8,17)| = 5818242451564408464
# |S_(9,17)| = 44238674278656; |K_(9,17)| = 6194115612958849356
# |S_(10,17)| = 33870234994596; |K_(10,17)| = 6194105244519565296
# |S_(11,17)| = 16658054519184; |K_(11,17)| = 5818221628996259484
# |S_(12,17)| = 5141374851600; |K_(12,17)| = 6280951297564133100
# |S_(13,17)| = 954044469504; |K_(13,17)| = 7382235252393987804
# |S_(14,17)| = 98568369936; |K_(14,17)| = 8140597424852646636
# |S_(15,17)| = 4867573824; |K_(15,17)| = 8392881446022576924
# |S_(16,17)| = 76055841; |K_(16,17)| = 8436856488574262841
# |S_(0,18)| = 324; |K_(0,18)| = 8441130277310300124
# |S_(1,18)| = 104329; |K_(1,18)| = 8441127646476444529
# |S_(2,18)| = 7485696; |K_(2,18)| = 8440962261218118696
# |S_(3,18)| = 211266225; |K_(3,18)| = 8437021873975180425
# |S_(4,18)| = 2944581696; |K_(4,18)| = 8393046829365291996
# |S_(5,18)| = 22850554896; |K_(5,18)| = 8140762734400538796
# |S_(6,18)| = 106004941056; |K_(6,18)| = 7382399789620166556
# |S_(7,18)| = 307213015824; |K_(7,18)| = 6281111848668004524
# |S_(8,18)| = 571263872400; |K_(8,18)| = 5818370927471319900
# |S_(9,18)| = 691229285604; |K_(9,18)| = 6194237450779563504
# |S_(10,18)| = 546156472576; |K_(10,18)| = 6194237305706750476
# |S_(11,18)| = 279919297476; |K_(11,18)| = 5818370636126744976
# |S_(12,18)| = 91402219584; |K_(12,18)| = 6281111632857208284
# |S_(13,18)| = 18403635600; |K_(13,18)| = 7382399702018861100
# |S_(14,18)| = 2163366144; |K_(14,18)| = 8140762713713350044
# |S_(15,18)| = 135210384; |K_(15,18)| = 8393046826555920684
# |S_(16,18)| = 3755844; |K_(16,18)| = 8437021873767670044
# |S_(17,18)| = 29241; |K_(17,18)| = 8440962261210662241
# |S_(0,19)| = 1; |K_(0,19)| = 8441132908144259401
# |S_(1,19)| = 324; |K_(1,19)| = 8441130277310300124
# |S_(2,19)| = 23409; |K_(2,19)| = 8440964892044616009
# |S_(3,19)| = 665856; |K_(3,19)| = 8437024504598539656
# |S_(4,19)| = 9363600; |K_(4,19)| = 8393049457264033500
# |S_(5,19)| = 73410624; |K_(5,19)| = 8140765342457354124
# |S_(6,19)| = 344622096; |K_(6,19)| = 7382402314793807196
# |S_(7,19)| = 1012766976; |K_(7,19)| = 6281114173301715276
# |S_(8,19)| = 1914762564; |K_(8,19)| = 5818372988956169664
# |S_(9,19)| = 2363904400; |K_(9,19)| = 6194239392748141900
# |S_(10,19)| = 1914762564; |K_(10,19)| = 6194239392299000064
# |S_(11,19)| = 1012766976; |K_(11,19)| = 5818372988054174076
# |S_(12,19)| = 344622096; |K_(12,19)| = 6281114172633570396
# |S_(13,19)| = 73410624; |K_(13,19)| = 7382402314522595724
# |S_(14,19)| = 9363600; |K_(14,19)| = 8140765342393307100
# |S_(15,19)| = 665856; |K_(15,19)| = 8393049457255335756
# |S_(16,19)| = 23409; |K_(16,19)| = 8437024504597897209
# |S_(17,19)| = 324; |K_(17,19)| = 8440964892044592924
# |S_(18,19)| = 1; |K_(18,19)| = 8441130277310299801
19 39179671942985764066189784720548069200
# n=20
# |S_(0,1)| = 1; |K_(0,1)| = 121805536572063331681
# |S_(0,2)| = 361; |K_(0,2)| = 121804719990433760641
# |S_(1,2)| = 36100; |K_(1,2)| = 121804708506757587760
# |S_(0,3)| = 29241; |K_(0,3)| = 121782454418229298521
# |S_(1,3)| = 5198400; |K_(1,3)| = 121782442934558259060
# |S_(2,3)| = 117288900; |K_(2,3)| = 121781626353040778160
# |S_(0,4)| = 938961; |K_(0,4)| = 121493582543202372141
# |S_(1,4)| = 211266225; |K_(1,4)| = 121493571059736490785
# |S_(2,4)| = 8474123025; |K_(2,4)| = 121492754486369776185
# |S_(3,4)| = 76267107225; |K_(3,4)| = 121470488981958269385
# |S_(0,5)| = 15023376; |K_(0,5)| = 119522225783187495636
# |S_(1,5)| = 3845984256; |K_(1,5)| = 119522214303342247896
# |S_(2,5)| = 195243794496; |K_(2,5)| = 119521397913110486736
# |S_(3,5)| = 3123900711936; |K_(3,5)| = 119499135269562913176
# |S_(4,5)| = 14106364152336; |K_(4,5)| = 119210274376998517476
# |S_(0,6)| = 135210384; |K_(0,6)| = 112194354190472757204
# |S_(1,6)| = 37558440000; |K_(1,6)| = 112194342744219778200
# |S_(2,6)| = 2169375494400; |K_(2,6)| = 112193528294407261200
# |S_(3,6)| = 43929853761600; |K_(3,6)| = 112171304482681037400
# |S_(4,6)| = 352659103808400; |K_(4,6)| = 111882741336903248100
# |S_(5,6)| = 902807305749504; |K_(5,6)| = 109911934725076228284
# |S_(0,7)| = 736145424; |K_(0,7)| = 97857214118135794644
# |S_(1,7)| = 216336614400; |K_(1,7)| = 97857202850060055000
# |S_(2,7)| = 13558596840000; |K_(2,7)| = 97856399610690709200
# |S_(3,7)| = 312390071193600; |K_(3,7)| = 97834432869960571800
# |S_(4,7)| = 3173931934275600; |K_(4,7)| = 97548422536795817700
# |S_(5,7)| = 14444916891992064; |K_(5,7)| = 95588336761724573244
# |S_(6,7)| = 22570182643737600; |K_(6,7)| = 88268590434641393340
# |S_(0,8)| = 2538950544; |K_(0,8)| = 85909597392490351764
# |S_(1,8)| = 777553604100; |K_(1,8)| = 85909586683828796700
# |S_(2,8)| = 51556564484100; |K_(2,8)| = 85908820881210105300
# |S_(3,8)| = 1288914112102500; |K_(3,8)| = 85887792666553232700
# |S_(4,8)| = 14899847135904900; |K_(4,8)| = 85612531724549199000
# |S_(5,8)| = 85823119502812224; |K_(5,8)| = 83712098236887145404
# |S_(6,8)| = 238397554174478400; |K_(6,8)| = 76536801078723886140
# |S_(7,8)| = 238397554174478400; |K_(7,8)| = 62199661005785988540
# |S_(0,9)| = 5712638724; |K_(0,9)| = 87155984572786727544
# |S_(1,9)| = 1805475942400; |K_(1,9)| = 87155974888873822600
# |S_(2,9)| = 124754156035600; |K_(2,9)| = 87155281255924344400
# |S_(3,9)| = 3299620126982400; |K_(3,9)| = 87136190549690800200
# |S_(4,9)| = 41388464266402500; |K_(4,9)| = 86885407518802384200
# |S_(5,9)| = 271243439416295424; |K_(5,9)| = 85143905733923316204
# |S_(6,9)| = 953590216697913600; |K_(6,9)| = 78498380918370008940
# |S_(7,9)| = 1695271496351846400; |K_(7,9)| = 64902922125086044140
# |S_(8,9)| = 1119144073763523600; |K_(8,9)| = 52379177975049473340
# |S_(0,10)| = 8533694884; |K_(0,10)| = 91642978413249459064
# |S_(1,10)| = 2764917142416; |K_(1,10)| = 91642969685956697976
# |S_(2,10)| = 197162486599936; |K_(2,10)| = 91642347501896584096
# |S_(3,10)| = 5434291036910736; |K_(3,10)| = 91625319058242403896
# |S_(4,10)| = 72115260137779716; |K_(4,10)| = 91403128152315436776
# |S_(5,10)| = 512819627646433536; |K_(5,10)| = 89872475759795129676
# |S_(6,10)| = 2051278510585734144; |K_(6,10)| = 84083063049899504844
# |S_(7,10)| = 4615376648817901824; |K_(7,10)| = 72310021115193774924
# |S_(8,10)| = 5416657317015454224; |K_(8,10)| = 61163685055943079324
# |S_(9,10)| = 2407403252006868544; |K_(9,10)| = 59400818168057181244
# |S_(0,11)| = 8533694884; |K_(0,11)| = 87155984575607783704
# |S_(1,11)| = 2821056160000; |K_(1,11)| = 87155975904454040200
# |S_(2,11)| = 206226257936400; |K_(2,11)| = 87155362728026245200
# |S_(3,11)| = 5865991336857600; |K_(3,11)| = 87138756920900675400
# |S_(4,11)| = 81121389962148900; |K_(4,11)| = 86925140444498130600
# |S_(5,11)| = 610297738686664704; |K_(5,11)| = 85482960033193685484
# |S_(6,11)| = 2648861713049760000; |K_(6,11)| = 80193652414721855340
# |S_(7,11)| = 6781085985407385600; |K_(7,11)| = 69988736614141583340
# |S_(8,11)| = 10072296663871712400; |K_(8,11)| = 61332330565157662140
# |S_(9,11)| = 7958357857873945600; |K_(9,11)| = 60464778936282582940
# |S_(10,11)| = 2407403252006868544; |K_(10,11)| = 59400818168057181244
# |S_(0,12)| = 5712638724; |K_(0,12)| = 85909597395664039944
# |S_(1,12)| = 1920081348900; |K_(1,12)| = 85909587826356541500
# |S_(2,12)| = 143212679122500; |K_(2,12)| = 85908912537324743700
# |S_(3,12)| = 4176081723212100; |K_(3,12)| = 85890679834164342300
# |S_(4,12)| = 59599388543619600; |K_(4,12)| = 85657231265956913700
# |S_(5,12)| = 467259206181977664; |K_(5,12)| = 84093534323566310844
# |S_(6,12)| = 2145577987570305600; |K_(6,12)| = 78443981512119713340
# |S_(7,12)| = 5959938854361960000; |K_(7,12)| = 67921202305973470140
# |S_(8,12)| = 10072296663871712400; |K_(8,12)| = 60085943388034974540
# |S_(9,12)| = 10072296663871712400; |K_(9,12)| = 61332330565157662140
# |S_(10,12)| = 5416657317015454224; |K_(10,12)| = 61163685055943079324
# |S_(11,12)| = 1119144073763523600; |K_(11,12)| = 52379177975049473340
# |S_(0,13)| = 2538950544; |K_(0,13)| = 97857214119938599764
# |S_(1,13)| = 865346457600; |K_(1,13)| = 97857203499069898200
# |S_(2,13)| = 65623608705600; |K_(2,13)| = 97856451675702574800
# |S_(3,13)| = 1952437944960000; |K_(3,13)| = 97836072917834338200
# |S_(4,13)| = 28565387408480400; |K_(4,13)| = 97573813992270022500
# |S_(5,13)| = 231118670271873024; |K_(5,13)| = 95805010515104454204
# |S_(6,13)| = 1105938949543142400; |K_(6,13)| = 89351959201540798140
# |S_(7,13)| = 3250106300698214400; |K_(7,13)| = 77158986479757972540
# |S_(8,13)| = 5959938854361960000; |K_(8,13)| = 67921202305973470140
# |S_(9,13)| = 6781085985407385600; |K_(9,13)| = 69988736614141583340
# |S_(10,13)| = 4615376648817901824; |K_(10,13)| = 72310021115193774924
# |S_(11,13)| = 1695271496351846400; |K_(11,13)| = 64902922125086044140
# |S_(12,13)| = 238397554174478400; |K_(12,13)| = 62199661005785988540
# |S_(0,14)| = 736145424; |K_(0,14)| = 112194354191073692244
# |S_(1,14)| = 253895054400; |K_(1,14)| = 112194342960556392600
# |S_(2,14)| = 19524379449600; |K_(2,14)| = 112193545649411216400
# |S_(3,14)| = 590612478350400; |K_(3,14)| = 112171851165305626200
# |S_(4,14)| = 8816477595210000; |K_(4,14)| = 111891205155394649700
# |S_(5,14)| = 73127391765709824; |K_(5,14)| = 109984159309536188604
# |S_(6,14)| = 361122922299801600; |K_(6,14)| = 102944283247235354940
# |S_(7,14)| = 1105938949543142400; |K_(7,14)| = 89351959201540798140
# |S_(8,14)| = 2145577987570305600; |K_(8,14)| = 78443981512119713340
# |S_(9,14)| = 2648861713049760000; |K_(9,14)| = 80193652414721855340
# |S_(10,14)| = 2051278510585734144; |K_(10,14)| = 84083063049899504844
# |S_(11,14)| = 953590216697913600; |K_(11,14)| = 78498380918370008940
# |S_(12,14)| = 238397554174478400; |K_(12,14)| = 76536801078723886140
# |S_(13,14)| = 22570182643737600; |K_(13,14)| = 88268590434641393340
# |S_(0,15)| = 135210384; |K_(0,15)| = 119522225783307682644
# |S_(1,15)| = 47113307136; |K_(1,15)| = 119522214346609570776
# |S_(2,15)| = 3666244585536; |K_(2,15)| = 119521401384111277776
# |S_(3,15)| = 112460425629696; |K_(3,15)| = 119499244606087830936
# |S_(4,15)| = 1706870062432656; |K_(4,15)| = 119211967140696797796
# |S_(5,15)| = 14444916891992064; |K_(5,15)| = 117253348427497396284
# |S_(6,15)| = 73127391765709824; |K_(6,15)| = 109984159309536188604
# |S_(7,15)| = 231118670271873024; |K_(7,15)| = 95805010515104454204
# |S_(8,15)| = 467259206181977664; |K_(8,15)| = 84093534323566310844
# |S_(9,15)| = 610297738686664704; |K_(9,15)| = 85482960033193685484
# |S_(10,15)| = 512819627646433536; |K_(10,15)| = 89872475759795129676
# |S_(11,15)| = 271243439416295424; |K_(11,15)| = 85143905733923316204
# |S_(12,15)| = 85823119502812224; |K_(12,15)| = 83712098236887145404
# |S_(13,15)| = 14444916891992064; |K_(13,15)| = 95588336761724573244
# |S_(14,15)| = 902807305749504; |K_(14,15)| = 109911934725076228284
# |S_(0,16)| = 15023376; |K_(0,16)| = 121493582543216456556
# |S_(1,16)| = 5281655625; |K_(1,16)| = 121493571064806880185
# |S_(2,16)| = 415232028225; |K_(2,16)| = 121492754893127681385
# |S_(3,16)| = 12889141121025; |K_(3,16)| = 121470501794832283185
# |S_(4,16)| = 198370745892225; |K_(4,16)| = 121181815401409218285
# |S_(5,16)| = 1706870062432656; |K_(5,16)| = 119211967140696797796
# |S_(6,16)| = 8816477595210000; |K_(6,16)| = 111891205155394649700
# |S_(7,16)| = 28565387408480400; |K_(7,16)| = 97573813992270022500
# |S_(8,16)| = 59599388543619600; |K_(8,16)| = 85657231265956913700
# |S_(9,16)| = 81121389962148900; |K_(9,16)| = 86925140444498130600
# |S_(10,16)| = 72115260137779716; |K_(10,16)| = 91403128152315436776
# |S_(11,16)| = 41388464266402500; |K_(11,16)| = 86885407518802384200
# |S_(12,16)| = 14899847135904900; |K_(12,16)| = 85612531724549199000
# |S_(13,16)| = 3173931934275600; |K_(13,16)| = 97548422536795817700
# |S_(14,16)| = 352659103808400; |K_(14,16)| = 111882741336903248100
# |S_(15,16)| = 14106364152336; |K_(15,16)| = 119210274376998517476
# |S_(0,17)| = 938961; |K_(0,17)| = 121782454418230208241
# |S_(1,17)| = 332697600; |K_(1,17)| = 121782442934885758260
# |S_(2,17)| = 26390002500; |K_(2,17)| = 121781626379313491760
# |S_(3,17)| = 827590478400; |K_(3,17)| = 121759361608309476660
# |S_(4,17)| = 12889141121025; |K_(4,17)| = 121470501794832283185
# |S_(5,17)| = 112460425629696; |K_(5,17)| = 119499244606087830936
# |S_(6,17)| = 590612478350400; |K_(6,17)| = 112171851165305626200
# |S_(7,17)| = 1952437944960000; |K_(7,17)| = 97836072917834338200
# |S_(8,17)| = 4176081723212100; |K_(8,17)| = 85890679834164342300
# |S_(9,17)| = 5865991336857600; |K_(9,17)| = 87138756920900675400
# |S_(10,17)| = 5434291036910736; |K_(10,17)| = 91625319058242403896
# |S_(11,17)| = 3299620126982400; |K_(11,17)| = 87136190549690800200
# |S_(12,17)| = 1288914112102500; |K_(12,17)| = 85887792666553232700
# |S_(13,17)| = 312390071193600; |K_(13,17)| = 97834432869960571800
# |S_(14,17)| = 43929853761600; |K_(14,17)| = 112171304482681037400
# |S_(15,17)| = 3123900711936; |K_(15,17)| = 119499135269562913176
# |S_(16,17)| = 76267107225; |K_(16,17)| = 121470488981958269385
# |S_(0,18)| = 29241; |K_(0,18)| = 121804719990433789521
# |S_(1,18)| = 10432900; |K_(1,18)| = 121804708506767984560
# |S_(2,18)| = 834054400; |K_(2,18)| = 121803891925962034660
# |S_(3,18)| = 26390002500; |K_(3,18)| = 121781626379313491760
# |S_(4,18)| = 415232028225; |K_(4,18)| = 121492754893127681385
# |S_(5,18)| = 3666244585536; |K_(5,18)| = 119521401384111277776
# |S_(6,18)| = 19524379449600; |K_(6,18)| = 112193545649411216400
# |S_(7,18)| = 65623608705600; |K_(7,18)| = 97856451675702574800
# |S_(8,18)| = 143212679122500; |K_(8,18)| = 85908912537324743700
# |S_(9,18)| = 206226257936400; |K_(9,18)| = 87155362728026245200
# |S_(10,18)| = 197162486599936; |K_(10,18)| = 91642347501896584096
# |S_(11,18)| = 124754156035600; |K_(11,18)| = 87155281255924344400
# |S_(12,18)| = 51556564484100; |K_(12,18)| = 85908820881210105300
# |S_(13,18)| = 13558596840000; |K_(13,18)| = 97856399610690709200
# |S_(14,18)| = 2169375494400; |K_(14,18)| = 112193528294407261200
# |S_(15,18)| = 195243794496; |K_(15,18)| = 119521397913110486736
# |S_(16,18)| = 8474123025; |K_(16,18)| = 121492754486369776185
# |S_(17,18)| = 117288900; |K_(17,18)| = 121781626353040778160
# |S_(0,19)| = 361; |K_(0,19)| = 121805536572063332041
# |S_(1,19)| = 129600; |K_(1,19)| = 121805525088387252660
# |S_(2,19)| = 10432900; |K_(2,19)| = 121804708506767984560
# |S_(3,19)| = 332697600; |K_(3,19)| = 121782442934885758260
# |S_(4,19)| = 5281655625; |K_(4,19)| = 121493571064806880185
# |S_(5,19)| = 47113307136; |K_(5,19)| = 119522214346609570776
# |S_(6,19)| = 253895054400; |K_(6,19)| = 112194342960556392600
# |S_(7,19)| = 865346457600; |K_(7,19)| = 97857203499069898200
# |S_(8,19)| = 1920081348900; |K_(8,19)| = 85909587826356541500
# |S_(9,19)| = 2821056160000; |K_(9,19)| = 87155975904454040200
# |S_(10,19)| = 2764917142416; |K_(10,19)| = 91642969685956697976
# |S_(11,19)| = 1805475942400; |K_(11,19)| = 87155974888873822600
# |S_(12,19)| = 777553604100; |K_(12,19)| = 85909586683828796700
# |S_(13,19)| = 216336614400; |K_(13,19)| = 97857202850060055000
# |S_(14,19)| = 37558440000; |K_(14,19)| = 112194342744219778200
# |S_(15,19)| = 3845984256; |K_(15,19)| = 119522214303342247896
# |S_(16,19)| = 211266225; |K_(16,19)| = 121493571059736490785
# |S_(17,19)| = 5198400; |K_(17,19)| = 121782442934558259060
# |S_(18,19)| = 36100; |K_(18,19)| = 121804708506757587760
# |S_(0,20)| = 1; |K_(0,20)| = 121805548055739540301
# |S_(1,20)| = 361; |K_(1,20)| = 121805536572063332041
# |S_(2,20)| = 29241; |K_(2,20)| = 121804719990433789521
# |S_(3,20)| = 938961; |K_(3,20)| = 121782454418230208241
# |S_(4,20)| = 15023376; |K_(4,20)| = 121493582543216456556
# |S_(5,20)| = 135210384; |K_(5,20)| = 119522225783307682644
# |S_(6,20)| = 736145424; |K_(6,20)| = 112194354191073692244
# |S_(7,20)| = 2538950544; |K_(7,20)| = 97857214119938599764
# |S_(8,20)| = 5712638724; |K_(8,20)| = 85909597395664039944
# |S_(9,20)| = 8533694884; |K_(9,20)| = 87155984575607783704
# |S_(10,20)| = 8533694884; |K_(10,20)| = 91642978413249459064
# |S_(11,20)| = 5712638724; |K_(11,20)| = 87155984572786727544
# |S_(12,20)| = 2538950544; |K_(12,20)| = 85909597392490351764
# |S_(13,20)| = 736145424; |K_(13,20)| = 97857214118135794644
# |S_(14,20)| = 135210384; |K_(14,20)| = 112194354190472757204
# |S_(15,20)| = 15023376; |K_(15,20)| = 119522225783187495636
# |S_(16,20)| = 938961; |K_(16,20)| = 121493582543202372141
# |S_(17,20)| = 29241; |K_(17,20)| = 121782454418229298521
# |S_(18,20)| = 361; |K_(18,20)| = 121804719990433760641
# |S_(19,20)| = 1; |K_(19,20)| = 121805536572063331681
20 8306860679362702467199172997481835436300
@Janakarodrigo
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This is really great stuff, thank you very much Mark for your remarkable support.

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