Smallest
Hitters
(wilsonization)
Hello Seqfans,
if we call "wilsonization" the operation visible here http://oeis.org/A100787, we could indeed wilsonize any integer
to produce a (not strictly)increasing sequence.
Take 137, for
instance and start a sequence S where the
differences "d" between two consecutive terms of S
spell, digit by digit, the sequence S itself:
S = 137 138 141 148
149 152 160 161 165 166 ...
d = 1 3 7 1 3 8 1 4 1 ...
We see that 137
"hits" 166 (for instance) – but is 137 the
smallest integer hitting 166? No, it is 1 (as one will see following the above
link).
What is the
sequence of the "smallest hitters" (SH) of
the natural numbers?
I guess SH starts:
n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
SH = 1 1 3 1 5 3 7 1 9 5 5 3 3 5 3 1 1 ...
Best,
É.
__________
[Lars Blomberg] :
Hi Eric,
I found the first
1000 values of SH to be
1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3,
3, 5, 3, 1, 1, 5, 3, 3, 11, 5, 1, 1, 3, 3, 5, 5, 19, 13, 1, 3, 1, 5, 7, 1, 7,
1, 7, 5, 5, 1, 13, 3, 1, 1, 11, 9, 1, 5, 3, 1, 3, 11, 1, 9, 20, 13, 3, 7, 1, 3,
5, 1, 5, 9, 3, 5, 9, 3, 11, 1, 7, 3, 11, 1, 5, 1, 5, 3, 11, 1, 7, 3, 11, 20, 1,
3, 15, 5, 1, 3, 5, 19, 11, 3, 1, 24, 11, 5, 1, 3, 24, 5, 9, 13, 3, 3, 5, 1, 9,
13, 3, 15, 1, 3, 1, 19, 33, 11, 3, 1, 24, 19, 9, 13, 1, 17, 27, 3, 9, 5, 1, 1,
31, 3, 9, 3, 7, 1, 5, 7, 9, 1, 15, 11, 5, 3, 7, 13, 1, 9, 1, 3, 17, 7, 5, 15, 7,
1, 3, 17, 5, 13, 13, 1, 7, 3, 26, 15, 11, 13, 1, 5, 3, 29, 9, 7, 3, 17, 1, 5,
26, 22, 9, 3, 7, 17, 1, 31, 1, 3, 9, 13, 19, 5, 26, 7, 1, 3, 20, 9, 5, 7, 7, 1,
17, 3, 25, 5, 7, 3, 7, 7, 1, 1, 19, 21, 5, 3, 7, 9, 9, 20, 1, 19, 5, 3, 7, 9,
7, 1, 1, 1, 1, 1, 1, 1, 3, 17, 11, 13, 1, 1, 1, 9, 7, 3, 11, 7, 7, 1, 1, 3, 1,
11, 1, 1, 13, 1, 7, 9, 9, 5, 3, 3, 1, 1, 17, 5, 1, 5, 21, 1, 1, 3, 5, 1, 3, 3,
3, 1, 1, 9, 13, 17, 1, 1, 11, 3, 3, 1, 13, 17, 3, 1, 1, 11, 3, 5, 5, 1, 1, 1,
3, 3, 15, 5, 1, 5, 5, 1, 1, 11, 13, 15, 3, 3, 1, 1, 5, 3, 5, 15, 11, 1, 3, 9,
15, 5, 3, 1, 1, 5, 34, 5, 5, 11, 3, 1, 5, 5, 1, 1, 3, 7, 5, 9, 3, 3, 13, 1, 1,
1, 5, 3, 3, 3, 5, 7, 7, 1, 9, 3, 9, 19, 5, 5, 11, 9, 1, 1, 3, 7, 17, 17, 5, 5,
3, 19, 1, 1, 1, 11, 9, 27, 3, 3, 7, 5, 5, 1, 9, 17, 3, 9, 5, 7, 9, 3, 1, 9, 1,
9, 7, 7, 5, 3, 1, 9, 1, 1, 29, 7, 5, 5, 1, 3, 1, 1, 13, 11, 5, 7, 9, 1, 5, 1,
17, 1, 11, 3, 3, 9, 1, 5, 1, 5, 5, 1, 7, 1, 7, 1, 9, 3, 1, 3, 7, 1, 22, 1, 13,
7, 1, 5, 5, 1, 9, 1, 3, 13, 1, 9, 3, 13, 1, 7, 1, 7, 3, 1, 17, 5, 5, 7, 1, 7, 1,
22, 3, 1, 11, 3, 20, 7, 7, 1, 7, 1, 3, 5, 1, 7, 5, 3, 5, 5, 1, 5, 1, 11, 7, 1,
3, 15, 3, 11, 7, 5, 1, 5, 1, 5, 9, 1, 7, 13, 3, 11, 3, 11, 5, 1, 15, 1, 9, 7,
17, 1, 11, 3, 1, 7, 1, 5, 3, 17, 1, 17, 5, 3, 1, 3, 1, 13, 7, 5, 1, 5, 7, 17,
9, 1, 5, 1, 5, 13, 5, 7, 1, 7, 1, 5, 1, 7, 9, 3, 5, 1, 5, 19, 1, 7, 1, 7, 5,
11, 7, 1, 5, 22, 3, 19, 1, 17, 1, 7, 11, 3, 9, 1, 15, 7, 20, 7, 11, 3, 1, 3, 1,
5, 7, 11, 7, 1, 13, 17, 5, 5, 3, 5, 3, 1, 7, 1, 23, 11, 3, 5, 15, 1, 17, 1, 3,
7, 3, 7, 5, 1, 5, 11, 3, 13, 7, 13, 1, 19, 1, 5, 3, 5, 7, 5, 1, 15, 13, 3, 19,
11, 5, 3, 1, 3, 1, 17, 5, 22, 5, 22, 3, 1, 1, 19, 1, 3, 13, 3, 9, 11, 9, 1, 5,
25, 3, 1, 44, 1, 20, 9, 3, 5, 3, 9, 1, 17, 13, 17, 5, 1, 5, 1, 9, 24, 23, 21,
20, 11, 1, 5, 3, 5, 24, 17, 9, 17, 1, 7, 1, 5, 3, 5, 34, 5, 17, 22, 1, 7, 1, 3,
1, 3, 7, 5, 7, 5, 9, 28, 1, 3, 11, 1, 19, 1, 5, 9, 3, 11, 3, 27, 7, 1, 24, 9,
22, 5, 3, 7, 1, 15, 1, 21, 13, 9, 3, 7, 3, 5, 1, 9, 13, 5, 9, 17, 5, 1, 19, 1,
5, 7, 5, 11, 9, 5, 11, 1, 3, 3, 5, 3, 17, 5, 9, 1, 21, 1, 11, 5, 3, 9, 3, 17, 3,
11, 1, 9, 1, 20, 1, 15, 21, 3, 5, 7, 13, 5, 3, 1, 3, 7, 5, 5, 7, 1, 5, 1, 15,
3, 20, 5, 7, 19, 3, 11, 1, 5, 7, 13, 5, 7, 5, 1, 19, 3, 1, 7, 1, 15, 13, 1, 24,
3, 1, 9, 15, 1, 5, 13, 15, 1, 3, 9, 1, 9, 7, 11, 5, 7, 11, 3, 13, 1, 3, 15, 1,
1, 11, 1, 5, 11, 1, 1, 20, 7, 1, 9, 3, 1, 1, 3, 13, 5, 7, 9, 5, 7, 9, 1, 3, 5,
1, 1, 3, 11, 7, 19, 5, 7, 5, 3, 1, 5, 3, 1, 31, 1, 11, 7, 1, 11, 1, 3, 25, 13,
3, 5, 1, 11, 3, 1, 9, 3, 1, 3, 1, 5, 15, 1, 9, 3, 1, 30, 3, 1, 3, 7, 1, 5, 13,
9, 1, 3, 5, 1, 3, 13, 28, 1, 3, 9, 1, 3, 9, 1, 3, 5, 26, 1, 17, 9, 7, 1, 13, 3,
1, 13, 3, 5, 7, 1, 3, 1, 19, 3, 1, 19, 9, 3, 7, 1, 5, 7, 1, 5, 7, 1, 13, 22,
15, 3, 1, 7, 11, 9, 1, 7, 19, 1, 3, 11, ...
In histogram form:
1 259
3 173
5 155
7 104
9 75
11 56
13 44
15 23
17 32
19 22
20 11
21 6
22 9
23 2
24 7
25 3
26 4
27 3
28 2
29 2
30 1
31 3
33 1
34 2
44 1
[Maximilian Hasler] :
>
n = 1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 ...
> SH = 1 1 3 1 5 3 7 1 9 5 5 3 3 5 3 1 1 ...
I confirm these
values and get
vector(150,n,SH(n))
= [1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 3, 5,
3, 1, 1, 5, 3, 3, 11, 5, 1, 1, 3, 3, 5, 5, 19, 13, 1, 3, 1, 5, 7, 1, 7, 1, 7, 5,
5, 1, 13, 3, 1, 1, 11, 9, 1, 5, 3, 1, 3, 11, 1, 9, 20, 13, 3, 7, 1, 3, 5, 1, 5,
9, 3, 5, 9, 3, 11, 1, 7, 3, 11, 1, 5, 1, 5, 3, 11, 1, 7, 3, 11, 20, 1, 3, 15,
5, 1, 3, 5, 19, 11, 3, 1, 24, 11, 5, 1, 3, 24, 5, 9, 13, 3, 3, 5, 1, 9, 13, 3,
15, 1, 3, 1, 19, 33, 11, 3, 1, 24, 19, 9, 13, 1, 17, 27, 3, 9, 5, 1, 1, 31, 3,
9, 3, 7, 1, 5, 7, 9, 1, 15, 11, 5, 3, 7, 13]
(PARI)
SH(n)={ for(k=1,n, my(seed=k,d=digits(seed));
while(seed<n,seed+=d[1];d=vecextract(concat(d,digits(seed)),"^1"));seed==n&return(k))}
I proposed this as https://oeis.org/draft/A211206
[Jean-Marc Falcoz]:
J’ai regardé ce que ça donnait jusqu’à 10000 ;
tous les entiers ne sont pas des smallest hitters (par exemple, pour 2, c’est facile à
expliquer, mais pour d’autres, ce n’est pas évident...)
Pour les 10000 premiers termes (cf. plus bas), les termes sont tous parmi {1, 3, 5, 7, 9, 11, 13,
15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39, 40, 42, 43, 44, 45, 48, 49, 50} ; il manque donc {2, 4, 6, 8,
10, 12, 14, 16, 18, 41, 46, 47}
{1,
1, 3, 1, 5, 3, 7, 1, 9, 5, 5, 3, 3, 5, 3, 1, 1, 5, 3, 3, 11, 5, 1, 1, 3, 3, 5,
5, 19, 13, 1, 3, 1, 5, 7, 1, 7, 1, 7, 5, 5, 1, 13, 3, 1, 1, 11, 9, 1, 5, 3, 1,
3, 11, 1, 9, 20, 13, 3, 7, 1, 3, 5, 1, 5, 9, 3, 5, 9, 3, 11, 1, 7, 3, 11, 1, 5,
1, 5, 3, 11, 1, 7, 3, 11, 20, 1, 3, 15, 5, 1, 3, 5, 19, 11, 3, 1, 24, 11, 5, 1,
3, 24, 5, 9, 13, 3, 3, 5, 1, 9, 13, 3, 15, 1, 3, 1, 19, 33, 11, 3, 1, 24, 19,
9, 13, 1, 17, 27, 3, 9, 5, 1, 1, 31, 3, 9, 3, 7, 1, 5, 7, 9, 1, 15, 11, 5, 3,
7, 13, 1, 9, 1, 3, 17, 7, 5, 15, 7, 1, 3, 17, 5, 13, 13, 1, 7, 3, 26, 15, 11,
13, 1, 5, 3, 29, 9, 7, 3, 17, 1, 5, 26, 22, 9, 3, 7, 17, 1, 31, 1, 3, 9, 13,
19, 5, 26, 7, 1, 3, 20, 9, 5, 7, 7, 1, 17, 3, 25, 5, 7, 3, 7, 7, 1, 1, 19, 21,
5, 3, 7, 9, 9, 20, 1, 19, 5, 3, 7, 9, 7, 1, 1, 1, 1, 1, 1, 1, 3, 17, 11, 13, 1,
1, 1, 9, 7, 3, 11, 7, 7, 1, 1, 3, 1, 11, 1, 1, 13, 1, 7, 9, 9, 5, 3, 3, 1, 1,
17, 5, 1, 5, 21, 1, 1, 3, 5, 1, 3, 3, 3, 1, 1, 9, 13, 17, 1, 1, 11, 3, 3, 1,
13, 17, 3, 1, 1, 11, 3, 5, 5, 1, 1, 1, 3, 3, 15, 5, 1, 5, 5, 1, 1, 11, 13, 15,
3, 3, 1, 1, 5, 3, 5, 15, 11, 1, 3, 9, 15, 5, 3, 1, 1, 5, 34, 5, 5, 11, 3, 1, 5,
5, 1, 1, 3, 7, 5, 9, 3, 3, 13, 1, 1, 1, 5, 3, 3, 3, 5, 7, 7, 1, 9, 3, 9, 19, 5,
5, 11, 9, 1, 1, 3, 7, 17, 17, 5, 5, 3, 19, 1, 1, 1, 11, 9, 27, 3, 3, 7, 5, 5,
1, 9, 17, 3, 9, 5, 7, 9, 3, 1, 9, 1, 9, 7, 7, 5, 3, 1, 9, 1, 1, 29, 7, 5, 5, 1,
3, 1, 1, 13, 11, 5, 7, 9, 1, 5, 1, 17, 1, 11, 3, 3, 9, 1, 5, 1, 5, 5, 1, 7, 1,
7, 1, 9, 3, 1, 3, 7, 1, 22, 1, 13, 7, 1, 5, 5, 1, 9, 1, 3, 13, 1, 9, 3, 13, 1,
7, 1, 7, 3, 1, 17, 5, 5, 7, 1, 7, 1, 22, 3, 1, 11, 3, 20, 7, 7, 1, 7, 1, 3, 5,
1, 7, 5, 3, 5, 5, 1, 5, 1, 11, 7, 1, 3, 15, 3, 11, 7, 5, 1, 5, 1, 5, 9, 1, 7,
13, 3, 11, 3, 11, 5, 1, 15, 1, 9, 7, 17, 1, 11, 3, 1, 7, 1, 5, 3, 17, 1, 17, 5,
3, 1, 3, 1, 13, 7, 5, 1, 5, 7, 17, 9, 1, 5, 1, 5, 13, 5, 7, 1, 7, 1, 5, 1, 7,
9, 3, 5, 1, 5, 19, 1, 7, 1, 7, 5, 11, 7, 1, 5, 22, 3, 19, 1, 17, 1, 7, 11, 3,
9, 1, 15, 7, 20, 7, 11, 3, 1, 3, 1, 5, 7, 11, 7, 1, 13, 17, 5, 5, 3, 5, 3, 1,
7, 1, 23, 11, 3, 5, 15, 1, 17, 1, 3, 7, 3, 7, 5, 1, 5, 11, 3, 13, 7, 13, 1, 19,
1, 5, 3, 5, 7, 5, 1, 15, 13, 3, 19, 11, 5, 3, 1, 3, 1, 17, 5, 22, 5, 22, 3, 1,
1, 19, 1, 3, 13, 3, 9, 11, 9, 1, 5, 25, 3, 1, 44, 1, 20, 9, 3, 5, 3, 9, 1, 17,
13, 17, 5, 1, 5, 1, 9, 24, 23, 21, 20, 11, 1, 5, 3, 5, 24, 17, 9, 17, 1, 7, 1,
5, 3, 5, 34, 5, 17, 22, 1, 7, 1, 3, 1, 3, 7, 5, 7, 5, 9, 28, 1, 3, 11, 1, 19,
1, 5, 9, 3, 11, 3, 27, 7, 1, 24, 9, 22, 5, 3, 7, 1, 15, 1, 21, 13, 9, 3, 7, 3,
5, 1, 9, 13, 5, 9, 17, 5, 1, 19, 1, 5, 7, 5, 11, 9, 5, 11, 1, 3, 3, 5, 3, 17,
5, 9, 1, 21, 1, 11, 5, 3, 9, 3, 17, 3, 11, 1, 9, 1, 20, 1, 15, 21, 3, 5, 7, 13,
5, 3, 1, 3, 7, 5, 5, 7, 1, 5, 1, 15, 3, 20, 5, 7, 19, 3, 11, 1, 5, 7, 13, 5, 7,
5, 1, 19, 3, 1, 7, 1, 15, 13, 1, 24, 3, 1, 9, 15, 1, 5, 13, 15, 1, 3, 9, 1, 9,
7, 11, 5, 7, 11, 3, 13, 1, 3, 15, 1, 1, 11, 1, 5, 11, 1, 1, 20, 7, 1, 9, 3, 1,
1, 3, 13, 5, 7, 9, 5, 7, 9, 1, 3, 5, 1, 1, 3, 11, 7, 19, 5, 7, 5, 3, 1, 5, 3,
1, 31, 1, 11, 7, 1, 11, 1, 3, 25, 13, 3, 5, 1, 11, 3, 1, 9, 3, 1, 3, 1, 5, 15,
1, 9, 3, 1, 30, 3, 1, 3, 7, 1, 5, 13, 9, 1, 3, 5, 1, 3, 13, 28, 1, 3, 9, 1, 3,
9, 1, 3, 5, 26, 1, 17, 9, 7, 1, 13, 3, 1, 13, 3, 5, 7, 1, 3, 1, 19, 3, 1, 19,
9, 3, 7, 1, 5, 7, 1, 5, 7, 1, 13, 22, 15, 3, 1, 7, 11, 9, 1, 7, 19, 1, 3, 11,
5, 3, 13, 1, 11, 1, 3, 5, 1, 3, 5, 11, 9, 5, 3, 1, 1, 11, 7, 1, 3, 17, 13, 3,
11, 17, 1, 5, 1, 15, 5, 1, 17, 21, 11, 3, 17, 5, 3, 1, 1, 13, 7, 1, 9, 5, 23,
9, 5, 17, 15, 1, 15, 1, 3, 9, 1, 20, 13, 5, 3, 20, 5, 7, 1, 9, 19, 1, 7, 19, 1,
5, 7, 9, 3, 15, 3, 13, 7, 1, 9, 1, 7, 5, 5, 1, 1, 5, 19, 3, 1, 7, 3, 1, 20, 9,
5, 1, 9, 3, 1, 15, 7, 5, 1, 11, 7, 5, 3, 23, 7, 3, 5, 1, 17, 9, 5, 1, 1, 1, 7,
20, 13, 1, 1, 7, 1, 5, 5, 3, 1, 1, 13, 5, 11, 13, 7, 3, 1, 17, 7, 26, 1, 1, 5,
3, 27, 7, 3, 9, 5, 7, 1, 5, 11, 7, 1, 3, 1, 5, 19, 9, 1, 11, 1, 26, 3, 15, 11,
19, 1, 3, 5, 13, 1, 3, 1, 13, 9, 7, 5, 15, 11, 3, 1, 11, 20, 3, 1, 11, 13, 1, 9,
5, 17, 1, 7, 5, 1, 3, 3, 9, 11, 1, 17, 7, 13, 1, 3, 7, 1, 20, 3, 7, 3, 5, 15,
1, 7, 9, 3, 1, 13, 11, 3, 1, 13, 3, 5, 1, 9, 11, 5, 1, 9, 1, 3, 15, 37, 1, 13,
21, 9, 1, 17, 15, 9, 1, 5, 3, 7, 1, 15, 3, 5, 1, 15, 3, 5, 9, 7, 3, 1, 5, 9, 3,
1, 7, 9, 3, 5, 1, 13, 7, 5, 1, 7, 11, 15, 3, 1, 9, 1, 3, 19, 5, 1, 9, 11, 3,
15, 1, 11, 3, 7, 22, 1, 3, 7, 11, 1, 19, 13, 3, 5, 1, 27, 3, 20, 7, 23, 3, 17,
1, 9, 19, 5, 1, 20, 3, 5, 15, 13, 1, 9, 11, 11, 1, 5, 13, 11, 20, 5, 1, 19, 3,
1, 7, 11, 3, 1, 15, 13, 3, 7, 5, 1, 9, 24, 5, 35, 3, 7, 1, 13, 3, 7, 1, 5, 11,
3, 9, 13, 1, 3, 15, 9, 13, 11, 3, 9, 7, 1, 3, 9, 5, 1, 15, 3, 5, 11, 9, 11, 1,
13, 1, 3, 7, 5, 1, 3, 7, 20, 5, 11, 32, 1, 5, 9, 7, 3, 13, 9, 1, 11, 7, 3, 1,
29, 7, 13, 3, 19, 5, 1, 9, 11, 3, 15, 13, 3, 38, 23, 1, 3, 15, 5, 1, 7, 11, 3,
17, 15, 13, 5, 1, 7, 1, 5, 3, 33, 1, 11, 7, 9, 3, 31, 5, 9, 1, 11, 13, 3, 9,
23, 5, 3, 1, 21, 21, 5, 1, 3, 19, 7, 5, 5, 13, 7, 3, 1, 5, 5, 3, 1, 13, 19, 5,
5, 3, 5, 7, 11, 1, 15, 5, 1, 9, 3, 20, 1, 7, 3, 15, 11, 5, 28, 5, 5, 1, 3, 13,
9, 5, 3, 5, 9, 7, 1, 17, 11, 3, 9, 1, 1, 5, 25, 26, 13, 1, 3, 5, 11, 1, 3, 20,
5, 11, 1, 1, 1, 11, 3, 3, 5, 1, 1, 3, 20, 1, 15, 9, 19, 7, 1, 1, 15, 5, 19, 3,
28, 1, 17, 3, 19, 13, 1, 21, 1, 20, 15, 5, 1, 3, 7, 37, 9, 1, 7, 1, 5, 13, 11,
9, 21, 1, 3, 7, 27, 3, 1, 28, 9, 1, 19, 5, 7, 15, 1, 5, 20, 1, 3, 17, 1, 15,
20, 7, 3, 1, 7, 15, 1, 3, 30, 7, 11, 1, 3, 7, 9, 5, 1, 3, 7, 1, 5, 11, 13, 26,
3, 5, 19, 29, 1, 3, 3, 3, 9, 1, 29, 5, 3, 1, 15, 7, 1, 9, 11, 15, 7, 1, 3, 11,
23, 1, 5, 3, 21, 3, 1, 7, 24, 5, 13, 1, 7, 3, 5, 1, 21, 11, 19, 3, 23, 20, 13,
15, 1, 7, 13, 3, 5, 1, 19, 9, 3, 5, 1, 3, 9, 3, 1, 5, 19, 9, 3, 1, 13, 3, 15, 20,
1, 27, 7, 13, 3, 11, 1, 9, 9, 3, 15, 1, 7, 3, 9, 3, 22, 1, 1, 22, 3, 30, 11, 1,
3, 7, 13, 5, 3, 1, 35, 13, 1, 3, 13, 9, 7, 1, 7, 21, 5, 20, 11, 1, 17, 9, 3, 5,
1, 20, 7, 3, 5, 1, 13, 7, 3, 9, 7, 15, 1, 5, 28, 7, 9, 1, 5, 17, 7, 9, 3, 7, 1,
20, 5, 1, 3, 5, 7, 19, 1, 3, 5, 7, 23, 13, 7, 1, 3, 11, 11, 5, 1, 3, 23, 7, 5,
1, 13, 3, 7, 20, 11, 11, 7, 1, 13, 3, 9, 20, 1, 7, 3, 17, 15, 21, 7, 9, 1, 3,
7, 5, 17, 1, 3, 21, 5, 24, 1, 7, 9, 3, 28, 11, 7, 5, 1, 17, 23, 7, 7, 3, 11, 1,
5, 7, 13, 21, 1, 3, 5, 7, 3, 9, 11, 23, 5, 1, 5, 1, 11, 15, 7, 9, 1, 3, 17, 19,
25, 7, 3, 20, 17, 1, 9, 3, 11, 22, 17, 5, 5, 21, 1, 15, 3, 7, 5, 5, 1, 1, 9, 7,
26, 11, 24, 1, 5, 7, 3, 13, 24, 1, 7, 9, 13, 5, 3, 1, 1, 39, 32, 5, 1, 5, 15,
9, 7, 13, 1, 1, 11, 5, 13, 5, 3, 1, 11, 15, 7, 5, 3, 1, 3, 1, 7, 1, 15, 13, 3,
3, 5, 1, 3, 1, 17, 1, 5, 15, 3, 3, 5, 1, 28, 1, 11, 9, 5, 1, 3, 5, 11, 17, 5,
1, 3, 13, 1, 13, 5, 9, 19, 3, 1, 13, 11, 1, 30, 3, 5, 3, 9, 27, 1, 22, 5, 9, 3,
13, 1, 7, 5, 1, 3, 9, 5, 3, 30, 7, 3, 13, 1, 23, 19, 9, 3, 7, 1, 3, 13, 5, 1,
28, 9, 7, 11, 1, 3, 26, 7, 17, 13, 1, 3, 7, 23, 17, 1, 3, 5, 1, 17, 7, 13, 3,
5, 1, 9, 3, 13, 5, 1, 21, 15, 19, 7, 1, 13, 31, 5, 19, 21, 1, 13, 7, 5, 13, 3,
1, 3, 1, 5, 20, 7, 11, 3, 1, 5, 20, 17, 3, 11, 1, 5, 3, 1, 9, 13, 7, 15, 3, 1,
9, 5, 7, 23, 3, 1, 17, 5, 7, 15, 1, 3, 11, 21, 5, 15, 1, 3, 9, 5, 20, 11, 7, 1,
9, 1, 13, 19, 7, 3, 9, 1, 9, 5, 27, 3, 19, 7, 1, 15, 9, 5, 19, 3, 1, 26, 9, 7,
11, 3, 1, 21, 23, 7, 7, 11, 3, 1, 5, 7, 9, 3, 11, 15, 5, 1, 7, 3, 13, 11, 15,
1, 11, 5, 5, 3, 3, 9, 17, 1, 5, 7, 3, 7, 1, 21, 11, 15, 9, 5, 1, 13, 25, 3, 11,
7, 9, 7, 5, 1, 13, 11, 9, 19, 23, 1, 11, 9, 3, 36, 19, 7, 5, 11, 1, 20, 1, 7,
13, 11, 9, 5, 1, 3, 13, 9, 7, 17, 31, 5, 5, 1, 3, 34, 9, 7, 17, 13, 7, 3, 1,
11, 20, 7, 5, 11, 9, 1, 23, 7, 22, 5, 11, 5, 1, 5, 3, 21, 13, 7, 9, 1, 5, 3, 5,
32, 9, 28, 5, 23, 1, 11, 3, 15, 7, 5, 17, 1, 1, 3, 3, 3, 19, 5, 11, 1, 23, 7,
3, 3, 5, 11, 1, 1, 21, 7, 11, 19, 3, 33, 11, 7, 1, 9, 13, 3, 7, 3, 5, 1, 25, 1,
1, 5, 3, 17, 3, 9, 3, 1, 5, 1, 26, 5, 11, 3, 13, 20, 3, 7, 1, 21, 22, 9, 7, 3, 20,
1, 3, 13, 1, 5, 1, 7, 19, 3, 21, 5, 13, 1, 20, 11, 1, 11, 5, 3, 1, 20, 5, 15,
11, 7, 9, 1, 3, 5, 11, 1, 21, 1, 24, 3, 5, 7, 13, 3, 1, 25, 22, 17, 1, 7, 3, 9,
19, 5, 13, 7, 9, 1, 25, 19, 5, 13, 3, 9, 1, 5, 17, 3, 13, 1, 1, 7, 9, 5, 3, 13,
13, 1, 17, 3, 5, 19, 1, 15, 22, 5, 3, 13, 19, 9, 9, 1, 9, 3, 5, 19, 13, 7, 1,
3, 9, 5, 19, 7, 1, 3, 21, 5, 19, 5, 1, 7, 3, 24, 9, 19, 5, 1, 3, 28, 7, 11, 5,
1, 3, 9, 7, 17, 13, 11, 22, 1, 26, 9, 19, 7, 11, 3, 1, 5, 15, 7, 13, 17, 11, 1,
5, 9, 15, 22, 7, 1, 3, 9, 13, 20, 22, 5, 1, 3, 9, 11, 9, 22, 5, 11, 1, 7, 27,
9, 1, 19, 11, 3, 39, 5, 7, 1, 28, 9, 3, 26, 5, 15, 13, 1, 23, 11, 3, 19, 20, 1,
9, 15, 5, 3, 31, 13, 1, 31, 7, 5, 11, 3, 9, 20, 31, 1, 7, 15, 3, 9, 1, 13, 13,
7, 5, 19, 3, 1, 17, 13, 24, 5, 19, 21, 23, 3, 1, 5, 7, 15, 22, 13, 3, 1, 17,
19, 5, 7, 13, 38, 1, 3, 3, 5, 7, 7, 7, 20, 9, 1, 5, 5, 9, 7, 7, 15, 20, 19, 1,
13, 21, 3, 7, 20, 19, 5, 1, 23, 11, 3, 9, 3, 13, 25, 1, 11, 5, 23, 31, 3, 15,
7, 1, 1, 11, 21, 3, 1, 7, 20, 15, 13, 21, 9, 3, 1, 1, 22, 7, 15, 7, 5, 1, 3, 22,
24, 9, 7, 21, 23, 1, 3, 1, 9, 39, 11, 23, 1, 17, 7, 3, 23, 9, 11, 21, 1, 7, 5,
1, 9, 1, 7, 11, 3, 5, 9, 20, 17, 1, 19, 11, 1, 5, 3, 5, 15, 1, 24, 3, 24, 7, 5,
11, 15, 1, 32, 3, 1, 17, 3, 19, 15, 1, 3, 11, 13, 11, 5, 7, 13, 1, 3, 23, 1, 5,
3, 33, 9, 13, 43, 1, 11, 13, 3, 5, 17, 21, 3, 1, 3, 13, 5, 1, 33, 9, 7, 48, 3,
15, 26, 1, 5, 3, 3, 1, 11, 22, 7, 5, 23, 24, 3, 1, 19, 7, 9, 1, 3, 20, 1, 7,
17, 9, 11, 15, 3, 5, 1, 7, 35, 9, 1, 15, 9, 3, 7, 5, 1, 11, 35, 9, 13, 3, 19,
5, 1, 24, 5, 3, 1, 11, 3, 13, 15, 9, 1, 7, 15, 5, 3, 17, 9, 11, 1, 22, 3, 5,
22, 1, 11, 9, 15, 5, 3, 27, 19, 1, 9, 20, 15, 5, 1, 17, 19, 1, 15, 9, 5, 3, 3,
29, 22, 1, 27, 13, 5, 15, 1, 29, 9, 1, 23, 15, 5, 3, 3, 15, 22, 1, 13, 27, 5,
5, 3, 1, 17, 1, 9, 20, 25, 3, 5, 5, 13, 1, 9, 17, 3, 9, 22, 1, 13, 5, 5, 37, 1,
9, 9, 5, 21, 7, 15, 42, 1, 11, 25, 5, 5, 13, 1, 23, 3, 11, 13, 7, 1, 15, 13,
11, 3, 9, 20, 7, 1, 25, 5, 7, 3, 9, 1, 13, 22, 25, 5, 7, 3, 9, 1, 9, 19, 11,
30, 24, 5, 3, 1, 13, 7, 5, 20, 17, 28, 1, 1, 9, 7, 5, 17, 5, 7, 19, 1, 15, 3,
21, 17, 22, 7, 1, 19, 1, 3, 23, 5, 9, 23, 7, 26, 1, 5, 3, 15, 13, 3, 7, 1, 7, 5,
27, 5, 1, 13, 3, 9, 11, 7, 19, 7, 1, 13, 21, 3, 11, 15, 3, 1, 5, 22, 7, 5, 5,
9, 22, 1, 20, 7, 13, 3, 5, 9, 11, 1, 32, 7, 19, 5, 3, 3, 1, 3, 39, 27, 17, 5,
7, 22, 5, 1, 3, 3, 11, 9, 13, 5, 3, 1, 7, 17, 11, 7, 13, 5, 29, 1, 3, 5, 11,
21, 13, 7, 9, 1, 7, 5, 28, 45, 22, 5, 9, 1, 3, 3, 28, 9, 22, 5, 15, 25, 1, 1,
3, 11, 5, 9, 7, 15, 20, 1, 9, 3, 5, 3, 7, 3, 5, 22, 1, 21, 1, 7, 5, 30, 3, 21,
3, 9, 23, 1, 1, 30, 11, 7, 5, 19, 25, 32, 13, 1, 21, 5, 3, 1, 19, 25, 17, 7, 9,
5, 9, 3, 1, 24, 3, 20, 24, 3, 1, 19, 22, 20, 5, 15, 9, 21, 3, 1, 21, 3, 5, 7, 9,
1, 3, 25, 7, 13, 5, 15, 9, 30, 1, 3, 7, 15, 13, 3, 9, 3, 5, 1, 25, 11, 11, 15,
9, 7, 3, 11, 1, 1, 1, 9, 5, 7, 17, 3, 11, 9, 22, 1, 1, 15, 23, 15, 3, 9, 5, 1,
3, 5, 23, 23, 20, 7, 11, 13, 1, 5, 1, 23, 15, 29, 22, 5, 7, 3, 11, 1, 11, 1, 7,
15, 1, 9, 11, 23, 7, 21, 3, 17, 5, 1, 13, 1, 7, 25, 11, 3, 1, 5, 7, 23, 3, 13,
3, 11, 29, 1, 11, 1, 17, 11, 15, 3, 5, 13, 50, 1, 3, 5, 11, 20, 32, 3, 7, 7, 1,
5, 13, 1, 1, 11, 3, 7, 26, 5, 26, 5, 3, 1, 7, 15, 1, 49, 7, 5, 1, 17, 9, 11,
31, 3, 7, 5, 22, 1, 17, 3, 1, 7, 9, 20, 11, 22, 3, 1, 5, 21, 21, 9, 9, 15, 19,
3, 1, 9, 33, 13, 1, 1, 3, 3, 7, 5, 9, 13, 9, 9, 1, 20, 3, 5, 1, 1, 13, 23, 9,
3, 3, 19, 5, 7, 1, 13, 9, 19, 1, 3, 5, 7, 1, 22, 13, 9, 3, 9, 15, 5, 3, 1, 5,
23, 15, 1, 9, 11, 11, 3, 5, 28, 21, 1, 17, 9, 3, 11, 9, 5, 17, 13, 1, 9, 3, 31,
5, 1, 1, 22, 11, 19, 9, 3, 5, 7, 9, 1, 22, 11, 13, 3, 1, 5, 3, 9, 1, 20, 11, 9,
28, 15, 5, 3, 25, 1, 20, 11, 15, 21, 1, 3, 13, 5, 11, 19, 9, 3, 1, 11, 23, 13,
5, 21, 20, 9, 3, 1, 5, 23, 7, 15, 26, 1, 21, 1, 11, 5, 36, 7, 7, 7, 17, 13, 1, 23,
5, 9, 15, 19, 1, 7, 13, 3, 27, 1, 5, 15, 5, 20, 21, 13, 3, 3, 1, 3, 3, 5, 5, 7,
13, 1, 17, 3, 3, 19, 11, 9, 7, 9, 1, 3, 3, 3, 3, 3, 11, 1, 5, 1, 3, 3, 11, 3,
3, 3, 25, 3, 1, 5, 20, 3, 3, 13, 3, 1, 7, 11, 9, 7, 1, 21, 7, 3, 3, 9, 11, 3,
5, 1, 15, 7, 11, 3, 3, 11, 9, 1, 15, 15, 5, 11, 17, 9, 15, 5, 1, 3, 11, 7, 29,
3, 17, 7, 1, 3, 3, 1, 21, 11, 11, 3, 15, 3, 3, 5, 1, 27, 7, 3, 7, 24, 17, 11,
1, 3, 17, 15, 5, 7, 1, 3, 3, 3, 15, 26, 11, 9, 7, 1, 5, 9, 19, 11, 3, 3, 25, 7,
1, 1, 9, 3, 5, 7, 15, 11, 11, 13, 1, 3, 3, 5, 7, 11, 15, 11, 5, 1, 20, 7, 15,
13, 1, 3, 11, 11, 5, 15, 7, 17, 3, 1, 9, 7, 9, 9, 9, 3, 3, 11, 1, 9, 9, 22, 9,
9, 3, 3, 1, 1, 15, 11, 5, 1, 1, 3, 9, 5, 21, 17, 1, 1, 3, 3, 15, 11, 5, 9, 9,
7, 1, 1, 1, 3, 13, 11, 17, 9, 1, 1, 1, 17, 3, 11, 11, 3, 3, 1, 1, 3, 1, 1, 11,
1, 7, 13, 5, 13, 3, 3, 1, 1, 9, 1, 3, 3, 11, 3, 3, 3, 11, 3, 1, 1, 15, 13, 1,
5, 1, 1, 3, 7, 20, 1, 1, 3, 9, 5, 1, 1, 1, 11, 11, 9, 1, 5, 3, 3, 1, 1, 7, 11,
3, 11, 1, 21, 1, 1, 3, 3, 3, 15, 1, 15, 3, 11, 1, 1, 21, 15, 9, 9, 1, 3, 3, 3, 5,
13, 21, 1, 1, 7, 15, 9, 9, 5, 1, 15, 3, 3, 3, 1, 1, 5, 5, 5, 3, 13, 1, 3, 3, 3,
21, 11, 5, 5, 1, 1, 5, 5, 7, 15, 13, 5, 1, 1, 1, 5, 5, 9, 5, 20, 3, 23, 1, 1,
11, 11, 5, 3, 3, 3, 5, 1, 5, 1, 1, 3, 11, 17, 13, 13, 23, 7, 1, 3, 3, 9, 11,
11, 1, 1, 7, 3, 3, 3, 3, 5, 9, 1, 7, 5, 7, 3, 3, 1, 1, 9, 9, 9, 5, 5, 11, 3, 1,
3, 3, 3, 9, 17, 15, 1, 1, 5, 3, 7, 7, 11, 11, 7, 3, 1, 1, 1, 9, 7, 7, 5, 13, 3,
5, 5, 1, 1, 1, 3, 3, 3, 5, 7, 5, 5, 9, 1, 7, 3, 7, 1, 1, 3, 3, 3, 9, 7, 7, 11, 20,
1, 5, 3, 7, 11, 11, 5, 5, 1, 1, 3, 3, 3, 21, 7, 5, 9, 13, 1, 5, 3, 11, 15, 9,
21, 7, 1, 1, 1, 1, 1, 1, 11, 5, 5, 7, 1, 1, 1, 13, 3, 13, 5, 1, 1, 1, 1, 3, 9,
3, 1, 1, 1, 1, 3, 9, 3, 7, 17, 11, 5, 1, 1, 1, 1, 3, 3, 5, 3, 3, 11, 11, 3, 1,
1, 1, 3, 1, 1, 1, 13, 1, 3, 5, 3, 1, 1, 1, 3, 1, 3, 9, 3, 5, 1, 1, 1, 3, 1, 7,
3, 11, 3, 5, 5, 1, 1, 1, 5, 5, 1, 1, 1, 1, 5, 5, 1, 3, 1, 1, 1, 5, 3, 1, 9, 7,
3, 3, 7, 3, 5, 5, 1, 1, 1, 9, 13, 7, 1, 3, 3, 1, 1, 1, 15, 21, 3, 1, 5, 3, 15,
1, 1, 1, 9, 23, 27, 3, 1, 5, 3, 1, 1, 1, 3, 23, 7, 7, 1, 13, 13, 9, 3, 3, 5, 1,
1, 1, 7, 7, 3, 3, 1, 3, 9, 9, 5, 7, 3, 7, 15, 1, 1, 1, 5, 3, 5, 7, 1, 5, 3, 7,
7, 7, 23, 7, 9, 1, 1, 1, 5, 3, 7, 15, 5, 1, 11, 3, 1, 1, 1, 5, 3, 13, 9, 5, 1,
7, 3, 9, 7, 1, 1, 1, 3, 3, 5, 3, 9, 7, 1, 1, 1, 1, 3, 3, 7, 3, 7, 5, 1, 11, 7,
5, 3, 1, 1, 1, 13, 7, 3, 3, 9, 3, 1, 7, 7, 15, 5, 5, 5, 1, 1, 1, 3, 9, 5, 5, 5,
7, 7, 1, 3, 11, 5, 7, 1, 1, 1, 3, 13, 5, 5, 5, 7, 15, 1, 9, 3, 3, 5, 3, 5, 5,
11, 1, 1, 1, 7, 13, 3, 7, 7, 5, 3, 3, 1, 3, 1, 1, 1, 19, 15, 5, 5, 5, 3, 7, 7,
1, 17, 1, 1, 1, 3, 3, 7, 7, 3, 5, 5, 5, 1, 3, 22, 13, 3, 7, 1, 1, 1, 9, 11, 13,
3, 3, 7, 5, 3, 1, 7, 3, 3, 13, 11, 3, 20, 3, 1, 1, 7, 1, 5, 3, 5, 1, 1, 3, 1,
7, 7, 3, 9, 3, 21, 11, 1, 1, 15, 1, 1, 1, 1, 21, 1, 1, 5, 7, 3, 7, 7, 7, 9, 1,
1, 3, 1, 5, 1, 7, 1, 1, 3, 1, 5, 1, 3, 5, 5, 9, 3, 1, 1, 11, 1, 3, 1, 5, 3, 5,
9, 11, 1, 1, 5, 1, 3, 5, 1, 1, 9, 1, 9, 9, 1, 7, 17, 7, 1, 1, 3, 1, 13, 9, 1,
11, 11, 5, 5, 7, 1, 1, 3, 1, 5, 3, 19, 1, 1, 7, 1, 3, 3, 3, 1, 5, 3, 23, 1, 1,
19, 1, 3, 21, 20, 1, 7, 3, 3, 7, 11, 3, 5, 1, 1, 7, 1, 7, 3, 3, 11, 1, 3, 1, 1,
5, 1, 5, 13, 3, 3, 1, 5, 3, 20, 9, 7, 1, 1, 7, 1, 5, 5, 21, 3, 3, 1, 7, 3, 1,
1, 17, 1, 13, 5, 3, 9, 5, 1, 7, 7, 9, 7, 9, 3, 1, 1, 9, 1, 19, 13, 17, 15, 9,
9, 1, 3, 1, 1, 7, 1, 5, 19, 3, 3, 11, 7, 1, 13, 1, 1, 5, 1, 5, 15, 5, 3, 3, 3,
1, 7, 3, 11, 5, 21, 1, 1, 7, 1, 5, 3, 15, 5, 21, 19, 15, 1, 1, 1, 7, 1, 3, 5,
17, 5, 11, 9, 9, 1, 17, 3, 1, 1, 5, 1, 11, 23, 3, 3, 9, 5, 5, 1, 3, 3, 5, 5,
13, 3, 1, 1, 9, 1, 11, 5, 3, 3, 7, 5, 5, 3, 1, 5, 1, 1, 5, 1, 9, 3, 3, 9, 17,
13, 3, 3, 1, 3, 3, 9, 5, 5, 3, 1, 1, 5, 7, 1, 1, 1, 7, 3, 1, 13, 11, 9, 3, 5,
1, 1, 3, 7, 1, 1, 3, 7, 3, 1, 1, 9, 5, 1, 1, 5, 7, 13, 3, 7, 7, 3, 1, 1, 11, 15,
1, 3, 1, 17, 3, 7, 1, 1, 7, 7, 1, 3, 1, 9, 5, 3, 1, 1, 5, 3, 1, 11, 1, 7, 3, 5,
7, 17, 3, 7, 1, 1, 17, 5, 1, 3, 9, 1, 13, 3, 7, 1, 1, 20, 3, 1, 11, 3, 1, 7,
15, 5, 3, 9, 11, 1, 1, 3, 19, 1, 25, 5, 5, 1, 1, 1, 5, 9, 1, 3, 7, 23, 1, 7, 7,
3, 20, 5, 3, 1, 1, 5, 7, 1, 20, 19, 9, 9, 1, 7, 3, 3, 1, 1, 11, 3, 1, 13, 22,
7, 13, 1, 3, 5, 7, 17, 3, 3, 9, 1, 1, 3, 15, 1, 7, 13, 7, 7, 11, 1, 3, 5, 5, 1,
1, 5, 21, 1, 17, 9, 9, 11, 3, 5, 1, 9, 13, 1, 1, 11, 20, 1, 3, 5, 11, 7, 3, 15,
1, 7, 7, 15, 11, 7, 9, 1, 1, 9, 3, 1, 5, 7, 9, 5, 3, 3, 13, 1, 15, 7, 3, 1, 1,
7, 11, 1, 9, 3, 13, 9, 5, 5, 3, 1, 7, 5, 13, 23, 3, 1, 1, 3, 3, 1, 7, 9, 11, 3,
5, 3, 3, 3, 1, 1, 20, 7, 1, 5, 3, 9, 19, 7, 7, 3, 3, 1, 5, 5, 15, 3, 7, 5, 1,
1, 13, 3, 3, 1, 15, 11, 5, 1, 1, 7, 3, 5, 1, 7, 3, 3, 9, 9, 20, 5, 1, 1, 13, 3,
5, 1, 1, 5, 11, 7, 9, 1, 1, 20, 11, 9, 1, 3, 1, 7, 7, 3, 1, 1, 7, 5, 13, 1, 3,
1, 17, 15, 7, 3, 5, 13, 15, 1, 1, 3, 9, 7, 1, 5, 3, 1, 13, 17, 9, 3, 5, 1, 1,
3, 3, 9, 1, 20, 13, 1, 5, 5, 5, 11, 9, 3, 5, 1, 1, 3, 7, 9, 1, 5, 3, 17, 1, 11,
1, 1, 3, 7, 7, 1, 3, 3, 5, 13, 1, 1, 3, 13, 7, 1, 13, 25, 3, 9, 1, 22, 15, 7,
5, 5, 3, 3, 1, 1, 13, 9, 3, 1, 15, 5, 11, 15, 19, 1, 9, 1, 1, 7, 7, 17, 1, 3,
7, 15, 15, 15, 3, 1, 1, 1, 9, 17, 11, 1, 3, 3, 21, 7, 5, 13, 1, 1, 1, 9, 28, 5,
1, 5, 3, 22, 7, 9, 3, 1, 22, 20, 15, 7, 1, 1, 9, 9, 5, 1, 30, 17, 7, 3, 7, 11,
3, 1, 7, 9, 5, 1, 1, 5, 5, 9, 1, 7, 5, 7, 7, 3, 19, 11, 1, 5, 20, 9, 9, 19, 3,
1, 1, 5, 5, 9, 1, 3, 5, 7, 7, 3, 3, 17, 19, 1, 1, 1, 3, 9, 7, 7, 1, 1, 5, 5, 7,
15, 1, 3, 9, 21, 17, 15, 7, 7, 11, 1, 1, 3, 7, 7, 11, 1, 1, 3, 3, 15, 1, 1, 3, 3,
7, 7, 1, 1, 9, 3, 3, 1, 1, 9, 3, 3, 23, 1, 1, 15, 17, 3, 5, 1, 1, 3, 22, 19,
11, 1, 5, 1, 1, 3, 5, 7, 11, 1, 13, 1, 1, 13, 19, 5, 5, 1, 3, 1, 3, 5, 11, 1,
1, 9, 17, 3, 3, 1, 5, 1, 17, 7, 3, 13, 3, 5, 7, 9, 1, 1, 17, 7, 3, 3, 1, 7, 19,
1, 1, 3, 24, 11, 3, 1, 7, 3, 1, 1, 1, 7, 13, 5, 3, 1, 7, 3, 1, 19, 13, 3, 3, 7,
1, 1, 9, 11, 3, 7, 1, 5, 3, 1, 17, 3, 3, 5, 13, 9, 1, 1, 3, 9, 20, 17, 1, 5, 9,
13, 1, 1, 7, 5, 3, 3, 1, 11, 26, 5, 1, 3, 7, 9, 9, 1, 1, 3, 5, 5, 23, 1, 11, 3,
5, 1, 19, 15, 3, 3, 3, 1, 1, 7, 9, 5, 3, 1, 7, 9, 13, 3, 1, 5, 1, 1, 7, 3, 3,
15, 1, 27, 5, 5, 3, 1, 13, 9, 5, 3, 5, 21, 1, 1, 9, 15, 20, 3, 1, 25, 7, 7, 20,
1, 3, 9, 5, 5, 23, 11, 3, 15, 1, 1, 3, 3, 5, 7, 1, 13, 19, 3, 9, 7, 1, 15, 19,
1, 1, 5, 5, 9, 7, 1, 20, 5, 3, 3, 5, 1, 9, 7, 21, 3, 15, 25, 5, 1, 1, 9, 3, 11,
3, 1, 22, 13, 5, 5, 7, 3, 1, 1, 5, 35, 7, 11, 1, 9, 3, 3, 11, 5, 5, 1, 9, 3,
11, 5, 9, 1, 1, 5, 3, 25, 25, 1, 23, 9, 7, 3, 3, 11, 9, 1, 1, 1, 3, 11, 11, 15,
1, 32, 7, 7, 3, 3, 25, 28, 1, 7, 5, 3, 1, 1, 22, 5, 7, 11, 1, 3, 22, 3, 3, 7,
5, 5, 1, 22, 3, 13, 1, 1, 11, 19, 11, 11, 1, 7, 5, 5, 19, 11, 11, 3, 1, 13, 9,
9, 19, 7, 3, 5, 5, 1, 1, 19, 7, 11, 5, 1, 3, 7, 22, 24, 17, 5, 3, 7, 1, 7, 1,
1, 5, 9, 20, 3, 1, 5, 17, 15, 15, 9, 3, 3, 20, 1, 5, 11, 11, 9, 1, 1, 3, 3, 11,
13, 17, 1, 1, 5, 3, 5, 7, 15, 1, 9, 3, 1, 1, 7, 17, 15, 21, 9, 1, 7, 13, 11,
20, 7, 5, 5, 1, 1, 15, 20, 5, 7, 11, 1, 1, 3, 13, 1, 1, 3, 5, 19, 19, 13, 1, 1,
3, 3, 7, 20, 7, 1, 1, 13, 3, 3, 15, 7, 1, 5, 1, 7, 3, 15, 3, 1, 1, 5, 7, 7, 11,
17, 1, 3, 15, 1, 1, 5, 5, 7, 13, 3, 1, 17, 5, 1, 13, 5, 5, 1, 1, 17, 3, 3, 5,
5, 1, 9, 9, 1, 3, 7, 5, 3, 22, 15, 1, 1, 7, 5, 19, 5, 3, 1, 5, 11, 9, 1, 15, 1,
1, 7, 5, 9, 3, 5, 1, 7, 3, 3, 1, 5, 7, 5, 13, 13, 1, 1, 28, 9, 3, 5, 15, 1, 19,
17, 26, 5, 1, 1, 1, 9, 5, 5, 22, 11, 1, 3, 7, 5, 9, 1, 3, 13, 7, 3, 3, 1, 1, 5,
5, 17, 15, 3, 1, 25, 5, 29, 3, 7, 1, 1, 5, 5, 17, 17, 3, 1, 9, 5, 9, 11, 11, 1,
3, 15, 13, 9, 20, 9, 3, 5, 1, 1, 3, 9, 9, 5, 13, 1, 20, 3, 5, 9, 7, 7, 1, 3,
22, 11, 1, 1, 25, 5, 9, 22, 3, 1, 5, 7, 11, 7, 7, 13, 1, 9, 9, 5, 5, 11, 17, 3,
19, 1, 1, 3, 3, 17, 11, 11, 1, 7, 9, 3, 5, 5, 11, 7, 1, 11, 9, 1, 1, 9, 13, 17,
7, 7, 1, 3, 11, 5, 5, 7, 15, 11, 1, 3, 3, 3, 13, 15, 7, 9, 1, 1, 3, 7, 7, 9,
13, 1, 11, 5, 3, 21, 9, 13, 13, 11, 1, 3, 9, 1, 1, 11, 11, 13, 3, 9, 1, 7, 5,
5, 9, 19, 24, 3, 7, 1, 3, 13, 19, 7, 7, 9, 11, 5, 1, 1, 9, 7, 7, 7, 19, 5, 1,
3, 9, 15, 1, 1, 3, 3, 7, 7, 11, 13, 1, 1, 1, 3, 3, 7, 3, 3, 7, 1, 1, 1, 1, 5,
15, 3, 3, 7, 3, 1, 1, 17, 5, 19, 9, 7, 1, 1, 3, 13, 13, 5, 5, 7, 1, 3, 1, 7, 1,
1, 9, 9, 20, 20, 3, 24, 1, 5, 1, 17, 3, 3, 11, 1, 1, 5, 5, 7, 11, 3, 5, 1, 9,
7, 1, 1, 15, 5, 21, 5, 3, 3, 1, 7, 15, 1, 21, 5, 9, 3, 5, 1, 1, 7, 17, 9, 3, 3,
5, 1, 5, 24, 26, 1, 1, 1, 5, 5, 13, 3, 11, 3, 1, 27, 5, 7, 1, 5, 11, 29, 3, 5,
1, 1, 3, 11, 9, 9, 5, 3, 1, 11, 5, 5, 9, 1, 13, 27, 1, 1, 5, 7, 7, 3, 3, 22, 1,
34, 29, 5, 5, 1, 3, 7, 1, 1, 7, 3, 20, 19, 9, 13, 1, 9, 7, 3, 3, 1, 7, 17, 9,
11, 20, 5, 3, 1, 1, 7, 5, 9, 3, 27, 5, 1, 3, 22, 9, 9, 15, 1, 5, 7, 3, 22, 1,
1, 9, 9, 3, 13, 13, 15, 1, 7, 5, 5, 3, 3, 1, 7, 7, 9, 5, 13, 11, 3, 1, 1, 5, 9,
9, 9, 3, 7, 1, 5, 5, 15, 17, 3, 3, 1, 7, 5, 1, 1, 11, 11, 3, 30, 5, 5, 1, 7,
11, 3, 20, 20, 5, 9, 1, 1, 3, 3, 20, 5, 13, 7, 1, 7, 5, 3, 15, 21, 13, 13, 1,
9, 5, 3, 15, 1, 1, 7, 30, 23, 5, 26, 15, 1, 3, 5, 9, 9, 27, 27, 13, 7, 1, 1, 3,
3, 11, 24, 7, 11, 1, 25, 22, 3, 5, 5, 20, 7, 7, 1, 19, 15, 3, 9, 17, 7, 11, 1,
1, 9, 5, 3, 3, 7, 11, 1, 11, 9, 24, 5, 5, 3, 7, 21, 1, 27, 3, 3, 9, 7, 11, 21,
1, 1, 15, 15, 3, 11, 7, 20, 20, 1, 3, 9, 1, 1, 22, 11, 13, 7, 24, 3, 5, 1, 1,
1, 1, 3, 7, 30, 13, 5, 9, 9, 1, 1, 3, 3, 3, 3, 5, 1, 1, 17, 7, 19, 11, 9, 3, 3,
1, 3, 1, 1, 1, 11, 20, 7, 9, 15, 3, 3, 1, 5, 1, 13, 7, 7, 3, 3, 25, 25, 5, 1, 1,
7, 7, 5, 3, 7, 3, 9, 1, 3, 3, 1, 5, 5, 7, 9, 7, 1, 1, 3, 15, 3, 5, 5, 11, 3, 1,
7, 11, 7, 1, 1, 1, 5, 9, 3, 7, 3, 20, 20, 1, 5, 3, 3, 11, 1, 1, 17, 7, 9, 5, 7,
3, 5, 1, 3, 3, 3, 9, 1, 5, 1, 1, 15, 11, 7, 3, 19, 17, 3, 1, 3, 3, 5, 7, 1, 5,
5, 9, 13, 17, 3, 1, 1, 3, 5, 7, 13, 20, 3, 3, 1, 5, 5, 7, 13, 13, 1, 7, 3, 20,
5, 7, 1, 1, 3, 17, 11, 5, 5, 20, 7, 1, 23, 3, 7, 17, 5, 3, 1, 3, 3, 20, 11, 1,
1, 13, 9, 7, 11, 3, 5, 7, 1, 19, 3, 3, 3, 9, 5, 17, 1, 1, 1, 15, 19, 3, 11, 9,
24, 7, 1, 5, 5, 11, 7, 9, 9, 3, 1, 1, 1, 17, 11, 15, 15, 5, 5, 3, 1, 27, 21,
17, 3, 7, 13, 5, 1, 9, 1, 1, 5, 3, 3, 13, 9, 9, 11, 1, 5, 7, 26, 3, 19, 11, 9,
1, 5, 3, 7, 9, 9, 3, 3, 1, 1, 20, 7, 11, 5, 5, 22, 3, 1, 19, 13, 11, 11, 5, 3,
3, 1, 7, 19, 5, 11, 13, 22, 9, 1, 1, 5, 9, 9, 11, 17, 3, 7, 1, 3, 7, 7, 9, 22,
22, 9, 5, 1, 3, 5, 11, 1, 1, 9, 9, 3, 7, 5, 20, 25, 34, 1, 1, 9, 3, 3, 33, 5, 5,
15, 9, 1, 1, 1, 3, 11, 5, 21, 19, 13, 9, 7, 1, 5, 9, 7, 5, 1, 1, 21, 13, 23, 9,
9, 7, 5, 15, 1, 1, 1, 1, 11, 5, 7, 7, 3, 13, 9, 26, 1, 1, 5, 1, 1, 3, 11, 13, 26,
23, 15, 5, 7, 1, 1, 11, 11, 7, 7, 5, 5, 15, 1, 1, 3, 3, 9, 7, 5, 7, 11, 22, 1,
13, 1, 19, 5, 20, 1, 1, 11, 15, 9, 3, 9, 9, 33, 5, 1, 11, 1, 11, 3, 19, 3, 5,
1, 1, 7, 15, 27, 9, 7, 3, 5, 3, 1, 11, 1, 11, 15, 3, 5, 3, 3, 7, 1, 1, 9, 15,
5, 9, 9, 3, 17, 3, 1, 3, 11, 1, 5, 3, 15, 1, 1, 13, 15, 3, 5, 3, 11, 7, 3, 1,
3, 21, 1, 3, 7, 7, 15, 15, 1, 1, 21, 3, 5, 3, 7, 17, 15, 3, 1, 13, 9, 1, 7, 3,
15, 5, 5, 3, 27, 1, 1, 7, 17, 20, 7, 5, 3, 13, 3, 1, 17, 5, 5, 1, 3, 9, 3, 1,
1, 17, 19, 3, 7, 13, 13, 24, 7, 1, 3, 7, 3, 1, 15, 11, 11, 9, 3, 1, 1, 7, 3, 5,
26, 9, 7, 7, 3, 1, 9, 24, 5, 5, 1, 1, 3, 5, 5, 21, 9, 7, 9, 3, 1, 3, 9, 3, 5,
1, 9, 19, 15, 15, 3, 1, 1, 7, 9, 19, 13, 19, 3, 7, 3, 1, 5, 9, 5, 5, 1, 3, 9,
11, 7, 19, 15, 15, 5, 1, 1, 23, 3, 21, 5, 5, 9, 20, 7, 1, 3, 19, 9, 15, 1, 3,
11, 3, 7, 9, 5, 5, 22, 1, 1, 7, 3, 3, 26, 3, 5, 9, 7, 1, 15, 9, 13, 17, 3, 1,
9, 17, 5, 5, 1, 1, 23, 3, 3, 11, 7, 3, 5, 3, 1, 9, 5, 15, 5, 5, 1, 17, 7, 3, 9,
3, 3, 3, 1, 1, 17, 7, 5, 21, 3, 5, 3, 3, 1, 3, 9, 7, 3, 11, 3, 1, 11, 15, 3, 5,
1, 1, 11, 7, 3, 9, 15, 11, 5, 3, 1, 3, 3, 7, 11, 20, 3, 3, 1, 1, 1, 21, 7, 5, 3,
5, 5, 11, 15, 1, 7, 19, 7, 3, 11, 3, 3, 1, 7, 11, 5, 1, 1, 3, 3, 5, 5, 11, 9,
3, 17, 1, 15, 7, 15, 3, 13, 3, 3, 7, 1, 5, 5, 1, 1, 13, 7, 13, 3, 11, 3, 3, 5,
1, 9, 15, 9, 3, 5, 23, 7, 11, 1, 5, 3, 9, 3, 3, 11, 13, 7, 1, 7, 1, 3, 17, 1,
3, 1, 3, 3, 13, 11, 13, 5, 5, 1, 11, 1, 1, 3, 7, 3, 1, 5, 1, 1, 7, 11, 9, 9, 3,
5, 3, 9, 1, 3, 1, 19, 1, 7, 1, 5, 1, 3, 1, 9, 9, 22, 5, 22, 9, 3, 1, 3, 1, 9,
7, 1, 9, 13, 1, 13, 1, 3, 13, 1, 9, 11, 9, 7, 3, 7, 3, 1, 3, 1, 9, 5, 5, 1, 3,
13, 3, 1, 3, 1, 7, 5, 3, 9, 1, 15, 1, 3, 7, 5, 3, 1, 3, 1, 3, 1, 9, 9, 20, 3,
1, 3, 5, 3, 7, 3, 3, 13, 1, 9, 1, 17, 3, 3, 13, 3, 1, 3, 5, 7, 1, 21, 1, 15, 3,
9, 19, 3, 1, 7, 17, 7, 11, 9, 3, 1, 3, 1, 3, 9, 7, 3, 9, 7, 1, 11, 11, 1, 3, 1,
3, 17, 3, 9, 15, 13, 1, 15, 7, 9, 7, 7, 3, 5, 3, 1, 3, 1, 7, 5, 7, 3, 5, 7, 3,
1, 3, 7, 3, 1, 15, 1, 15, 3, 7, 5, 5, 3, 7, 3, 1, 3, 1, 11, 5, 5, 3, 5, 7, 5,
17, 1, 7, 3, 7, 3, 5, 7, 1, 17, 1, 3, 11, 3, 7, 3, 7, 3, 11, 1, 5, 17, 5, 3,
13, 9, 3, 7, 1, 7, 1, 1, 19, 5, 17, 5, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 19, 17,
25, 3, 7, 13, 7, 1, 13, 1, 1, 7, 1, 7, 3, 9, 1, 9, 1, 1, 5, 13, 1, 1, 3, 1, 1,
3, 15, 1, 7, 15, 11, 11, 5, 7, 5, 3, 1, 13, 1, 1, 3, 7, 9, 1, 9, 11, 7, 20, 1,
24, 1, 1, 9, 7, 9, 7, 1, 13, 3, 1, 3, 1, 1, 9, 11, 7, 19, 1, 7, 3, 19, 3, 13,
3, 7, 1, 11, 1, 1, 5, 13, 13, 3, 7, 1, 7, 3, 15, 1, 17, 1, 1, 9, 5, 7, 13, 7,
3, 1, 20, 13, 1, 5, 1, 1, 20, 3, 11, 3, 17, 15, 1, 9, 3, 1, 3, 1, 1, 3, 11, 3,
5, 3, 5, 1, 3, 15, 9, 15, 7, 13, 7, 7, 1, 3, 1, 1, 5, 26, 3, 3, 13, 3, 11, 1,
5, 9, 3, 3, 17, 5, 7, 1, 5, 1, 1, 5, 3, 5, 3, 5, 5, 3, 7, 1, 22, 1, 1, 9, 11, 3,
11, 3, 7, 5, 3, 1, 3, 24, 5, 7, 11, 1, 11, 1, 13, 1, 31, 3, 5, 22, 1, 15, 1, 3,
1, 1, 9, 19, 9, 1, 5, 1, 5, 1, 11, 1, 1, 7, 1, 9, 1, 15, 1, 1, 5, 1, 13, 1, 13,
1, 3, 5, 7, 9, 3, 27, 5, 1, 7, 1, 9, 1, 13, 3, 1, 3, 5, 7, 3, 1, 20, 1, 11, 1,
7, 15, 1, 22, 7, 3, 7, 1, 15, 1, 3, 1, 19, 5, 5, 1, 3, 7, 9, 1, 7, 1, 9, 1, 3,
7, 19, 7, 1, 1, 3, 1, 5, 1, 11, 17, 9, 7, 1, 7, 1, 7, 1, 3, 1, 11, 20, 29, 19,
1, 3, 5, 5, 3, 7, 3, 7, 22, 1, 23, 1, 19, 1, 15, 7, 9, 3, 9, 1, 5, 9, 3, 7, 9,
1, 20, 1, 5, 1, 3, 7, 9, 7, 5, 1, 5, 3, 9, 19, 3, 7, 1, 7, 1, 5, 1, 17, 15, 3,
7, 3, 9, 1, 11, 5, 3, 7, 15, 1, 9, 1, 9, 1, 19, 3, 22, 7, 7, 9, 5, 1, 5, 5, 1,
11, 1, 19, 1, 9, 3, 11, 5, 9, 15, 3, 1, 3, 5, 7, 5, 1, 3, 1, 11, 1, 17, 22, 7,
3, 3, 15, 13, 1, 11, 7, 5, 7, 3, 1, 3, 1, 15, 1, 3, 5, 3, 5, 11, 7, 3, 5, 1, 5,
22, 1, 3, 1, 19, 1, 11, 3, 9, 5, 9, 3, 5, 9, 1, 5, 17, 5, 11, 1, 5, 1, 13, 3,
1, 7, 5, 3, 1, 5, 1, 3, 9, 1, 1, 1, 3, 1, 7, 5, 1, 1, 17, 5, 11, 1, 3, 1, 3,
11, 1, 1, 3, 34, 5, 19, 17, 1, 20, 1, 17, 5, 1, 5, 1, 3, 7, 1, 11, 1, 17, 3, 1,
9, 1, 15, 5, 3, 5, 19, 1, 9, 1, 5, 3, 1, 9, 7, 1, 5, 1, 5, 17, 1, 9, 3, 1, 3,
19, 3, 7, 9, 7, 1, 5, 1, 5, 7, 1, 28, 3, 19, 1, 1, 5, 1, 5, 11, 1, 3, 9, 3, 1,
7, 20, 1, 7, 1, 13, 7, 1, 5, 23, 3, 7, 1, 7, 1, 13, 3, 1, 3, 11, 5, 7, 1, 7,
17, 13, 1, 5, 1, 15, 7, 1, 11, 20, 5, 3, 5, 1, 5, 7, 1, 13, 1, 3, 5, 1, 11, 7,
5, 9, 3, 20, 1, 11, 1, 9, 13, 1, 5, 3, 9, 3, 11, 7, 1, 5, 3, 5, 24, 1, 17, 1,
13, 11, 1, 3, 5, 3, 5, 9, 5, 1, 3, 3, 13, 7, 20, 1, 7, 1, 9, 3, 1, 11, 9, 7, 3,
15, 3, 11, 1, 7, 3, 1, 3, 1, 9, 9, 1, 3, 5, 17, 3, 19, 5, 3, 1, 3, 9, 13, 7,
20, 3, 24, 1, 11, 1, 20, 3, 1, 9, 5, 11, 3, 9, 5, 9, 3, 1, 11, 9, 13, 21, 23,
5, 1, 3, 1, 3, 17, 5, 1, 5, 3, 7, 1, 11, 1, 3, 15, 3, 1, 1, 19, 1, 3, 7, 9, 1,
1, 3, 9, 13, 5, 7, 1, 7, 1, 9, 3, 7, 1, 5, 1, 3, 7, 1, 21, 1, 5, 3, 11, 1, 13,
1, 5, 3, 5, 3, 13, 5, 13, 5, 1, 7, 1, 11, 9, 5, 1, 5, 9, 1, 15, 7, 9, 20, 15,
3, 1, 3, 1, 22, 5, 20, 1, 5, 13, 5, 1, 5, 9, 3, 1, 17, 1, 5, 7, 13, 1, 20, 3,
9, 7, 1, 1, 3, 1, 7, 13, 5, 1, 15, 3, 5, 13, 1, 13, 7, 7, 3, 7, 3, 1, 13, 1,
20, 3, 11, 1, 5, 9, 5, 15, 3, 1, 7, 9, 7, 1, 5, 1, 7, 3, 13, 1, 17, 7, 13, 5,
3, 5, 1, 7, 1, 7, 1, 15, 3, 7, 1, 11, 23, 9, 7, 3, 5, 1, 5, 9, 17, 5, 3, 1, 7,
1, 9, 21, 5, 1, 3, 5, 11, 9, 5, 13, 26, 1, 7, 3, 1, 5, 1, 13, 3, 9, 1, 9, 11,
9, 5, 7, 5, 3, 7, 1, 1, 3, 1, 3, 7, 9, 1, 5, 15, 3, 9, 3, 7, 3, 7, 1, 7, 13, 5,
3, 7, 3, 1, 3, 1, 9, 9, 5, 5, 1, 3, 3, 9, 1, 5, 1, 5, 11, 7, 3, 1, 1, 7, 23, 1,
13, 1, 5, 17, 3, 39, 1, 1, 5, 5, 17, 9, 3, 7, 3, 1, 3, 1, 5, 5, 7, 17, 1, 19,
1, 11, 5, 9, 7, 1, 5, 1, 3, 7, 3, 9, 1, 7, 19, 1, 3, 28, 5, 1, 7, 1, 11, 9, 7,
3, 1, 3, 5, 11, 1, 1, 5, 1, 9, 5, 3, 5, 1, 9, 15, 5, 1, 7, 3, 7, 3, 17, 7, 11,
1, 5, 1, 5, 17, 7, 3, 1, 7, 3, 9, 5, 1, 7, 5, 3, 5, 11, 13, 1, 5, 1, 20, 9, 5, 15,
1, 9, 3, 5, 3, 5, 1, 19, 7, 5, 3, 11, 1, 9, 1, 3, 3, 15, 3, 1, 9, 7, 5, 19, 3,
13, 1, 5, 11, 3, 1, 9, 1, 19, 13, 3, 9, 1, 24, 15, 9, 5, 22, 3, 1, 11, 7, 5, 1,
3, 1, 9, 5, 3, 11, 1, 5, 11, 7, 21, 7, 3, 7, 1, 11, 1, 13, 1, 17, 5, 19, 21, 1,
11, 3, 7, 3, 7, 28, 17, 9, 1, 3, 1, 5, 29, 13, 7, 1, 3, 3, 7, 3, 7, 13, 22, 5,
1, 1, 5, 1, 9, 25, 5, 7, 1, 9, 7, 13, 21, 17, 5, 7, 9, 1, 11, 3, 21, 7, 1, 7,
1, 3, 9, 11, 5, 13, 1, 11, 21, 1, 20, 1, 3, 5, 3, 7, 26, 1, 13, 5, 3, 1, 17, 1,
5, 13, 5, 7, 3, 1, 1, 3, 1, 3, 7, 22, 7, 15, 1, 1, 5, 7, 19, 13, 15, 5, 5, 1,
3, 1, 19, 3, 15, 13, 22, 1, 5, 1, 5, 1, 5, 19, 5, 19, 7, 1, 3, 1, 11, 5, 17, 3,
1, 3, 1, 13, 7, 15, 5, 3, 1, 7, 11, 1, 27, 5, 1, 9, 1, 7, 15, 21, 21, 5, 1, 3,
11, 1, 7, 15, 5, 13, 15, 1, 3, 1, 24, 37, 5, 3, 5, 1, 9, 21, 1, 5, 9, 7, 3, 3,
5, 3, 1, 5, 1, 9, 19, 13, 3, 3, 1, 7, 3, 5, 1, 13, 11, 7, 17, 3, 1, 5, 1, 5,
15, 7, 13, 11, 1, 3, 7, 3, 1, 5, 13, 15, 7, 9, 3, 9, 3, 1, 5, 1, 5, 3, 11, 3,
9, 1, 7, 33, 11, 13, 1, 5, 3, 21, 1, 9, 1, 3, 23, 3, 11, 17, 1, 7, 5, 20, 3,
22, 1, 3, 1, 5, 1, 19, 3, 21, 5, 7, 1, 9, 13, 3, 23, 21, 1, 7, 13, 7, 5, 1, 13,
1, 15, 3, 29, 3, 19, 1, 9, 20, 9, 20, 3, 23, 1, 15, 1, 20, 3, 17, 3, 9, 1, 7,
5, 15, 5, 3, 13, 1, 13, 5, 3, 24, 3, 7, 13, 1, 7, 1, 5, 3, 13, 5, 13, 1, 3, 15,
5, 19, 13, 9, 3, 1, 1, 13, 1, 5, 9, 9, 20, 3, 1, 19, 5, 19, 3, 9, 7, 24, 1, 17,
5, 17, 5, 3, 11, 3, 1, 15, 1, 20, 9, 20, 3, 11, 1, 11, 13, 5, 3, 5, 7, 21, 11,
1, 15, 3, 5, 3, 13, 1, 15, 1, 13, 7, 3, 17, 5, 11, 1, 9, 1, 3, 5, 17, 3, 23, 3,
1, 7, 1, 11, 5, 24, 3, 7, 9, 1, 5, 11, 15, 5, 3, 3, 5, 1, 5, 1, 7, 15, 11, 15, 3,
9, 1, 1, 13, 1, 9, 1, 3, 7, 5, 7, 20, 17, 1, 1, 5, 1, 13, 1, 5, 27, 5, 17, 5,
17, 1, 11, 1, 15, 1, 24, 7, 25, 9, 3, 9, 1, 7, 1, 11, 3, 26, 1, 9, 1, 7, 13, 5,
7, 3, 7, 1, 17, 1, 13, 15, 7, 5, 3, 9, 1, 19, 1, 23, 7, 3, 11, 3, 11, 1, 22, 5,
1, 5, 7, 3, 9, 1, 9, 1, 3, 17, 3, 22, 17, 5, 1, 15, 9, 1, 3, 3, 5, 3, 5, 3, 11,
7, 1, 15, 1, 17, 13, 3, 3, 15, 20, 1, 9, 3, 9, 1, 5, 19, 5, 19, 1, 3, 1, 3, 3,
9, 3, 15, 9, 1, 20, 7, 5, 17, 1, 9, 3, 1, 7, 1, 15, 13, 5, 17, 3, 15, 1, 9, 13,
9, 23, 1, 5, 7, 3, 7, 9, 3, 1, 7, 1, 9, 3, 11, 3, 19, 7, 1, 7, 5, 11, 5, 3, 1,
13, 21, 1, 19, 1, 3, 15, 3, 9, 13, 9, 1, 9, 13, 5, 3, 11, 15, 1, 1, 3, 1, 7, 3,
15, 5, 20, 19, 1, 7, 13, 3, 5, 7, 9, 1, 3, 3, 7, 3, 5, 1, 5, 1, 13, 7, 21, 3,
11, 5, 1, 13, 3, 27, 13, 23, 11, 1, 5, 7, 5, 3, 13, 1, 7, 1, 7, 5, 5, 28, 11,
3, 1, 7, 5, 13, 5, 3, 7, 23, 1, 13, 9, 5, 1, 5, 1, 7, 29, 11, 5, 9, 5, 1, 3,
17, 11, 19, 27, 5, 3, 1, 5, 13, 7, 11, 5, 3, 5, 3, 1, 15, 1, 7, 23, 5, 13, 3,
22, 1, 7, 5, 9, 5, 3, 7, 9, 13, 1, 3, 1, 3, 1, 11, 5, 23, 5, 22, 5, 3, 1, 11, 1,
11, 15, 5, 9, 3, 13, 5, 1, 11, 3, 5, 29, 1, 22, 1, 22, 15, 3, 13, 5, 9, 9, 1,
22, 5, 19, 3, 9, 3, 9, 1, 7, 1, 13, 25, 5, 20, 9, 19, 3, 1, 1, 5, 15, 5, 22, 9,
1, 11, 1, 3, 5, 17, 19, 9, 19, 5, 1, 13, 1, 9, 1, 9, 1, 15, 7, 20, 13, 17, 11,
3, 1, 3, 1, 3, 15, 5, 1, 9, 1, 7, 5, 11, 3, 3, 7, 9, 1, 5, 9, 1, 19, 1, 3, 1,
3, 15, 5, 7, 5, 7, 20, 1, 17, 3, 1, 3, 11, 7, 7, 19, 7, 5, 1, 3, 1, 3, 15, 5,
15, 5, 7, 20, 1, 7, 3, 7, 1, 3, 3, 1, 3, 1, 17, 5, 21, 7, 27, 5, 15, 1, 15, 9,
21, 3, 1, 1, 5, 1, 15, 7, 19, 9, 21, 5, 3, 1, 17, 5, 3, 5, 1, 9, 21, 19, 17, 19,
5, 1, 7, 1, 9, 7, 9, 3, 5, 3, 5, 1, 21, 7, 9, 7, 17, 1, 3, 9, 1, 13, 1, 7, 9,
5, 9, 7, 7, 27, 1, 3, 13, 3, 9, 5, 15, 1, 1, 9, 1, 13, 3, 23, 15,
24, 3, 23, 1, 13, 5, 13, 7, 19, 20, 1, 13, 3, 5, 15, 5, 31, 1, 33, 1, 7, 3, 5,
11, 13, 19, 3, 1, 3, 7, 3, 5, 20, 11, 13, 1, 5, 7, 5, 3, 1, 11, 1, 7, 17, 3, 3,
7, 3, 5, 1, 5, 9, 17, 19, 7, 11, 3, 11, 1, 9, 22, 1, 3, 1, 21, 3, 9, 15, 19,
11, 23, 5, 1, 5, 1, 5, 15, 13, 7, 13, 3, 32, 9, 1, 1, 3, 1, 3, 7, 11, 9, 13,
19, 5, 9, 1, 3, 15, 11, 7, 20, 7, 17, 3, 1, 5, 1, 3, 15, 3, 15, 38, 9, 19, 13,
1, 1, 5, 3, 7, 5, 7, 1, 20, 1, 3, 31, 15, 5, 7, 3, 19, 3, 1, 1, 19, 13, 7, 15,
5, 7, 3, 1, 24, 1, 21, 20, 13, 3, 5, 7, 17, 5, 1, 5, 1, 22, 3, 7, 15, 11, 1, 5,
1, 20, 5, 3, 5, 13, 5, 15, 7, 1, 11, 3, 1, 9, 5, 1, 15, 1, 5, 3, 5, 17, 20, 11,
9, 9, 1, 15, 3, 1, 11, 20, 5, 5, 9, 5, 3, 1, 24, 1, 13, 7, 13, 3, 11, 3, 27, 5,
1, 7, 13, 9, 1, 5, 3, 5, 33, 20, 1, 20, 1, 22, 9, 3, 13, 3, 13, 22, 3, 1, 9,
19, 3, 20, 1, 11, 20, 1, 21, 1, 17, 26, 5, 13, 15, 17, 3, 5, 1, 3, 3, 19, 5,
15, 1, 1, 17, 1, 3, 17, 9, 3, 3, 7, 30, 17, 1, 9, 5, 9, 7, 3, 1, 5, 3, 25, 3,
15, 9, 21, 30, 1, 7, 1, 3, 9, 11, 3, 5, 5, 3, 5, 1, 40, 9, 11, 17, 3, 7, 1, 3,
13, 13, 3, 24, 1, 5, 1, 20, 5, 20, 5, 3, 19, 15, 3, 1, 19, 7, 3, 3, 22, 7, 3,
1, 9, 5, 9, 3, 1, 20, 1, 15, 7, 11, 17, 3, 19, 3, 5, 1, 3, 13, 17, 13, 11, 3,
5, 5, 1, 5, 17, 1, 13, 11, 1, 1, 21, 5, 1, 11, 3, 20, 11, 17, 15, 3, 7, 1, 3,
7, 1, 1, 17, 9, 3, 9, 7, 26, 1, 21, 13, 1, 3, 1, 9, 3, 5, 11, 17, 1, 17, 3, 1,
13, 1, 23, 26, 11, 19, 3, 11, 1, 3, 7, 1, 15, 17, 1, 5, 3, 9, 5, 1, 9, 7, 1, 3,
11, 19, 1, 13, 19, 13, 1, 9, 15, 1, 3, 5, 20, 1, 5, 9, 5, 23, 7, 1, 11, 3, 1,
11, 3, 13, 21, 1, 11, 17, 30, 11, 1, 5, 19, 1, 3, 19, 3, 5, 1, 3, 9, 17, 11, 1,
13, 7, 1, 15, 3, 9, 7, 1, 5, 3, 5, 13, 3, 1, 7, 19, 1, 3, 13, 5, 15, 13, 1, 7,
9, 5, 3, 1, 11, 3, 1, 3, 7, 9, 3, 17, 1, 3, 3, 3, 5, 1, 9, 7, 1, 11, 17, 3, 3,
5, 1, 7, 9, 7, 3, 19, 9, 3, 3, 1, 3, 5, 1, 26, 9, 17, 21, 9, 3, 1, 5, 3, 3, 5,
9, 3, 19, 1, 3, 9, 1, 3, 3, 9, 5, 9, 3, 1, 3, 11, 13, 3, 3, 5, 9, 1, 3, 7, 1,
13, 15, 9, 3, 17, 5, 3, 1, 5, 11, 11, 1, 3, 5, 1, 5, 3, 7, 9, 3, 3, 15, 9, 1,
5, 15, 1, 5, 7, 1, 9, 17, 3, 3, 5, 15, 5, 13, 1, 3, 13, 1, 25, 7, 1, 5, 3, 11,
15, 3, 3, 15, 7, 1, 13, 5, 15, 3, 17, 9, 7, 15, 1, 3, 11, 1, 1, 3, 7, 22, 9, 5,
15, 13, 1, 3, 13, 1, 1, 13, 3, 9, 15, 3, 3, 20, 1, 11, 15, 1, 1, 1, 7, 3, 11,
13, 3, 3, 1, 23, 5, 1, 1, 11, 1, 11, 3, 19, 3, 5, 1, 3, 9, 1, 1, 9, 1, 3, 11,
3, 24, 11, 5, 1, 5, 3, 1, 1, 3, 1, 3, 3, 3, 5, 21, 3, 9, 1, 23, 3, 1, 1, 3, 17,
1, 5, 3, 5, 9, 7, 11, 1, 3, 19, 1, 1, 5, 3, 1, 7, 3, 21, 5, 3, 7, 3, 1, 9, 3,
1, 1, 5, 7, 5, 1, 9, 17, 3, 11, 1, 3, 13, 1, 1, 20, 9, 3, 11, 1, 5, 13, 3, 1,
19, 3, 1, 1, 9, 9, 7, 11, 1, 15, 3, 11, 30, 3, 1, 3, 9, 1, 1, 5, 13, 3, 3, 1,
7, 3, 13, 3, 7, 1}
__________
Many thanks Lars, Maximilian and Jean-Marc, this is now https://oeis.org/A211206
Best,
É.
P.-S. See also here for
the same idea, but with Hofstadter
instead of Wilson.