An afaik unnamed involution

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Problem

f is an involution on positive integers, i.e. f is a function that satisfies

f(f(x)) = x

for any positive integer x.

Please detect f and print the values of f(x) for the first 100 positive integers.

-- tails

Options

exec is denied

rejudge feature is enabled

now post-mortem time, all source codes will be revealed

Sample input:_

*NOTHING*

Sample output:

1 : 1
2 : 3
3 : 2
4 : 5
5 : 4
6 : 6
7 : 8
8 : 7
9 : 16
10 : 12
11 : 32
12 : 10
13 : 64
14 : 24
15 : 128
16 : 9
17 : 256
18 : 48
19 : 512
20 : 20
21 : 1024
22 : 96
23 : 2048
24 : 14
25 : 4096
26 : 192
27 : 8192
28 : 40
29 : 16384
30 : 384
31 : 32768
32 : 11
33 : 65536
34 : 768
35 : 131072
36 : 80
37 : 262144
38 : 1536
39 : 524288
40 : 28
41 : 1048576
42 : 3072
43 : 2097152
44 : 160
45 : 4194304
46 : 6144
47 : 8388608
48 : 18
49 : 16777216
50 : 12288
51 : 33554432
52 : 320
53 : 67108864
54 : 24576
55 : 134217728
56 : 56
57 : 268435456
58 : 49152
59 : 536870912
60 : 640
61 : 1073741824
62 : 98304
63 : 2147483648
64 : 13
65 : 4294967296
66 : 196608
67 : 8589934592
68 : 1280
69 : 17179869184
70 : 393216
71 : 34359738368
72 : 112
73 : 68719476736
74 : 786432
75 : 137438953472
76 : 2560
77 : 274877906944
78 : 1572864
79 : 549755813888
80 : 36
81 : 1099511627776
82 : 3145728
83 : 2199023255552
84 : 5120
85 : 4398046511104
86 : 6291456
87 : 8796093022208
88 : 224
89 : 17592186044416
90 : 12582912
91 : 35184372088832
92 : 10240
93 : 70368744177664
94 : 25165824
95 : 140737488355328
96 : 22
97 : 281474976710656
98 : 50331648
99 : 562949953421312
100 : 20480

Ranking

Ruby _

RankUserSizeTimeDateStatistics
1mitchs560.01242016/01/28 00:45:560B / 24B / 29B
2Histocrat560.01192016/02/04 05:22:310B / 21B / 32B
3mitchs (alt)580.01242016/01/28 00:46:590B / 24B / 31B

Ruby2 _

RankUserSizeTimeDateStatistics
1mitchs570.06822016/01/28 00:47:540B / 26B / 28B
2Histocrat570.06832016/02/04 05:24:440B / 23B / 31B
3olg590.16422016/02/04 10:30:000B / ?B / ?B
4olf590.10222016/02/04 10:32:450B / ?B / ?B
5angel620.08822016/01/21 16:14:070B / ?B / ?B
6gmk640.06462016/01/22 12:46:380B / 23B / 38B
7shinh690.06632016/01/25 20:39:260B / 32B / 32B

Perl _

RankUserSizeTimeDateStatistics
1llhuii520.01612016/01/31 16:24:440B / 17B / 32B
2tails520.02512016/02/01 14:48:440B / 17B / 32B
3teebee530.02232016/01/28 08:38:030B / 20B / 30B
4%20850.00012016/01/22 20:03:420B / 39B / 43B

Python _

RankUserSizeTimeDateStatistics
1whatisgolf590.04892016/01/21 23:36:510B / ?B / ?B
2mitchs590.04102016/01/22 00:47:340B / 31B / 27B
3llhuii590.03372016/01/31 15:32:090B / 31B / 28B
4xsot610.09372016/01/25 21:53:560B / 32B / 27B
5xnor610.12212016/01/28 07:32:290B / ?B / ?B
6rolf720.03352016/01/22 05:49:270B / 38B / 31B
7mitchs (whatisgolf)570.03592016/02/04 11:06:530B / 28B / 28B

Python3 _

RankUserSizeTimeDateStatistics
1mitchs620.06062016/02/03 19:25:590B / 32B / 29B
2llhuii620.05812016/02/04 00:59:220B / 32B / 29B
3xsot640.06322016/02/03 18:56:400B / 33B / 30B

JavaScript _

RankUserSizeTimeDateStatistics
1...840.07602016/01/28 09:28:420B / 48B / 34B
2Jakzo840.01802016/01/28 09:55:050B / 48B / 34B
3teebee(...,Jakzo)730.02892016/02/04 12:12:190B / 38B / 33B

PARI/GP _

RankUserSizeTimeDateStatistics
1mitchs580.02482016/01/21 11:49:210B / 32B / 24B

C _

RankUserSizeTimeDateStatistics
1llhuii700.01282016/01/31 15:32:540B / 34B / 34B
2tails710.01502016/01/30 22:26:230B / 35B / 34B

Haskell _

RankUserSizeTimeDateStatistics
1henkma890.01772016/01/29 22:01:380B / 43B / 40B

ObjC _

RankUserSizeTimeDateStatistics
1llhuii700.00012016/01/31 15:37:200B / 34B / 34B

AWK _

RankUserSizeTimeDateStatistics
1llhuii700.01382016/01/30 20:01:360B / ?B / ?B

sed _

RankUserSizeTimeDateStatistics
1tails1780.32482016/01/23 13:45:120B / 52B / 98B
2mitchs (tails)1740.22482016/02/05 03:25:390B / 64B / 83B

Bash (builtins) _

RankUserSizeTimeDateStatistics
1tails830.03352016/02/01 10:37:130B / 32B / 44B
2tails650.04092016/02/04 14:06:190B / 22B / 36B

make _

RankUserSizeTimeDateStatistics
1tails4200.08792016/01/27 18:18:160B / 216B / 161B

dc _

RankUserSizeTimeDateStatistics
1tails440.01302016/01/23 21:26:330B / 28B / 14B

xgawk _

RankUserSizeTimeDateStatistics
1llhuii630.01452016/01/30 19:59:330B / ?B / ?B
2teebee640.01142016/01/30 16:52:090B / 36B / 26B
3llhuii(teebee)600.01512016/02/04 11:34:140B / ?B / ?B
4teebee(llhuii)610.03122016/02/04 11:26:300B / 29B / 30B

Brainfuck _

RankUserSizeTimeDateStatistics
1mitchs (cheat)2890.04872016/02/04 10:40:400B / 1B / 286B
2mitchs3260.03812016/02/04 10:38:540B / 0B / 326B
3mitchs (cheat)2770.06342016/02/06 09:38:580B / 1B / 274B
4mitchs3100.04472016/02/07 12:04:050B / 0B / 310B

GolfScript _

RankUserSizeTimeDateStatistics
1tails370.03402016/01/22 19:28:200B / 9B / 25B

gs2 _

RankUserSizeTimeDateStatistics
1mitchs200.09882016/01/21 14:41:197B / 6B / 6B

Language Ranking_

RankLangUserSizeScore
1gs2mitchs2010000
2GolfScripttails375405
3dctails444545
4Perlllhuii523846
5Rubymitchs563571
6Ruby2mitchs573508
7Pythonmitchs (whatisgolf)573508
8PARI/GPmitchs583448
9xgawkllhuii(teebee)603333
10Python3mitchs623225
11Bash (builtins)tails653076
12AWKllhuii702857
13Cllhuii702857
14ObjCllhuii702857
15JavaScriptteebee(...,Jakzo)732739
16Haskellhenkma892247
17sedmitchs (tails)1741149
18Brainfuckmitchs (cheat)277722
19maketails420476

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