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Beating Go Thanks to the Power of Randomness

Beating Go Thanks to the Power of Randomness

Go is a board game that is more than 2,500 years old (yes, this is not about the programming language!) and it is fascinating from multiple viewpoints. For instance, go bots still can’t beat professional players, unlike in chess.

This talk will show you what is so special about Go that computers still can’t beat humans. We will take a look at the most popular underlying algorithm and show you how the Monte Carlo method, basically random simulation, plays a vital role in conquering Go's complexity and creating the strong Go bots of today.

Tobias Pfeiffer

November 17, 2015
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  1. 1997

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  2. Ing cup 1985 – 2000
    (up to 1,400,000$)
    (1985-2000)

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  3. 2001

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  4. 2009

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  5. 2014

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  6. 31st October
    2015

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  7. 3rd November 2015

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  8. 13th November 2015

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  9. Beating Go thanks to the power
    of randomness
    Tobias Pfeiffer
    @PragTob
    pragtob.info

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  47. Go vs. Chess

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  48. Complex vs. Complicated

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  49. „While the Baroque rules of chess could only
    have been created by humans, the rules of
    go are so elegant, organic, and rigorously
    logical that if intelligent life forms exist
    elsewhere in the universe, they almost
    certainly play go.“
    Edward Lasker (chess grandmaster)

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  50. Range Stage
    30k-20k Beginner
    19k-10k Casual Player
    9k-1k Intermediate Amateur
    1d-7d Advanced Amateur
    1p-9p Professional

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  55. 5d win 1998

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  56. Why is Go so hard?

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  57. Larger board
    19x19 vs. 8x8

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  58. Almost every move is legal

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  59. Average branching factor:
    250 vs 35

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  60. State Space Complexity:
    10171 vs 1047

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  61. 1080

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  62. Global impact of moves

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  63. Artifical Intelligence

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  64. 6
    8
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    3
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    MAX
    MIN
    MAX
    MIN
    MAX

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  65. 6
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    MAX
    MIN
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    MIN
    MAX

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  66. 6
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    MAX
    MIN
    MAX
    MIN
    MAX

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  67. 6
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    MAX
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  68. 6
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    MAX
    MIN
    MAX
    MIN
    MAX

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  69. Evaluation function

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  71. Monte Carlo Method

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  72. What is Pi?

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  73. How do you determine Pi?

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  75. 2006

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  76. Browne, Cb, and Edward Powley. 2012. A survey of monte carlo tree search methods. Intelligence and AI 4, no. 1: 1-49

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  77. 2/4
    1/1 0/1 1/1 0/1
    A1
    D5
    F13
    C7

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  78. 2/4
    1/1 0/1 1/1 0/1
    A1
    D5
    F13
    C7
    Selection

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  79. 2/4
    1/1 0/1 1/1 0/1
    A1
    D5
    F13
    C7
    0/0
    B5
    Expansion

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  80. 2/4
    1/1 0/1 1/1 0/1
    A1
    D5
    F13
    C7
    0/0
    B5
    Simulation

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  82. 3/5
    2/2 0/1 1/1 0/1
    A1
    D5
    F13
    C7
    1/1
    B5
    Backpropagation

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  83. 3/5
    2/2 0/1 1/1 0/1
    A1
    D5
    F13
    C7
    1/1
    B5
    Perspective

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  84. 2/5
    1/2 0/1 1/1 0/1
    A1
    D5
    F13
    C7
    1/1
    B5
    Perspective

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  85. 2/4
    1/1 0/1 1/1 0/1
    A1
    D5
    F13
    C7
    Selection

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  86. Multi Armed Bandit

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  87. Exploitation vs Exploration

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  88. wins
    visits
    +explorationFactor
    √ln(totalVisits)
    visits

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  89. 15042
    86/193
    0/1 1/2 0/2
    36/1116
    2/2
    58/151
    1/2 0/2
    3/3

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  90. 15042
    86/193
    0/1 1/2 0/2
    36/1116
    2/2
    58/151
    1/2 0/2
    3/3

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  91. 15042
    86/193
    0/1 1/2 0/2
    36/1116
    2/2
    58/151
    1/2 0/2
    3/3

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  92. Not Human like?

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  93. Characteristics

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  94. Aheuristic

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  95. Generate a valid random move

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  96. Who has won?

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  98. General Game Playing

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  99. Anytime

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  100. Lazy

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  105. -2 -1 0 1 2
    8 86% 88% 90% 94% 98%
    16 86% 92% 94% 94% 96%
    32 94% 96% 98% 96% 95%
    64 98% 99,6% 99,9% 99,4% 96%
    100 99,8% 99,9% 100% 99,99% 98%

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  106. -2 -1 0 1 2
    8 86% 88% 90% 94% 98%
    16 86% 92% 94% 94% 96%
    32 94% 96% 98% 96% 95%
    64 98% 99,6% 99,9% 99,4% 96%
    100 99,8% 99,9% 100% 99,99% 98%

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  107. -2 -1 0 1 2
    8 86% 88% 90% 94% 98%
    16 86% 92% 94% 94% 96%
    32 94% 96% 98% 96% 95%
    64 98% 99,6% 99,9% 99,4% 96%
    100 99,8% 99,9% 100% 99,99% 98%

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  108. -2 -1 0 1 2
    8 86% 88% 90% 94% 98%
    16 86% 92% 94% 94% 96%
    32 94% 96% 98% 96% 95%
    64 98% 99,6% 99,9% 99,4% 96%
    100 99,8% 99,9% 100% 99,99% 98%

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  109. View Slide

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  111. Enhancements

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  112. All Moves As First

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  113. RAVE

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  114. Expert Knowledge

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  118. Selection

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  119. Oh yeah

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  120. PragTob/Rubykon

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  121. PragTob/web-go

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  122. pasky/michi

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  123. ujh/iomrascalai

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  124. What have I learned?

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  125. Making X faster
    vs
    Doing less of X

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  126. Modularizing small components

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  127. Benchmark everything

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  128. Solving problems the human way
    vs
    Solving problems the computer
    way

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  129. Joy of Creation

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  130. Beating Go thanks to the power
    of randomness
    Tobias Pfeiffer
    @PragTob
    pragtob.info

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  131. Photo Credit

    https://en.wikipedia.org/wiki/Emperor_Yao#/media/File:Ma_Lin_-_Emperor_Yao.jpg

    https://en.wikipedia.org/wiki/Zuo_Zhuan#/media/File:Li_Yuanyang_Zuo_zhuan_first_page.png

    https://en.wikipedia.org/wiki/Four_arts#/media/File:The_Eighteen_Scholars_by_an_anonymous_Ming_artist_2.jpg

    https://en.wikipedia.org/wiki/Kibi_no_Makibi#/media/File:Kibino_Makibi.jpg

    https://en.wikipedia.org/wiki/Honinbo_Sansa#/media/File:Honinbo_Sansa.jpg

    http://www.bbc.co.uk/arts/yourpaintings/paintings/thomas-hyde-16361703-228754

    https://en.wikipedia.org/wiki/Oskar_Korschelt#/media/File:Oscar_Korschelt.jpg

    https://en.wikipedia.org/wiki/Atari#/media/File:Atari_Official_2012_Logo.svg

    http://www.computer-go.info/events/ing/2000/images/bigcup.jpg

    http://www.wired.com/2014/05/the-world-of-computer-go/

    https://en.wikipedia.org/wiki/File:Radha-Krishna_chess.jpg

    https://en.wikipedia.org/wiki/File:EnxadrismoGravuras.003.jpg

    http://archive.is/QG6a

    http://giphy.com/gifs/monkey-bubbles-chimp-2Faz9OUQfOcltIJTG

    https://en.wikipedia.org/wiki/The_Turk#/media/File:Turk-engraving5.jpg

    https://en.wikipedia.org/wiki/File:Kasparov-29.jpg

    CC BY 2.0
    – https://en.wikipedia.org/wiki/File:Deep_Blue.jpg


    CC BY-SA 3.0
    – https://en.wikipedia.org/wiki/Konrad_Zuse#/media/File:Konrad_Zuse_%281992%29.jpg
    – https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning#/media/File:AB_pruning.svg
    – https://en.wikipedia.org/wiki/Go_%28programming_language%29#/media/File:Golang.png

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  132. Photo Credit

    https://en.wikipedia.org/wiki/Emperor_Yao#/media/File:Ma_Lin_-_Emperor_Yao.jpg

    https://en.wikipedia.org/wiki/Atari#/media/File:Atari_Official_2012_Logo.svg

    http://www.computer-go.info/events/ing/2000/images/bigcup.jpg

    http://www.wired.com/2014/05/the-world-of-computer-go/

    http://archive.is/QG6a

    https://en.wikipedia.org/wiki/The_Turk#/media/File:Turk-engraving5.jpg

    https://en.wikipedia.org/wiki/File:Kasparov-29.jpg

    CC BY 2.0
    – https://en.wikipedia.org/wiki/File:Deep_Blue.jpg


    CC BY-SA 3.0
    – https://en.wikipedia.org/wiki/Konrad_Zuse#/media/File:Konrad_Zuse_%281992%29.jpg
    – https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning#/media/File:AB_pruning.svg
    – https://en.wikipedia.org/wiki/Go_%28programming_language%29#/media/File:Golang.png

    CC BY-SA 2.0
    – https://www.flickr.com/photos/mike_miley/7762037662/in/photolist-cPUtny-2Jyv1K-6rkH7Y-pDdKnE-6W7Amw-
    pDYyb5-pVK2bG-5cavw1-jbNWJC-6rgxSr-cKt4c-5w7uns-pDbh7H-4swKk-9TAvoC-nMY3Do-51yJaD-eUrQ5d-mHs87x-nEkW
    87-hmMnyg-o3Enjw-rf7AY5-8hAiN6-eY3iqs-9fmGiN-sSzYQ-oq6rm2-oA9xdT-froGke-gJ8cJ8-igt2FS-mRz9Gc-gMexAK-
    eSKEzV-nPy1Zu-527E2U-pEgLhp-ivCWw8-bpCbU-qb22fr-odobP9-htytWv-k4NMKa-dCNpPk-foM8Lk-o73rga-dNvVbs-na2
    qUc-eXLwhK

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  133. Photo Credit

    https://en.wikipedia.org/wiki/Emperor_Yao#/media/File:Ma_Lin_-_Emperor_Yao.jpg

    https://en.wikipedia.org/wiki/Zuo_Zhuan#/media/File:Li_Yuanyang_Zuo_zhuan_first_page.png

    https://en.wikipedia.org/wiki/Four_arts#/media/File:The_Eighteen_Scholars_by_an_anonymous_Ming_artist_2.jpg

    https://en.wikipedia.org/wiki/Kibi_no_Makibi#/media/File:Kibino_Makibi.jpg

    https://en.wikipedia.org/wiki/Honinbo_Sansa#/media/File:Honinbo_Sansa.jpg

    http://www.bbc.co.uk/arts/yourpaintings/paintings/thomas-hyde-16361703-228754

    https://en.wikipedia.org/wiki/Oskar_Korschelt#/media/File:Oscar_Korschelt.jpg

    https://en.wikipedia.org/wiki/Atari#/media/File:Atari_Official_2012_Logo.svg

    http://www.computer-go.info/events/ing/2000/images/bigcup.jpg

    http://www.wired.com/2014/05/the-world-of-computer-go/

    https://en.wikipedia.org/wiki/File:Radha-Krishna_chess.jpg

    https://en.wikipedia.org/wiki/File:EnxadrismoGravuras.003.jpg

    http://archive.is/QG6a

    http://giphy.com/gifs/monkey-bubbles-chimp-2Faz9OUQfOcltIJTG

    https://en.wikipedia.org/wiki/The_Turk#/media/File:Turk-engraving5.jpg

    https://en.wikipedia.org/wiki/File:Kasparov-29.jpg

    CC BY 2.0
    – https://en.wikipedia.org/wiki/File:Deep_Blue.jpg


    CC BY-SA 3.0
    – https://en.wikipedia.org/wiki/Konrad_Zuse#/media/File:Konrad_Zuse_%281992%29.jpg
    – https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning#/media/File:AB_pruning.svg
    – https://en.wikipedia.org/wiki/Go_%28programming_language%29#/media/File:Golang.png

    View Slide

  134. Photo Credit

    https://en.wikipedia.org/wiki/Emperor_Yao#/media/File:Ma_Lin_-_Emperor_Yao.jpg

    https://en.wikipedia.org/wiki/Zuo_Zhuan#/media/File:Li_Yuanyang_Zuo_zhuan_first_page.png

    https://en.wikipedia.org/wiki/Four_arts#/media/File:The_Eighteen_Scholars_by_an_anonymous_Ming_artist_2.jpg

    https://en.wikipedia.org/wiki/Kibi_no_Makibi#/media/File:Kibino_Makibi.jpg

    https://en.wikipedia.org/wiki/Honinbo_Sansa#/media/File:Honinbo_Sansa.jpg

    http://www.bbc.co.uk/arts/yourpaintings/paintings/thomas-hyde-16361703-228754

    https://en.wikipedia.org/wiki/Oskar_Korschelt#/media/File:Oscar_Korschelt.jpg

    https://en.wikipedia.org/wiki/Atari#/media/File:Atari_Official_2012_Logo.svg

    http://www.computer-go.info/events/ing/2000/images/bigcup.jpg

    http://www.wired.com/2014/05/the-world-of-computer-go/

    https://en.wikipedia.org/wiki/File:Radha-Krishna_chess.jpg

    https://en.wikipedia.org/wiki/File:EnxadrismoGravuras.003.jpg

    http://archive.is/QG6a

    http://www.usgo.org/news/2011/07/hikaru-anime-on-hulu-and-netflix/

    https://en.wikipedia.org/wiki/The_Turk#/media/File:Turk-engraving5.jpg

    https://en.wikipedia.org/wiki/File:Kasparov-29.jpg

    CC BY 2.0
    – https://en.wikipedia.org/wiki/File:Deep_Blue.jpg
    – https://www.flickr.com/photos/aigle_dore/14110664878/in/photolist-nuUR4u-e1q7YM-5Mqchf-rMcnKt-6rF4Td-aiMGos-nVks3G-7eKpi2-4iRRUa-ecdN2m-t33akk-8
    CQwoX-firCja-8TAfbC-5Do92i-4U6yXA-dQUgdC-2hkKMK-cMgbim-iniaf-7xxKyM-eqqmuT-a7WHU1-5ZbrEE-g97Nph-35ASJL-gJtoKD-9TDrt-fz3bSd-4qAGhJ-ge5BS1-bxiUwu-
    6wYoR8-5UbciZ-84AZHc-59efoV-8gZ1yt-9Le6DZ-dy74yw-pWJVFe-2xCwen-omzMF4-nGgBMj-rq82wx-4GrWvo-yPvGeK-6NuTMt-9eGoR4-9ZifBq-db2fLW

    CC BY-SA 3.0
    – https://en.wikipedia.org/wiki/Konrad_Zuse#/media/File:Konrad_Zuse_%281992%29.jpg
    – https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning#/media/File:AB_pruning.svg
    – https://en.wikipedia.org/wiki/Go_%28programming_language%29#/media/File:Golang.png

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  135. Photo Credit

    CC BY-NC-ND 2.0
    – https://www.flickr.com/photos/aerialcamera/15753422176/in/photolist-q15pzb-5o8noQ-9kzjxL-2j8Cjg
    -e5yjMU-7xTuVB-n75WB6-dCg74N-71JXoJ-8NwBqb-j3typA-79oGNv-aEvcKT-r9j7s2-6pSzwn-aURgGr-j69RDV-4Tw
    VKe-6dGZqk-6FjmMs-8kWfPL-jJMnA2-aA4SnC-7rCdVT-92CTsh-9vbC6n-92CTME-7bhyei-92zK8B-qzprcx-7yhuE8-
    gmpP3A-gmq6uT-9m5Gyx-9m5F9B-2G7F7A-o9fpEY-q2uByi-92DKJr-7T8jPc-92qCsX-acbDAF-7QutRi-cZLZLU-azER
    ev-a3Lcnj-gmoQYw-93s1fE-noZEfj-6jrkdA
    – https://www.flickr.com/photos/stargardener/7037360553/in/photolist-bHSj7D-ipFVRk-dbQMMF-9pkdk1-
    akZXq-ocP2RE-6Rog8i-4NZtZG-aM7Tr4-83N9cr-avkRuq-wUzMF-xvV8G-6EoNDC-bqG35H-8tZTNm-bit9C-xiQv5-7p
    W2xg-5z58z8-wtDY8-bA2bvb-duBtzt-9hnK36-pTKW9S-6GEZSe-9KaFui-9ZAgm1-djUsDh-oPTkQ4-7wwnMo-4wSaYW-
    JyEqK-4tZTqD-9cdenf-na9Bzc-pwiEWL-9ipZiR-prY2Z1-pyTq4i-6Qq3bR-bjFP7x-bXCB3s-77WG8U-pbnQ5v-avy5c
    r-3YdbZj-4wuUvu-qs91kS-dg6cjy
    – https://www.flickr.com/photos/andreastsonis/11518720353/in/photolist-ixSsfM-iFE9j2-8R7Now-cXNz
    15-9iL3iz-iw1VTu-9GvRkV-egTDcw-9iK9Nx-9CpqPB-oDZVWG-egMSC6-egMT2r-egMTez-r54iiS-egMSjr-egMR4Z-
    egTAMQ-egTCfj-egTFt3-egTCrs-egMTWc-egM1Nx-eeDtNx-9iKvwP-9iLhCp-9iPgrL-egTE8J-egTERq-egTDU5-egM
    Rpv-egTC5u-egTBXf-egTBEC-egTFg3-egTF5h-egMUca-egMQRF-egaYGL-9BRUZh-efDsaf-9B7mJK-efDtPh-9BNXsk
    -9Ctoyf-egN3dk-9BaGPu-9iLfpZ-9GvRFM-9GyJR7


    https://en.wikipedia.org/wiki/Alphabet_Inc.#/media/File:Alphabet_Inc_Logo_2015.svg

    CC BY-NC 2.0
    – https://www.flickr.com/photos/sutekidane/2199385255/in/photolist-4mmqBr-7NqSe4-abChUK-9NA6gV-
    755hWp-q4tjgW-8FCyzU-4zcMni-abESMd-4hMNYF-6c24D1-tBRRPr-qDt6Bt-4hRU9J-sEKsZd-a2x9tv-ampYHm-7m
    2UsB-abDDQy-tkiVfc-pJr2of-4t4uQA-enwU-3d2tQV-d8cmaf-4Ymd6d-enwJ-huAHMi-gE97EH-zFu7N-otJ1TR-4V
    AkNv-utVH9-tkak53-56vGR-6LbDW8-c4R6PN-3Hn7Le-abEBUA-7JMTVd-7XodLF-eb2Sme-77gM4Z-6WxHh8-oLcvhR
    -9NA4Yk-4YgWen-oLctgr-otH1Dd-oLcrXe


    CC BY 3.0

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