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1997

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

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2001

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2009

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2014

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31st October 2015

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3rd November 2015

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13th November 2015

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

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Go vs. Chess

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Complex vs. Complicated

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

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5d win 1998

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Why is Go so hard?

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Larger board 19x19 vs. 8x8

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Almost every move is legal

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Average branching factor: 250 vs 35

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State Space Complexity: 10171 vs 1047

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1080

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Global impact of moves

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Artifical Intelligence

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6 8 9 5 7 9 6 6 3 5 4 7 6 5 6 8 5 7 6 6 3 4 5 8 5 7 6 3 5 5 6 3 6 MAX MIN MAX MIN MAX

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6 8 9 5 7 9 6 6 3 5 4 7 6 5 6 8 5 7 6 6 3 4 5 8 5 7 6 3 5 5 6 3 6 MAX MIN MAX MIN MAX

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6 8 9 5 7 9 6 6 3 5 4 7 6 5 6 8 5 7 6 6 3 4 5 8 5 7 6 3 5 5 6 3 6 MAX MIN MAX MIN MAX

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Evaluation function

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Monte Carlo Method

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What is Pi?

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How do you determine Pi?

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2006

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

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

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

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

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

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

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

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

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Multi Armed Bandit

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Exploitation vs Exploration

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wins visits +explorationFactor √ln(totalVisits) visits

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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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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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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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Not Human like?

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Characteristics

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Aheuristic

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Generate a valid random move

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Who has won?

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General Game Playing

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Anytime

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Lazy

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-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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-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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-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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-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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Enhancements

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All Moves As First

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RAVE

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Expert Knowledge

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Selection

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Oh yeah

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PragTob/Rubykon

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PragTob/web-go

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pasky/michi

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ujh/iomrascalai

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What have I learned?

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Making X faster vs Doing less of X

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Modularizing small components

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Benchmark everything

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Solving problems the human way vs Solving problems the computer way

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Joy of Creation

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

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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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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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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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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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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