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HASM quantum machine learning

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Abstract

The miniaturization of transistors led to advances in computers mainly to speed up their computation. Such miniaturization has approached its fundamental limits. However, many practices require better computational resources than the capabilities of existing computers. Fortunately, the development of quantum computing brings light to solve this problem. We briefly review the history of quantum computing and highlight some of its advanced achievements. Based on current studies, the Quantum Computing Advantage (QCA) seems indisputable. The challenge is how to actualize the practical quantum advantage (PQA). It is clear that machine learning can help with this task. The method used for high accuracy surface modelling (HASM) incorporates reinforced machine learning. It can be transformed into a large sparse linear system and combined with the Harrow-Hassidim-Lloyd (HHL) quantum algorithm to support quantum machine learning. HASM has been successfully used with classical computers to conduct spatial interpolation, upscaling, downscaling, data fusion and model-data assimilation of eco-environmental surfaces. Furthermore, a training experiment on a supercomputer indicates that our HASM-HHL quantum computing approach has a similar accuracy to classical HASM and can realize exponential acceleration over the classical algorithms. A universal platform for hybrid classical-quantum computing would be an obvious next step along with further work to improve the approach because of the many known limitations of the HHL algorithm. In addition, HASM quantum machine learning might be improved by: (1) considerably reducing the number of gates required for operating HASM-HHL; (2) evaluating cost and benchmark problems of quantum machine learning; (3) comparing the performance of the quantum and classical algorithms to clarify their advantages and disadvantages in terms of accuracy and computational speed; and (4) the algorithms would be added to a cloud platform to support applications and gather active feedback from users of the algorithms.

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References

  • Aaronson S. 2015. Read the fine print. Nat Phys, 11: 291–293

    Google Scholar 

  • Abigail L, Downs J A. 2021. Machine learning in geography—Past, present, and future. Geography Compass, 15, https://doi.org/10.1111/gec3.12563

  • Alaminos D, Salas M B, Fernández-Gámez M A. 2022. Quantum machine learning algorithms: Read the fine print. Comput Econ, 59: 803–829

    Google Scholar 

  • Alkhasawneh M S, Ngah U K, Tay LT, Isa N AM. 2014. Determination of importance for comprehensive topographic factors on landslide hazard mapping using artificial neural network. Environ Earth Sci, 72: 787–799

    Google Scholar 

  • Arute F, Arya K, Babbush R, Bacon D, Bardin J C, Barends R, Biswas R, Boixo S, Brandao F G S L, Buell D A, Burkett B, Chen Y, Chen Z, Chiaro B, Collins R, Courtney W, Dunsworth A, Farhi E, Foxen B, Fowler A, Gidney C, Giustina M, Graff R, Guerin K, Habegger S, Harrigan M P, Hartmann M J, Ho A, Hoffmann M, Huang T, Humble T S, Isakov S V, Jeffrey E, Jiang Z, Kafri D, Kechedzhi K, Kelly J, Klimov P V, Knysh S, Korotkov A, Kostritsa F, Landhuis D, Lindmark M, Lucero E, Lyakh D, Mandrà S, McClean J R, McEwen M, Megrant A, Mi X, Michielsen K, Mohseni M, Mutus J, Naaman O, Neeley M, Neill C, Niu M Y, Ostby E, Petukhov A, Platt J C, Quintana C, Rieffel E G, Roushan P, Rubin N C, Sank D, Satzinger K J, Smelyanskiy V, Sung K J, Trevithick M D, Vainsencher A, Villalonga B, White T, Yao Z J, Yeh P, Zalcman A, Neven H, Martinis J M. 2019. Quantum supremacy using a programmable superconducting processor. Nature, 574: 505–510

    Google Scholar 

  • Bacon D. 2006. Operator quantum error-correcting subsystems for self-correcting quantum memories. Phys Rev A, 73: 012340

    Google Scholar 

  • Benioff P. 1980. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J Stat Phys, 22: 563–591

    Google Scholar 

  • Bennett C H, Bernstein E, Brassard G, Vazirani U. 1997. Strengths and weaknesses of quantum computing. SIAM J Comput, 26: 1510–1523

    Google Scholar 

  • Bennewitz E R, Hopfmueller F, Kulchytskyy B, Carrasquilla J, Ronagh P. 2022. Neural error mitigation of near-term quantum simulations. Nat Mach Intell, 4: 618–624

    Google Scholar 

  • Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S. 2017. Quantum machine learning. Nature, 549: 195–202

    Google Scholar 

  • Bravo-Prieto C, LaRose R, Cerezo M, Subasi Y, Cincio L,Coles P J. 2019. Variational quantum linear solver. DOI: https://doi.org/10.48550/arXiv.1909.05820

  • Brill K F, Uccellini L W, Manobianco J, Kocin P J, Homan J H. 1991 The use of successive dynamic initialization by nudging to simulate cyclogenesis during GALE IOP 1. Meteorl Atmos Phys, 45: 15–40

    Google Scholar 

  • Bush A B G, Bishop M P, Huo D, Chi Z H, Tiwari U. 2020. Issues in climate analysis and modeling for understanding mountain erosion dynamics. Treatise Geomorphol, 1: 121–140, DOI: https://doi.org/10.1016/B978-0-12-818234-5.00022-5

    Google Scholar 

  • Butt N, Epps K, Overman H, Iwamura T, Fragoso J M V. 2015. Assessing carbon stocks using indigenous peoples’ field measurements in Amazonian Guyana. For Ecol Manage, 338: 191–199

    Google Scholar 

  • Caro M C, Huang H Y, Cerezo M, Sharma K, Sornborger A, Cincio L, Coles P J. 2022. Generalization in quantum machine learning from few training data. Nat Commun, 13: 4919

    Google Scholar 

  • Cavender-Bares J, Schneider F D, Santos M J, Armstrong A, Carnaval A, Dahlin K M, Fatoyinbo L, Hurtt G C, Schimel D, Townsend P A, Ustin S L, Wang Z, Wilson A M. 2022. Integrating remote sensing with ecology and evolution to advance biodiversity conservation. Nat Ecol Evol, 6: 506–519

    Google Scholar 

  • Chalumuri A, Kune R, Manoj B S. 2020. Training an artificial neural network using qubits as artificial neurons: A quantum computing approach. Procedia Comput Sci, 171: 568–575

    Google Scholar 

  • Chambers J Q, Asner G P, Morton D C, Anderson L O, Saatchi S S, Espirito-Santo F D B, Palace M, Souza Jr C. 2007. Regional ecosystem structure and function: Ecological insights from remote sensing of tropical forests. Trends Ecol Evol, 22: 414–423

    Google Scholar 

  • Chiesi M, Fibbi L, Genesio L, Gioli B, Magno R, Maselli F, Moriondo M, Vaccari F P. 2011. Integration of ground and satellite data to model Mediterranean forest processes. Int J Appl Earth Observation GeoInf, 13: 504–515

    Google Scholar 

  • Cohen L Z, Kim I H, Bartlett S D, Brown B J. 2022. Low-overhead fault-tolerant quantum computing using long-range connectivity. Sci Adv, 8: eabn1717

    Google Scholar 

  • Daley A J, Bloch I, Kokail C, Flannigan S, Pearson N, Troyer M, Zoller P. 2022. Practical quantum advantage in quantum simulation. Nature, 607: 667–676

    Google Scholar 

  • Davis M. 1958. Computability and Unsolvability. New York: Dover Publications

    Google Scholar 

  • Deshpande A, Mehta A, Vincent T, Quesada N, Hinsche M, Ioannou M, Madsen L, Lavoie J, Qi H, Eisert J, Hangleiter D, Fefferman B, Dhand I. 2022. Quantum computational advantage via high-dimensional Gaussian boson sampling. Sci Adv, 8: eabi7894

    Google Scholar 

  • Deutsch D. 1985. Quantum theory, the Church-Turing principle and the universal quantum computer. Proc R Soc Lond A, 400: 97–117

    Google Scholar 

  • Djaferis T E, Schick I C. 2000. System theory: Modeling, analysis, and control. Boston: Kluwer

    Google Scholar 

  • Dobermann A, Ping J L. 2004. Geostatistical integration of yield monitor data and remote sensing improves yield maps. Agron J, 96: 285–297

    Google Scholar 

  • Emili E, Popp C, Wunderle S, Zebisch M, Petitta M. 2011. Mapping particulate matter in alpine regions with satellite and ground-based measurements: An exploratory study for data assimilation. Atmos Environ, 45: 4344–4353

    Google Scholar 

  • Farhi E, Gutmann S. 1998. Quantum computation and decision trees. Phys Rev A, 58: 915–928

    Google Scholar 

  • Fawzi A, Balog M, Huang A, Hubert T, Romera-Paredes B, Barekatain M, Novikov A, R. Ruiz F J, Schrittwieser J, Swirszcz G, Silver D, Hassabis D, Kohli P. 2022. Discovering faster matrix multiplication algorithms with reinforcement learning. Nature, 610: 47–53

    Google Scholar 

  • Feynman R P. 1982. Simulating physics with computers. Int J Theor Phys, 21: 467–488

    Google Scholar 

  • Fritz S, McCallum I, Schill C, Perger C, See L, Schepaschenko D, van der Velde M, Kraxner F, Obersteiner M. 2012. Geo-Wiki: An online platform for improving global land cover. Environ Model Software, 31: 110–123

    Google Scholar 

  • Grover L K. 1997. Quantum mechanics helps in searching for a needle in a haystack. Phys Rev Lett, 79: 325–328

    Google Scholar 

  • Haber W. 2021. Eco-environmental surface modelling requires integration of both extrinsic and intrinsic informations. Sci China Earth Sci, 64: 185–186

    Google Scholar 

  • Harrow A W, Hassidim A, Lloyd S. 2009. Quantum algorithm for linear systems of equations. Phys Rev Lett, 103: 150502

    Google Scholar 

  • Hilbert D, von N J, Nordheim L. 1928. Ueber die Grundlagen der Quantenmechanik. Math Ann, 98: 1–30

    Google Scholar 

  • Hull D J. 2003. Optimal Control Theory for Applications. New York: Springer

    Google Scholar 

  • IPBES. 2016. The Methodological Assessment Report on Scenarios and Models of Biodiversity and Ecosystem Services. Secretariat of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services. Bonn. 209–215

    Google Scholar 

  • Kempe J. 2003. Quantum random walks: An introductory overview. Contemp Phys, 44: 307–327

    Google Scholar 

  • Khrennikov A. 2021. Roots of quantum computing supremacy: Super-position, entanglement, or complementarity? Eur Phys J Spec Top, 230: 1053–1057

    Google Scholar 

  • Li L, Wu K, Zhou D W. 2014. Extraction algorithm of mining subsidence information on water area based on support vector machine. Environ Earth Sci, 72: 3991–4000

    Google Scholar 

  • Liu Z P, Shao M A, Wang Y Q. 2013. Large-scale spatial interpolation of soil pH across the Loess Plateau, China. Environ Earth Sci, 69: 2731–2741

    Google Scholar 

  • Mandayam P, Ng H K. 2012. Towards a unified framework for approximate quantum error correction. Phys Rev A, 86: 012335

    Google Scholar 

  • Medvidović M, Carleo G. 2021. Classical variational simulation of the quantum approximate optimization algorithm. Npj Quantum Information 7, 101, https://doi.org/10.1038/s41534-021-00440-z

    Google Scholar 

  • Mooij H. 2005. The road to quantum computing. Science, 307: 1210–1211

    Google Scholar 

  • Morrell Jr H J, Wong H Y. 2021. Step-by-step HHL algorithm walkthrough to enhance the understanding of critical quantum computing concepts. DOI: https://doi.org/10.48550/arXiv.2108.09004

  • Mueller N, Tarasov A, Venugopalan R. 2021 Computing real time correlation functions on a hybrid classical/quantum computer. Nucl Phys A, 1005: 121889

    Google Scholar 

  • Nielsen M A, Chuang I L. 2010. Quantum Computation and Quantum Information. New York: Cambridge University Press

    Google Scholar 

  • Nimbe P, Weyori B A, Adekoya A F. 2021. Models in quantum computing: A systematic review. Quantum Inf Process, 20: 80

    Google Scholar 

  • Pereira H M, Ferrier S, Walters M, Geller G N, Jongman R H G, Scholes R J, Bruford M W, Brummitt N, Butchart S H M, Cardoso A C, Coops N C, Dulloo E, Faith D P, Freyhof J, Gregory R D, Heip C, Höft R, Hurtt G, Jetz W, Karp D S, McGeoch M A, Obura D, Onoda Y, Pettorelli N, Reyers B, Sayre R, Scharlemann J P W, Stuart S N, Turak E, Walpole M, Wegmann M. 2013. Essential biodiversity variables. Science, 339: 277–278

    Google Scholar 

  • Pereira L M, and other 32 coauthors. 2020. Developing multiscale and integrative nature-people scenarios using the nature futures framework. People Nature, 2: 1172–1195

    Google Scholar 

  • Perelshtein M R, Pakhomchik A I, Melnikov A A, Novikov A A, Glatz A, Paraoanu G S, Vinokur V M, Lesovik G B. 2022. Solving large-scale linear systems of equations by a quantum Hybrid Algorithm. Annalen der Physik, 534: 2200082

    Google Scholar 

  • Phillips J D. 2002. Global and local factors in earth surface systems. Ecol Model, 149: 257–272

    Google Scholar 

  • Ponsar S, Luyten P, Dulière V. 2016. Data assimilation with the ensemble Kalman filter in a numerical model of the North Sea. Ocean Dyn, 66: 955–971

    Google Scholar 

  • Rebentrost P, Bromley T R, Weedbrook C, Lloyd S. 2018. Quantum Hopfield neural network. Phys Rev A, 98: 042308

    Google Scholar 

  • Rebentrost P, Mohseni M, Lloyd S. 2014. Quantum support vector machine for big data classification. Phys Rev Lett, 113: 130503

    Google Scholar 

  • Rønnow T F, Wang Z, Job J, Boixo S, Isakov S V, Wecker D, Martinis J M, Lidar D A, Troyer M. 2014. Defining and detecting quantum speedup. Science, 345: 420–424

    Google Scholar 

  • Shao C. 2018. Reconsider HHL algorithm and its related quantum machine learning algorithms. DOI: https://doi.org/10.48550/arXiv.1803.01486.

  • Shi W, Liu J, Du Z, Stein A, Yue T. 2011. Surface modelling of soil properties based on land use information. Geoderma 162: 347–357

    Google Scholar 

  • Shi W, Liu J, Du Z, Song Y, Chen C, Yue T. 2009. Surface modelling of soil pH. Geoderma, 150: 113–119

    Google Scholar 

  • Shor P W. 1994. Algorithms for quantum computation: Discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science. New York. 124–134

  • Silver D, Hubert T, Schrittwieser J, Antonoglou I, Lai M, Guez A, Lanctot M, Sifre L, Kumaran D, Graepel T, Lillicrap T, Simonyan K, Hassabis D. 2018. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science, 362: 1140–1144

    Google Scholar 

  • Somasundaram D. 2005. Differential Geometry. Harrow: Alpha Science International Ltd

    Google Scholar 

  • Srivastava P K, Han D, Rico-Ramirez M A, Bray M, Islam T, Gupta M, Dai Q. 2014. Estimation of land surface temperature from atmospherically corrected LANDSAT TM image using 6S and NCEP global reanalysis product. Environ Earth Sci, 72: 5183–5196

    Google Scholar 

  • Turing A M. 1937. On computable numbers, with an application to the Entscheidungs-problem. Proc London Mathemat Soc, 42: 230–265

    Google Scholar 

  • Waldrop M M. 2016. More than Moore. Nature, 530: 145–147

    Google Scholar 

  • Wiebe N, Braun D, Lloyd S. 2012. Quantum algorithm for data fitting. Phys Rev Lett, 109: 050505

    Google Scholar 

  • Yang W, Zheng Z, Zheng C, Lu K, Ding D, Zhu J. 2018. Temporal variations in a phytoplankton community in a subtropical reservoir: An interplay of extrinsic and intrinsic community effects. Sci Total Environ, 612: 720–727

    Google Scholar 

  • Yue T X, Chen C F, Li B L. 2010a. An adaptive method of high accuracy surface modeling and its application to simulating elevation surfaces. Trans GIS, 14: 615–630

    Google Scholar 

  • Yue T X, Chen C F, Li B L. 2012. A high-accuracy method for filling voids and its verification. Int J Remote Sens, 33: 2815–2830

    Google Scholar 

  • Yue T X, Du Z P, Liu J Y. 2004. High accuracy surface modelling and its error analysis (in Chinese). Prog Phys Sci, 14: 300–306

    Google Scholar 

  • Yue T X, Du Z P, Lu M, Fan Z M, Wang C L, Tian Y Z, Xu B. 2015c. Surface modeling of ecosystem responses to climatic change in Poyang Lake Basin of China. Ecol Model, 306: 16–23

    Google Scholar 

  • Yue T X, Du Z P, Song D J, Gong Y. 2007. A new method of surface modeling and its application to DEM construction. Geomorphology, 91: 161–172

    Google Scholar 

  • Yue T X, Liu Y, Du Z P, Wilson J, Zhao D Y, Wang Y, Zhao N, Shi W J, Fan Z M, Zhao X M, Zhang Q, Huang H S, Wu Q Y, Zhou W, Jiao Y M, Xu Z, Li S B, Yang Y, Fu B J. 2022. Quantum machine learning of eco-environmental surfaces. Sci Bull, 67: 1031–1033

    Google Scholar 

  • Yue T X, Liu Y, Zhao M W, Du Z P, Zhao N. 2016a. A fundamental theorem of Earth’s surface modelling. Environ Earth Sci, 75: 751

    Google Scholar 

  • Yue T X, Song D J, Du Z P, Wang W. 2010b. High-accuracy surface modelling and its application to DEM generation. Int J Remote Sens, 31: 2205–2226

    Google Scholar 

  • Yue T X, Wang S H. 2010. Adjustment computation of HASM: A high-accuracy and high-speed method. Int J Geogr Inf Sci, 24: 1725–1743

    Google Scholar 

  • Yue T X, Song Y J. 2008. The YUE-HASM method. In: Li D, Ge Y, Foody G M, eds. Accuracy in geomatics. Edgbaston, UK: World Academic Union. 148–153

    Google Scholar 

  • Yue T X, Wang Y F, Du Z P, Zhao M W, Li Zhang L, Zhao N, Lu M, Larocque G R, Wilson J P. 2016c. Analysing the uncertainty of estimating forest carbon stocks in China. Biogeosciences, 13: 3991–4004

    Google Scholar 

  • Yue T X, Zhang L L, Zhao N, Zhao M W, Chen C F, Du Z P, Song D J, Fan Z M, Shi W J, Wang S H, Yan C Q, Li Q Q, Sun X F, Yang H, Wilson J, Xu B. 2015a. A review of recent developments in HASM. Environ Earth Sci, 74: 6541–6549

    Google Scholar 

  • Yue T X, Zhao M W, Zhang X Y. 2015b. A high-accuracy method for filling voids on remotely sensed XCO2 surfaces and its verification. J Cleaner Production, 103: 819–827

    Google Scholar 

  • Yue T X, Zhao N, Fan Z M, Li J, Chen C F, Lu Y M, Wang C L, Xu B, Wilson J. 2016b. CMIP5 downscaling and its uncertainty in China. Glob Planet Change, 146: 30–37

    Google Scholar 

  • Yue T X, Zhao N, Fan Z M, Li J, Chen C F, Lu Y M, Wang C L, Gao J, Xu B, Jiao Y M, Wilson J P. 2019. Methods for simulating climate scenarios with improved spatiotemporal specificity and less uncertainty. Glob Planet Change, 181: 102973

    Google Scholar 

  • Yue T X, Zhao N, Liu Y, Wang Y F, Zhang B, Du Z P, Fan Z M, Shi W J, Chen C F, Zhao M W, Song D J, Wang S H, Song Y J, Yan C Q, Li Q Q, Sun X F, Zhang L L, Tian Y Z, Wang W, Wang Y A, Ma S N, Huang H S, Lu Y M, Wang Q, Wang C L, Wang Y Z, Lu M, Zhou W, Liu Y, Yin X Z, Wang Z, Bao Z Y, Zhao M M, Zhao Y P, Jiao Y M, Naseer U, Fan B, Li S B, Yang Y, Wilson J P. 2020. A fundamental theorem for eco-environmental surface modelling and its applications. Sci China Earth Sci, 63: 1092–1112

    Google Scholar 

  • Yue T X, Zhao N, Ramsey R D, Wang C L, Fan Z M, Chen C F, Lu Y M, Li B L. 2013a. Climate change trend in China, with improved accuracy. Climatic Change, 120: 137–151

    Google Scholar 

  • Yue T X, Zhao N, Yang H, Song Y J, Du Z P, Fan Z M, Song D J. 2013b. A multi-grid method of high accuracy surface modeling and its validation. Trans GIS, 17: 943–952

    Google Scholar 

  • Yue T X. 2011. Surface Modelling: High Accuracy and High Speed Methods. New York: CRC Press

    Google Scholar 

  • Zhong H S, Wang H, Deng Y H, Chen M C, Peng L C, Luo Y H, Qin J, Wu D, Ding X, Hu Y, Hu P, Yang X Y, Zhang W J, Li H, Li Y, Jiang X, Gan L, Yang G, You L, Wang Z, Li L, Liu N L, Lu C Y, Pan J W. 2020. Quantum computational advantage using photons. Science, 370: 1460–1463

    Google Scholar 

  • Zhu Q, Cao S, Chen F, Chen M C, Chen X, Chung T H, Deng H, Du Y, Fan D, Gong M, Guo C, Guo C, Guo S, Han L, Hong L, Huang H L, Huo Y H, Li L, Li N, Li S, Li Y, Liang F, Lin C, Lin J, Qian H, Qiao D, Rong H, Su H, Sun L, Wang L, Wang S, Wu D, Wu Y, Xu Y, Yan K, Yang W, Yang Y, Ye Y, Yin J, Ying C, Yu J, Zha C, Zhang C, Zhang H, Zhang K, Zhang Y, Zhao H, Zhao Y, Zhou L, Lu C Y, Peng C Z, Zhu X, Pan J W. 2022. Quantum computational advantage via 60-qubit 24-cycle random circuit sampling. Sci Bull, 67: 240–245

    Google Scholar 

  • Zidan M, Eleuch H, Abdel-Aty M. 2021. Non-classical computing problems: Toward novel type of quantum computing problems. Results Phys, 21: 103536

    Google Scholar 

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Acknowledgements

We thank Professor John Wilson for his useful recommendations. This work was supported by the Open Research Program of the International Research Center of Big Data for Sustainable Development Goals (Grant No. CBAS2022ORP02), the National Natural Science Foundation of China (Grant Nos. 41930647, 72221002), and the Key Project of Innovation LREIS (Grant No. KPI005).

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  1. State Key Laboratory of Resources and Environment Information System, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China

    Tianxiang Yue, Chenchen Wu, Zhengping Du, Na Zhao, Yimeng Jiao, Zhe Xu & Wenjiao Shi

  2. Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, 101408, China

    Yi Liu

  3. College of Resources and Environment, University of Chinese Academy of Sciences, Beijing, 101499, China

    Tianxiang Yue, Chenchen Wu, Na Zhao, Yimeng Jiao & Wenjiao Shi

  4. College of Land Resources and Environment, Jiangxi Agricultural University, Nanchang, 330045, China

    Tianxiang Yue

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Yue, T., Wu, C., Liu, Y. et al. HASM quantum machine learning. Sci. China Earth Sci. 66, 1937–1945 (2023). https://doi.org/10.1007/s11430-022-1144-7

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