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ORCIDBadih Ghazi
Person information
- affiliation: Google Research, Mountain View, CA, USA
- affiliation (PhD 2018): Massachusetts Institute of Technology, Cambridge, MA, USA
- affiliation (former): American University of Beirut, Lebanon
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2020 – today
- 2023
[c37]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Thomas Steinke:
Algorithms with More Granular Differential Privacy Guarantees. ITCS 2023: 54:1-54:24- [c36]Badih Ghazi, Ravi Kumar, Jelani Nelson, Pasin Manurangsi:
Private Counting of Distinct and k-Occurring Items in Time Windows. ITCS 2023: 55:1-55:24 - [c35]Justin Y. Chen, Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Shyam Narayanan, Jelani Nelson, Yinzhan Xu:
Differentially Private All-Pairs Shortest Path Distances: Improved Algorithms and Lower Bounds. SODA 2023: 5040-5067 - [i54]Badih Ghazi, Rahul Ilango, Pritish Kamath, Ravi Kumar, Pasin Manurangsi:
Separating Computational and Statistical Differential Privacy (Under Plausible Assumptions). CoRR abs/2301.00104 (2023) - 2022
- [j9]Badih Ghazi, Ben Kreuter, Ravi Kumar, Pasin Manurangsi, Jiayu Peng, Evgeny Skvortsov, Yao Wang, Craig Wright:
Multiparty Reach and Frequency Histogram: Private, Secure, and Practical. Proc. Priv. Enhancing Technol. 2022(1): 373-395 (2022) - [j8]Vadym Doroshenko, Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi:
Connect the Dots: Tighter Discrete Approximations of Privacy Loss Distributions. Proc. Priv. Enhancing Technol. 2022(4): 552-570 (2022) - [j7]Badih Ghazi, Neel Kamal, Ravi Kumar, Pasin Manurangsi, Annika Zhang:
Private Aggregation of Trajectories. Proc. Priv. Enhancing Technol. 2022(4): 626-644 (2022) - [c34]Daniel Alabi, Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
Private Rank Aggregation in Central and Local Models. AAAI 2022: 5984-5991 - [c33]James Bell, Adrià Gascón, Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Mariana Raykova, Phillipp Schoppmann:
Distributed, Private, Sparse Histograms in the Two-Server Model. CCS 2022: 307-321 - [c32]Rohan Anil, Badih Ghazi, Vineet Gupta, Ravi Kumar, Pasin Manurangsi:
Large-Scale Differentially Private BERT. EMNLP (Findings) 2022: 6481-6491 - [c31]Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi:
Faster Privacy Accounting via Evolving Discretization. ICML 2022: 7470-7483 - [i53]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Jelani Nelson:
Differentially Private All-Pairs Shortest Path Distances: Improved Algorithms and Lower Bounds. CoRR abs/2203.16476 (2022) - [i52]Vadym Doroshenko, Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi:
Connect the Dots: Tighter Discrete Approximations of Privacy Loss Distributions. CoRR abs/2207.04380 (2022) - [i51]Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi:
Faster Privacy Accounting via Evolving Discretization. CoRR abs/2207.04381 (2022) - [i50]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Thomas Steinke:
Algorithms with More Granular Differential Privacy Guarantees. CoRR abs/2209.04053 (2022) - [i49]Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi:
Private Isotonic Regression. CoRR abs/2210.15175 (2022) - [i48]Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi:
Anonymized Histograms in Intermediate Privacy Models. CoRR abs/2210.15178 (2022) - [i47]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Jelani Nelson:
Private Counting of Distinct and k-Occurring Items in Time Windows. CoRR abs/2211.11718 (2022) - [i46]Carson Denison, Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, Krishna Giri Narra, Amer Sinha, Avinash Varadarajan, Chiyuan Zhang:
Private Ad Modeling with DP-SGD. CoRR abs/2211.11896 (2022) - [i45]Badih Ghazi, Junfeng He, Kai Kohlhoff, Ravi Kumar, Pasin Manurangsi, Vidhya Navalpakkam, Nachiappan Valliappan:
Differentially Private Heatmaps. CoRR abs/2211.13454 (2022) - [i44]Badih Ghazi, Pritish Kamath, Ravi Kumar, Ethan Leeman, Pasin Manurangsi, Avinash Varadarajan, Chiyuan Zhang:
Regression with Label Differential Privacy. CoRR abs/2212.06074 (2022) - [i43]Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, Kewen Wu:
On Differentially Private Counting on Trees. CoRR abs/2212.11967 (2022) - [i42]James Bell, Adrià Gascón, Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Mariana Raykova, Phillipp Schoppmann:
Distributed, Private, Sparse Histograms in the Two-Server Model. IACR Cryptol. ePrint Arch. 2022: 920 (2022) - 2021
- [j6]Peter Kairouz, H. Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis
, Arjun Nitin Bhagoji, Kallista A. Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G. L. D'Oliveira, Hubert Eichner, Salim El Rouayheb, David Evans, Josh Gardner, Zachary Garrett, Adrià Gascón, Badih Ghazi, Phillip B. Gibbons, Marco Gruteser, Zaïd Harchaoui, Chaoyang He, Lie He, Zhouyuan Huo, Ben Hutchinson, Justin Hsu, Martin Jaggi, Tara Javidi, Gauri Joshi, Mikhail Khodak, Jakub Konecný, Aleksandra Korolova, Farinaz Koushanfar, Sanmi Koyejo, Tancrède Lepoint, Yang Liu, Prateek Mittal, Mehryar Mohri, Richard Nock, Ayfer Özgür, Rasmus Pagh, Hang Qi, Daniel Ramage, Ramesh Raskar, Mariana Raykova, Dawn Song, Weikang Song, Sebastian U. Stich, Ziteng Sun, Ananda Theertha Suresh, Florian Tramèr, Praneeth Vepakomma, Jianyu Wang, Li Xiong, Zheng Xu, Qiang Yang, Felix X. Yu, Han Yu, Sen Zhao:
Advances and Open Problems in Federated Learning. Found. Trends Mach. Learn. 14(1-2): 1-210 (2021) - [c30]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Thao Nguyen:
Robust and Private Learning of Halfspaces. AISTATS 2021: 1603-1611 - [c29]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi:
Near-tight closure b ounds for the Littlestone and threshold dimensions. ALT 2021: 686-696 - [c28]Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
On Avoiding the Union Bound When Answering Multiple Differentially Private Queries. COLT 2021: 2133-2146 - [c27]Badih Ghazi, Noah Golowich, Ravi Kumar, Rasmus Pagh, Ameya Velingker:
On the Power of Multiple Anonymous Messages: Frequency Estimation and Selection in the Shuffle Model of Differential Privacy. EUROCRYPT (3) 2021: 463-488 - [c26]Alisa Chang, Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
Locally Private k-Means in One Round. ICML 2021: 1441-1451 - [c25]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh, Amer Sinha:
Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message. ICML 2021: 3692-3701 - [c24]Lijie Chen, Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
On Distributed Differential Privacy and Counting Distinct Elements. ITCS 2021: 56:1-56:18 - [c23]Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
User-Level Differentially Private Learning via Correlated Sampling. NeurIPS 2021: 20172-20184 - [c22]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi, Chiyuan Zhang:
Deep Learning with Label Differential Privacy. NeurIPS 2021: 27131-27145 - [c21]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi:
Sample-efficient proper PAC learning with approximate differential privacy. STOC 2021: 183-196 - [i41]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi, Chiyuan Zhang:
On Deep Learning with Label Differential Privacy. CoRR abs/2102.06062 (2021) - [i40]Alisa Chang, Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
Locally Private k-Means in One Round. CoRR abs/2104.09734 (2021) - [i39]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh:
Private Counting from Anonymous Messages: Near-Optimal Accuracy with Vanishing Communication Overhead. CoRR abs/2106.04247 (2021) - [i38]Shailesh Bavadekar, Adam Boulanger, John Davis, Damien Desfontaines, Evgeniy Gabrilovich, Krishna Gadepalli, Badih Ghazi, Tague Griffith, Jai Prakash Gupta, Chaitanya Kamath, Dennis Kraft, Ravi Kumar, Akim Kumok, Yael Mayer, Pasin Manurangsi, Arti Patankar, Irippuge Milinda Perera, Chris Scott, Tomer Shekel, Benjamin Miller, Karen Smith, Charlotte Stanton, Mimi Sun, Mark Young, Gregory Wellenius:
Google COVID-19 Vaccination Search Insights: Anonymization Process Description. CoRR abs/2107.01179 (2021) - [i37]Rohan Anil, Badih Ghazi, Vineet Gupta, Ravi Kumar, Pasin Manurangsi:
Large-Scale Differentially Private BERT. CoRR abs/2108.01624 (2021) - [i36]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh, Amer Sinha:
Differentially Private Aggregation in the Shuffle Model: Almost Central Accuracy in Almost a Single Message. CoRR abs/2109.13158 (2021) - [i35]Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
User-Level Private Learning via Correlated Sampling. CoRR abs/2110.11208 (2021) - [i34]Daniel Alabi, Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
Private Rank Aggregation in Central and Local Models. CoRR abs/2112.14652 (2021) - 2020
- [j5]Mohammad Bavarian, Badih Ghazi, Elad Haramaty, Pritish Kamath, Ronald L. Rivest, Madhu Sudan:
Optimality of Correlated Sampling Strategies. Theory Comput. 16: 1-18 (2020) - [c20]Badih Ghazi, Pasin Manurangsi, Rasmus Pagh, Ameya Velingker:
Private Aggregation from Fewer Anonymous Messages. EUROCRYPT (2) 2020: 798-827 - [c19]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh, Ameya Velingker:
Pure Differentially Private Summation from Anonymous Messages. ITC 2020: 15:1-15:23 - [c18]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh:
Private Counting from Anonymous Messages: Near-Optimal Accuracy with Vanishing Communication Overhead. ICML 2020: 3505-3514 - [c17]Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
Differentially Private Clustering: Tight Approximation Ratios. NeurIPS 2020 - [i33]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh, Ameya Velingker:
Pure Differentially Private Summation from Anonymous Messages. CoRR abs/2002.01919 (2020) - [i32]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi:
Near-tight closure bounds for Littlestone and threshold dimensions. CoRR abs/2007.03668 (2020) - [i31]Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
Differentially Private Clustering: Tight Approximation Ratios. CoRR abs/2008.08007 (2020) - [i30]Lijie Chen, Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
On Distributed Differential Privacy and Counting Distinct Elements. CoRR abs/2009.09604 (2020) - [i29]Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Thao Nguyen:
Robust and Private Learning of Halfspaces. CoRR abs/2011.14580 (2020) - [i28]Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi:
Sample-efficient proper PAC learning with approximate differential privacy. CoRR abs/2012.03893 (2020) - [i27]Badih Ghazi, Ravi Kumar, Pasin Manurangsi:
On Avoiding the Union Bound When Answering Multiple Differentially Private Queries. CoRR abs/2012.09116 (2020)
2010 – 2019
- 2019
- [c16]Badih Ghazi, Rina Panigrahy, Joshua R. Wang:
Recursive Sketches for Modular Deep Learning. ICML 2019: 2211-2220 - [c15]Madhu Sudan, Badih Ghazi, Noah Golowich, Mitali Bafna:
Communication-Rounds Tradeoffs for Common Randomness and Secret Key Generation. SODA 2019: 1861-1871 - [i26]Badih Ghazi, Rina Panigrahy, Joshua R. Wang:
Recursive Sketches for Modular Deep Learning. CoRR abs/1905.12730 (2019) - [i25]Badih Ghazi, Rasmus Pagh, Ameya Velingker:
Scalable and Differentially Private Distributed Aggregation in the Shuffled Model. CoRR abs/1906.08320 (2019) - [i24]Badih Ghazi, Noah Golowich, Ravi Kumar, Rasmus Pagh, Ameya Velingker:
Private Heavy Hitters and Range Queries in the Shuffled Model. CoRR abs/1908.11358 (2019) - [i23]Badih Ghazi, Pasin Manurangsi, Rasmus Pagh, Ameya Velingker:
Private Aggregation from Fewer Anonymous Messages. CoRR abs/1909.11073 (2019) - [i22]Peter Kairouz, H. Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Kallista A. Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, Rafael G. L. D'Oliveira, Salim El Rouayheb, David Evans, Josh Gardner, Zachary Garrett, Adrià Gascón, Badih Ghazi, Phillip B. Gibbons, Marco Gruteser, Zaïd Harchaoui, Chaoyang He, Lie He, Zhouyuan Huo, Ben Hutchinson, Justin Hsu, Martin Jaggi, Tara Javidi, Gauri Joshi, Mikhail Khodak, Jakub Konecný, Aleksandra Korolova, Farinaz Koushanfar, Sanmi Koyejo, Tancrède Lepoint, Yang Liu, Prateek Mittal, Mehryar Mohri, Richard Nock, Ayfer Özgür, Rasmus Pagh, Mariana Raykova, Hang Qi, Daniel Ramage, Ramesh Raskar, Dawn Song, Weikang Song, Sebastian U. Stich, Ziteng Sun, Ananda Theertha Suresh, Florian Tramèr, Praneeth Vepakomma, Jianyu Wang, Li Xiong, Zheng Xu, Qiang Yang, Felix X. Yu, Han Yu, Sen Zhao:
Advances and Open Problems in Federated Learning. CoRR abs/1912.04977 (2019) - [i21]Badih Ghazi, Noah Golowich, Ravi Kumar, Rasmus Pagh, Ameya Velingker:
On the Power of Multiple Anonymous Messages. IACR Cryptol. ePrint Arch. 2019: 1382 (2019) - 2018
- [b1]Badih Ghazi:
Computational aspects of communication amid uncertainty. Massachusetts Institute of Technology, Cambridge, USA, 2018 - [j4]Badih Ghazi, Ilan Komargodski, Pravesh K. Kothari, Madhu Sudan:
Communication with Contextual Uncertainty. Comput. Complex. 27(3): 463-509 (2018) - [j3]Venkata Gandikota, Badih Ghazi, Elena Grigorescu:
NP-Hardness of Reed-Solomon Decoding, and the Prouhet-Tarry-Escott Problem. SIAM J. Comput. 47(4): 1547-1584 (2018) - [j2]Badih Ghazi, Euiwoong Lee:
LP/SDP Hierarchy Lower Bounds for Decoding Random LDPC Codes. IEEE Trans. Inf. Theory 64(6): 4423-4437 (2018) - [c14]Badih Ghazi, Pritish Kamath, Prasad Raghavendra:
Dimension Reduction for Polynomials over Gaussian Space and Applications. CCC 2018: 28:1-28:37 - [c13]Badih Ghazi, T. S. Jayram:
Resource-Efficient Common Randomness and Secret-Key Schemes. SODA 2018: 1834-1853 - [i20]Mitali Bafna, Badih Ghazi, Noah Golowich, Madhu Sudan:
Communication-Rounds Tradeoffs for Common Randomness and Secret Key Generation. CoRR abs/1808.08907 (2018) - [i19]Mitali Bafna, Badih Ghazi, Noah Golowich, Madhu Sudan:
Communication-Rounds Tradeoffs for Common Randomness and Secret Key Generation. Electron. Colloquium Comput. Complex. TR18 (2018) - 2017
- [c12]Badih Ghazi, Madhu Sudan:
The Power of Shared Randomness in Uncertain Communication. ICALP 2017: 49:1-49:14 - [c11]Badih Ghazi, Elad Haramaty, Pritish Kamath, Madhu Sudan:
Compression in a Distributed Setting. ITCS 2017: 19:1-19:22 - [c10]Vitaly Feldman, Badih Ghazi:
On the Power of Learning from k-Wise Queries. ITCS 2017: 41:1-41:32 - [i18]Vitaly Feldman, Badih Ghazi:
On the Power of Learning from k-Wise Queries. CoRR abs/1703.00066 (2017) - [i17]Badih Ghazi, Madhu Sudan:
The Power of Shared Randomness in Uncertain Communication. CoRR abs/1705.01082 (2017) - [i16]Badih Ghazi, T. S. Jayram:
Resource-Efficient Common Randomness and Secret-Key Schemes. CoRR abs/1707.08086 (2017) - [i15]Badih Ghazi, Pritish Kamath, Prasad Raghavendra:
Dimension Reduction for Polynomials over Gaussian Space and Applications. CoRR abs/1708.03808 (2017) - [i14]Badih Ghazi, T. S. Jayram:
Resource-Efficient Common Randomness and Secret-Key Schemes. Electron. Colloquium Comput. Complex. TR17 (2017) - [i13]Badih Ghazi, Pritish Kamath, Prasad Raghavendra:
Dimension Reduction for Polynomials over Gaussian Space and Applications. Electron. Colloquium Comput. Complex. TR17 (2017) - [i12]Badih Ghazi, Madhu Sudan:
The Power of Shared Randomness in Uncertain Communication. Electron. Colloquium Comput. Complex. TR17 (2017) - 2016
- [c9]Badih Ghazi, Pritish Kamath, Madhu Sudan:
Decidability of Non-interactive Simulation of Joint Distributions. FOCS 2016: 545-554 - [c8]Venkata Gandikota, Badih Ghazi, Elena Grigorescu:
NP-Hardness of Reed-Solomon Decoding and the Prouhet-Tarry-Escott Problem. FOCS 2016: 760-769 - [c7]Badih Ghazi, Pritish Kamath, Madhu Sudan:
Communication Complexity of Permutation-Invariant Functions. SODA 2016: 1902-1921 - [c6]Badih Ghazi, Ilan Komargodski, Pravesh Kothari, Madhu Sudan:
Communication with Contextual Uncertainty. SODA 2016: 2072-2085 - [i11]Badih Ghazi, Pritish Kamath, Madhu Sudan:
Decidability of Non-Interactive Simulation of Joint Distributions. CoRR abs/1607.04322 (2016) - [i10]Venkata Gandikota, Badih Ghazi, Elena Grigorescu:
NP-Hardness of Reed-Solomon Decoding, and the Prouhet-Tarry-Escott Problem. CoRR abs/1611.03069 (2016) - [i9]Mohammad Bavarian, Badih Ghazi, Elad Haramaty, Pritish Kamath, Ronald L. Rivest, Madhu Sudan:
The Optimality of Correlated Sampling. CoRR abs/1612.01041 (2016) - [i8]Mohammad Bavarian, Badih Ghazi, Elad Haramaty, Pritish Kamath, Ronald L. Rivest, Madhu Sudan:
The Optimality of Correlated Sampling. Electron. Colloquium Comput. Complex. TR16 (2016) - [i7]Venkata Gandikota, Badih Ghazi, Elena Grigorescu:
NP-Hardness of Reed-Solomon Decoding, and the Prouhet-Tarry-Escott Problem. Electron. Colloquium Comput. Complex. TR16 (2016) - [i6]Badih Ghazi, Pritish Kamath, Madhu Sudan:
Decidability of Non-Interactive Simulation of Joint Distributions. Electron. Colloquium Comput. Complex. TR16 (2016) - 2015
- [c5]Venkata Gandikota, Badih Ghazi, Elena Grigorescu:
On the NP-hardness of bounded distance decoding of Reed-Solomon codes. ISIT 2015: 2904-2908 - [c4]Badih Ghazi, Euiwoong Lee:
LP/SDP Hierarchy Lower Bounds for Decoding Random LDPC Codes. SODA 2015: 1326-1342 - [i5]Badih Ghazi, Pritish Kamath, Madhu Sudan:
Communication Complexity of Permutation-Invariant Functions. CoRR abs/1506.00273 (2015) - [i4]Badih Ghazi, Pritish Kamath, Madhu Sudan:
Communication Complexity of Permutation-Invariant Functions. Electron. Colloquium Comput. Complex. TR15 (2015) - 2014
- [j1]Louay Bazzi, Badih Ghazi, Rüdiger L. Urbanke:
Linear Programming Decoding of Spatially Coupled Codes. IEEE Trans. Inf. Theory 60(8): 4677-4698 (2014) - [c3]Eric Blais, Joshua Brody, Badih Ghazi:
The Information Complexity of Hamming Distance. APPROX-RANDOM 2014: 465-489 - [i3]Badih Ghazi, Euiwoong Lee:
LP/SDP Hierarchy Lower Bounds for Decoding Random LDPC Codes. CoRR abs/1410.4241 (2014) - 2013
- [c2]Badih Ghazi, Haitham Hassanieh, Piotr Indyk, Dina Katabi, Eric Price, Lixin Shi:
Sample-optimal average-case sparse Fourier Transform in two dimensions. Allerton 2013: 1258-1265 - [c1]Louay Bazzi, Badih Ghazi, Rüdiger L. Urbanke:
Linear programming decoding of spatially coupled codes. ISIT 2013: 1486-1490 - [i2]Louay Bazzi, Badih Ghazi, Rüdiger L. Urbanke:
Linear Programming Decoding of Spatially Coupled Codes. CoRR abs/1301.6410 (2013) - [i1]Badih Ghazi, Haitham Hassanieh, Piotr Indyk, Dina Katabi, Eric Price, Lixin Shi:
Sample-Optimal Average-Case Sparse Fourier Transform in Two Dimensions. CoRR abs/1303.1209 (2013)
Coauthor Index
[c37] [c36] [c35] [i54] [j9] [j8] [j7] [c34] [c33] [c32] [c31] [i53] [i52] [i51] [i50] [i49] [i48] [i47] [i46] [i45] [i44] [i43] [i42] [c30] [c29] [c28] [c27] [c26] [c25] [c24] [c23] [c22] [c21] [i41] [i40] [i39] [i38] [i37] [i36] [i35] [i34] [c19] [c18] [c17] [i33] [i32] [i31] [i30] [i29] [i28] [i27] [i24] [i21]
[c37] [c36] [c35] [i54] [j9] [j8] [j7] [c34] [c33] [c32] [c31] [i53] [i52] [i51] [i50] [i49] [i48] [i47] [i46] [i45] [i44] [i43] [i42] [c30] [c29] [c28] [c26] [c25] [c24] [c23] [c22] [c21] [i41] [i40] [i39] [i38] [i37] [i36] [i35] [i34] [c20] [c19] [c18] [c17] [i33] [i32] [i31] [i30] [i29] [i28] [i27] [i23]
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