Problem D
Sum Squared Digits Function — Problem Statistics

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Submissions	6188
Accepted submissions	3977
Submission ratio	64.27%
Authors	3679
Accepted authors	3538
Author ratio	96.17%

#	User	Runtime	Language	Date
1	Thomas Feld	0.13 s	APL	2023-05-01 11:00:25
2	Steve Allen	0.14 s	APL	2023-04-30 07:23:27

#	User	Runtime	Language	Date
1	Saito Ta	0.04 s	Bash	2024-04-02 10:45:21
2	Chandler McFarland	0.07 s	Bash	2025-02-20 12:26:08
3	Chenzhang Hu	0.10 s	Bash	2024-05-09 15:30:49

#	User	Runtime	Language	Date
1	Benjamin Bilbeau	0.02 s	C#	2018-11-12 19:24:25
2	Armin Krauss	0.02 s	C#	2018-11-15 09:44:58
3	Niklas Sandén	0.02 s	C#	2018-11-29 00:44:47
4	李陆屿	0.02 s	C#	2018-12-23 16:16:13
5	Ryo Kochi	0.02 s	C#	2018-12-27 02:51:52
6	Josenildo Silva	0.02 s	C#	2019-01-04 17:17:09
7	Eric Bäckhage	0.02 s	C#	2019-02-03 21:00:41
8	Csaba Varga	0.02 s	C#	2019-03-09 18:20:26
9	Jahurul Satvik	0.02 s	C#	2019-04-07 15:11:59
10	Fredrik Stigsson	0.02 s	C#	2019-04-16 13:39:53

#	User	Runtime	Language	Date
1	John Dandy	0.01 s	Common Lisp	2020-01-31 02:21:29
2	wibi	0.01 s	Common Lisp	2020-08-20 07:42:06
3	Michal Žáček	0.01 s	Common Lisp	2023-04-30 20:53:09
4	Mohideen Imran Khan	0.03 s	Common Lisp	2019-01-10 15:01:43
5	David Cawthon	0.03 s	Common Lisp	2019-04-20 17:08:50
6	Hidden user	0.03 s	Common Lisp	2019-05-22 00:30:40

#	User	Runtime	Language	Date
1	Jesper Bech Christensen	0.03 s	F#	2022-04-05 11:05:19
2	Jacob Harris Cryer Kragh	0.04 s	F#	2022-06-11 13:05:38

#	User	Runtime	Language	Date
1	Neal McCarthy	0.01 s	Go	2019-04-10 15:00:10
2	Hidden user	0.02 s	Go	2023-11-02 14:45:16
3	Shashwati Shradha	0.03 s	Go	2019-02-19 08:03:10
4	Giovanni Dejan	0.04 s	Go	2019-09-16 12:36:20
5	Erik Pettersson	0.04 s	Go	2019-12-25 16:50:37
6	Mohamed Ramrami	0.04 s	Go	2020-04-24 12:19:43
7	Hidden user	0.04 s	Go	2021-12-16 16:26:05
8	David Vinje	0.04 s	Go	2022-08-10 20:46:22
9	Felix Fatum	0.04 s	Go	2022-09-21 19:06:39
10	dick move	0.05 s	Go	2022-11-07 16:13:58

#	User	Runtime	Language	Date
1	Brent Yorgey	0.01 s	Haskell	2018-11-04 06:16:46
2	Kellen Watt	0.01 s	Haskell	2018-11-18 05:40:48
3	Patrick Bahr	0.01 s	Haskell	2018-11-24 21:07:58
4	Håkon Flatval	0.01 s	Haskell	2018-11-29 02:13:27
5	Olle Eriksson	0.01 s	Haskell	2018-12-08 21:00:15
6	Morten Clausen	0.01 s	Haskell	2018-12-31 20:33:42
7	Micah Stairs	0.01 s	Haskell	2019-03-12 03:07:35
8	Michael Wong	0.01 s	Haskell	2019-03-26 06:19:50
9	Jan Hrček	0.01 s	Haskell	2019-05-03 12:16:04
10	Matthew Johnson	0.01 s	Haskell	2019-05-10 00:29:58

#	User	Runtime	Language	Date
1	Guangyi Zhou	0.04 s	Java	2024-12-12 11:56:00
2	Lee Heng Sheng	0.05 s	Java	2024-04-17 04:20:07
3	José Vander Meulen	0.06 s	Java	2018-11-04 22:06:42
4	Mike Beckers	0.06 s	Java	2018-11-16 01:14:01
5	Laurens Versluis	0.06 s	Java	2018-12-19 22:38:16
6	Bjørn Dons	0.06 s	Java	2018-12-19 22:39:15
7	John Ladera	0.07 s	Java	2018-11-04 08:14:45
8	James Black	0.07 s	Java	2018-11-04 18:21:13
9	Peter Bell	0.07 s	Java	2018-12-13 06:54:24
10	Liam Keliher	0.07 s	Java	2018-12-14 07:52:16

#	User	Runtime	Language	Date
1	Carl Sundvall	0.06 s	JavaScript (Node.js)	2018-11-12 13:31:51
2	Hidden user	0.06 s	JavaScript (Node.js)	2023-11-19 03:08:44
3	Yassin Swag	0.06 s	JavaScript (Node.js)	2023-12-02 17:00:02
4	Amir Konjkav	0.06 s	JavaScript (Node.js)	2024-09-25 12:44:17
5	Gurpartap Singh Bhatti	0.07 s	JavaScript (Node.js)	2019-04-09 01:16:36
6	Sanjiv Dinakar	0.07 s	JavaScript (Node.js)	2019-04-20 02:27:02
7	John Ladera	0.08 s	JavaScript (Node.js)	2019-05-03 07:23:23
8	Vu Van Dung	0.11 s	JavaScript (Node.js)	2022-09-14 20:51:13
9	Howard Tin Chi Chan	0.43 s	JavaScript (Node.js)	2021-02-09 10:36:36
10	Karim Dridi	0.43 s	JavaScript (Node.js)	2022-01-15 00:31:46

#	User	Runtime	Language	Date
1	Jeremy Loh	0.03 s	JavaScript (SpiderMonkey)	2018-11-06 16:40:52
2	Bernard Perrin	0.03 s	JavaScript (SpiderMonkey)	2019-01-16 18:05:01
3	Casey Smith	0.03 s	JavaScript (SpiderMonkey)	2019-05-29 17:07:48
4	Peter Menyes	0.03 s	JavaScript (SpiderMonkey)	2021-01-01 18:38:13
5	Jimmy Gustafsson	0.03 s	JavaScript (SpiderMonkey)	2022-08-16 11:09:09
6	Christian Cederquist	0.03 s	JavaScript (SpiderMonkey)	2022-11-09 15:31:00
7	Andrea Bianchessi	0.03 s	JavaScript (SpiderMonkey)	2022-12-21 16:20:58
8	Zach Tschetter	0.03 s	JavaScript (SpiderMonkey)	2023-06-17 21:08:20
9	Evan Magill	0.03 s	JavaScript (SpiderMonkey)	2024-04-12 06:39:14
10	Bjørn Chr. Soltvedt	0.04 s	JavaScript (SpiderMonkey)	2018-11-04 08:51:47

#	User	Runtime	Language	Date
1	Danny Robinson	0.62 s	Julia	2023-06-22 02:50:35
2	Timothy Gaede	0.66 s	Julia	2024-03-19 14:49:14

#	User	Runtime	Language	Date
1	Jacob Huebner	0.16 s	Kotlin	2020-05-31 06:34:00
2	Hidden user	0.17 s	Kotlin	2019-12-26 08:49:36
3	Albert Pala	0.17 s	Kotlin	2021-06-29 17:35:03
4	Adam Rankin	0.25 s	Kotlin	2023-05-01 05:58:05
5	Merih Bora Poçan	0.27 s	Kotlin	2020-09-16 07:33:55
6	Dayan Ruben Gonzalez	0.27 s	Kotlin	2020-10-09 05:15:04
7	Magnus Wass	0.27 s	Kotlin	2020-12-17 20:53:38
8	Troy Warmboe	0.27 s	Kotlin	2023-04-10 23:15:41
9	Gabriel Wu	0.28 s	Kotlin	2019-10-21 05:22:52
10	Sarek Høverstad Skotåm	0.28 s	Kotlin	2020-10-10 17:30:03

#	User	Runtime	Language	Date
1	Enzo Crance	0.00 s	OCaml	2019-02-13 23:32:04
2	Sam Henke	0.00 s	OCaml	2023-09-30 08:09:57
3	Fredrik Eriksson	0.00 s	OCaml	2024-10-16 18:03:54

#	User	Runtime	Language	Date
1	Hidden user	0.00 s	Odin	2025-04-27 06:37:39

#	User	Runtime	Language	Date
1	Ingemar Ragnemalm	0.00 s	Pascal	2018-11-06 19:09:55
2	David Connolly	0.00 s	Pascal	2021-11-22 16:46:52

#	User	Runtime	Language	Date
1	Nicolai Robinson	0.00 s	Perl	2024-05-15 15:44:51

#	User	Runtime	Language	Date
1	Connor Billings	0.01 s	PHP	2019-12-30 17:33:08
2	Helbin Grégory	0.01 s	PHP	2020-02-02 13:36:47
3	Renate	0.01 s	PHP	2021-04-20 18:47:08

#	User	Runtime	Language	Date
1	Andriy Zyevakov	0.03 s	Prolog	2018-11-11 22:55:43
2	Hakan Kjellerstrand	0.04 s	Prolog	2023-01-22 20:54:48

#	User	Runtime	Language	Date
1	Daniel Hackman - Student	0.04 s	Python 2	2018-11-05 04:29:59
2	Mark van Helvoort	0.04 s	Python 2	2018-11-05 15:38:31
3	Andreas Eisele	0.04 s	Python 2	2018-11-06 03:44:52
4	Catalin Popa	0.04 s	Python 2	2018-11-15 16:17:53
5	Jeppe Lillevang Salling	0.04 s	Python 2	2018-11-25 21:48:18
6	Sergii Bondariev	0.04 s	Python 2	2018-12-19 02:52:47
7	Andrei Stoica	0.04 s	Python 2	2018-12-27 23:26:21
8	Daryl Vogel	0.04 s	Python 2	2019-02-17 01:08:32
9	Hidden user	0.04 s	Python 2	2019-03-15 09:53:35
10	Zander Thannhauser	0.04 s	Python 2	2019-05-31 03:25:48

#	User	Runtime	Language	Date
1	Ben Stutzman	0.02 s	Python 3	2018-11-04 22:23:34
2	Ram Basnet	0.02 s	Python 3	2018-11-05 20:49:18
3	Alex Wice	0.02 s	Python 3	2018-11-19 00:35:41
4	Aaron Lamoreaux	0.02 s	Python 3	2018-11-24 07:46:22
5	Carlo Fantozzi	0.02 s	Python 3	2018-12-11 10:00:24
6	spaem	0.02 s	Python 3	2018-12-18 23:21:37
7	Wayne	0.02 s	Python 3	2018-12-22 16:48:15
8	James Lawson	0.02 s	Python 3	2019-02-01 16:22:23
9	Subramanian Ramasamy	0.02 s	Python 3	2019-02-15 13:21:31
10	Grégoire Biette	0.02 s	Python 3	2019-06-03 12:23:38

#	User	Runtime	Language	Date
1	Miorel Palii	0.05 s	Ruby	2018-11-04 17:17:11
2	Lim Ming Yean	0.05 s	Ruby	2018-11-15 07:20:32
3	Donald Dong	0.05 s	Ruby	2018-11-30 01:22:17
4	Stefan Kennedy	0.05 s	Ruby	2019-01-19 19:29:32
5	Hidden user	0.05 s	Ruby	2019-02-16 17:03:09
6	Régis Hanol	0.05 s	Ruby	2022-01-09 16:36:27
7	Troy Sornson	0.05 s	Ruby	2022-01-27 00:49:42
8	Patrick Elsen	0.06 s	Ruby	2022-09-11 14:28:32
9	Thomas Feld	0.06 s	Ruby	2022-10-31 10:26:05
10	Eugen Neagoe	0.06 s	Ruby	2023-03-22 01:43:26

#	User	Length	Language	Date
1	Thomas Feld	48	APL	2023-05-01 11:00:25
2	Steve Allen	53	APL	2023-04-30 07:23:27

#	User	Length	Language	Date
1	Chenzhang Hu	5	Bash	2024-05-09 15:30:49
2	Saito Ta	70	Bash	2024-04-02 10:46:26
3	Chandler McFarland	495	Bash	2025-02-20 12:26:08

#	User	Length	Language	Date
1	Martin Blom	125	C	2023-09-26 22:25:00
2	Zachariah Goldthorpe	126	C	2020-07-18 07:03:29
3	Osama Albahrani	146	C	2023-05-07 08:46:52
4	Muhammed Ali Aytürk	230	C	2020-02-29 23:18:09
5	Solar Solar	249	C	2021-11-22 22:57:16
6	Neelapu Sai Chaitanya Reddy	267	C	2018-12-26 12:20:29
7	Wesley Stephanak	270	C	2019-02-04 17:13:48
8	Illa Somasekhar	274	C	2018-12-13 02:04:07
9	sama	277	C	2020-12-10 11:10:51
10	Hidden user	281	C	2025-03-23 17:23:26

#	User	Length	Language	Date
1	Jan Matthiessen	311	C#	2024-03-28 23:34:03
2	rf	328	C#	2023-08-29 04:51:42
3	李陆屿	470	C#	2018-12-23 16:16:13
4	Gretel Rojas	608	C#	2023-06-01 06:46:04
5	Santiago Sarabia Martínez	608	C#	2023-06-01 07:35:41
6	Esty Crow	612	C#	2022-10-09 04:16:11
7	Göran Andersson	673	C#	2022-05-08 01:23:05
8	Niklas Sandén	682	C#	2018-11-29 00:44:47
9	Armin Krauss	698	C#	2018-11-15 09:44:58
10	Hari Suaents Reyes	710	C#	2023-11-03 16:17:04

#	User	Length	Language	Date
1	Osama Albahrani	151	C++	2023-05-07 08:39:48
2	Robert Logi Jonsson	155	C++	2023-04-09 04:01:16
3	Nathaniel McComas	189	C++	2023-08-28 15:31:49
4	Garðar Ingvarsson	226	C++	2019-04-08 04:35:44
5	Ganapathy Sanath Balaji	229	C++	2019-08-10 05:42:57
6	Mohammed Alrefaei	230	C++	2019-01-04 16:56:04
7	Hưng Phạm	233	C++	2018-12-11 08:00:31
8	妹様万歳	234	C++	2019-12-30 06:54:59
9	Chan Wei Qiang Jason	237	C++	2019-03-19 15:43:21
10	Yu Ting Yeh	237	C++	2020-03-05 06:55:33

#	User	Length	Language	Date
1	Mohideen Imran Khan	213	Common Lisp	2019-01-16 08:26:48
2	Michal Žáček	273	Common Lisp	2023-04-30 20:53:09
3	John Dandy	317	Common Lisp	2020-01-31 02:21:29
4	Hidden user	376	Common Lisp	2019-05-22 00:30:40
5	David Cawthon	418	Common Lisp	2019-04-20 17:08:50
6	wibi	532	Common Lisp	2020-08-20 07:42:06

#	User	Length	Language	Date
1	Jesper Bech Christensen	338	F#	2022-04-05 11:05:19
2	Jacob Harris Cryer Kragh	482	F#	2022-06-11 13:05:38

#	User	Length	Language	Date
1	Hidden user	241	Go	2021-12-16 16:26:05
2	dick move	268	Go	2022-11-07 16:13:58
3	Bruno Volpato	289	Go	2020-06-01 21:43:08
4	David Vinje	293	Go	2022-08-10 20:46:22
5	Erik Pettersson	301	Go	2019-12-25 16:50:37
6	Hidden user	302	Go	2023-02-11 15:21:24
7	brett warrender	347	Go	2020-08-22 10:04:21
8	Patrik Lilja	381	Go	2018-11-05 20:34:27
9	Shashwati Shradha	385	Go	2019-02-19 08:03:10
10	Felix Fatum	410	Go	2022-09-21 19:06:39

#	User	Length	Language	Date
1	Steinar Simonnes	244	Haskell	2023-09-30 21:14:30
2	Håkon Flatval	271	Haskell	2018-11-29 02:13:27
3	Patrick Bahr	273	Haskell	2018-11-24 21:07:58
4	Joshua Coward	290	Haskell	2022-01-27 02:16:32
5	Sebastian Banert	319	Haskell	2023-04-14 14:23:34
6	David Zacek	347	Haskell	2021-05-03 20:29:37
7	Morten Clausen	404	Haskell	2018-12-31 20:33:42
8	Jan Hrček	407	Haskell	2019-05-03 12:16:04
9	Knut Anders Stokke	418	Haskell	2020-08-26 16:17:13
10	Olle Eriksson	441	Haskell	2018-12-08 21:00:15

#	User	Length	Language	Date
1	Joseph Durie	371	Java	2018-11-17 19:08:13
2	Hidden user	378	Java	2020-03-13 17:28:11
3	Darrin Wiley	390	Java	2019-04-30 21:46:58
4	Ásmundur Óskar Ásmundsson	391	Java	2018-12-06 17:58:53
5	Mark Jason Galang	406	Java	2022-10-16 17:22:46
6	Amena Deeb	408	Java	2018-12-18 23:02:11
7	Jatinkumar Nakrani	417	Java	2023-05-01 13:37:29
8	Jamie Walton	419	Java	2021-11-15 23:40:28
9	Prakash Sanyasi	423	Java	2018-11-06 07:59:01
10	Emilie Hyslop	430	Java	2020-12-09 09:49:09

#	User	Length	Language	Date
1	Karim Dridi	381	JavaScript (Node.js)	2022-01-15 00:31:46
2	Peter Kedemo	438	JavaScript (Node.js)	2020-01-01 12:13:52
3	Vu Van Dung	454	JavaScript (Node.js)	2022-09-14 20:51:13
4	Gurpartap Singh Bhatti	499	JavaScript (Node.js)	2019-04-09 01:32:10
5	Hidden user	544	JavaScript (Node.js)	2023-11-19 03:08:44
6	Ali	570	JavaScript (Node.js)	2021-12-22 13:44:38
7	Chris Wong	640	JavaScript (Node.js)	2021-02-02 15:14:10
8	Howard Tin Chi Chan	656	JavaScript (Node.js)	2021-02-09 10:36:36
9	Amir Konjkav	703	JavaScript (Node.js)	2024-09-25 12:44:17
10	Yassin Swag	752	JavaScript (Node.js)	2023-12-02 17:00:02

#	User	Length	Language	Date
1	Christian Cederquist	124	JavaScript (SpiderMonkey)	2022-11-09 15:34:21
2	Evan Magill	205	JavaScript (SpiderMonkey)	2024-04-12 06:39:14
3	Jimmy Gustafsson	221	JavaScript (SpiderMonkey)	2022-08-16 11:09:09
4	Zach Tschetter	237	JavaScript (SpiderMonkey)	2023-06-17 21:08:20
5	Peter Menyes	280	JavaScript (SpiderMonkey)	2021-01-01 18:38:13
6	Bernard Perrin	300	JavaScript (SpiderMonkey)	2019-01-16 18:05:01
7	Casey Smith	323	JavaScript (SpiderMonkey)	2019-05-29 17:07:48
8	Bjørn Chr. Soltvedt	368	JavaScript (SpiderMonkey)	2018-11-04 08:51:47
9	Nicklas Utgaard	701	JavaScript (SpiderMonkey)	2019-10-26 22:19:52
10	Jeremy Loh	960	JavaScript (SpiderMonkey)	2018-11-06 16:40:52

#	User	Length	Language	Date
1	Danny Robinson	96	Julia	2023-10-03 23:54:00
2	Timothy Gaede	686	Julia	2024-03-19 14:49:14

#	User	Length	Language	Date
1	Magnus Wass	269	Kotlin	2020-12-17 20:53:38
2	Sergey Jakobsen	322	Kotlin	2021-06-11 01:50:03
3	Merih Bora Poçan	350	Kotlin	2020-09-16 07:33:55
4	Chris Johnson	409	Kotlin	2023-04-21 22:04:38
5	Dayan Ruben Gonzalez	419	Kotlin	2020-10-09 05:15:04
6	Troy Warmboe	500	Kotlin	2023-04-10 23:15:41
7	Jacob Huebner	502	Kotlin	2020-05-31 06:34:00
8	Gabriel Wu	528	Kotlin	2019-10-21 05:22:52
9	Adam Rankin	570	Kotlin	2023-05-01 05:58:05
10	Sarek Høverstad Skotåm	575	Kotlin	2020-10-10 17:30:03

#	User	Length	Language	Date
1	Fredrik Eriksson	366	OCaml	2024-10-16 18:03:54
2	Enzo Crance	497	OCaml	2019-02-13 23:32:04
3	Sam Henke	587	OCaml	2023-09-30 08:09:57

#	User	Length	Language	Date
1	Hidden user	368	Odin	2025-04-27 06:37:39

#	User	Length	Language	Date
1	Ingemar Ragnemalm	295	Pascal	2018-11-06 19:09:55
2	David Connolly	482	Pascal	2021-11-22 16:46:52

#	User	Length	Language	Date
1	Nicolai Robinson	271	Perl	2024-05-15 15:44:51

#	User	Length	Language	Date
1	Renate	408	PHP	2021-04-20 18:47:08
2	Helbin Grégory	572	PHP	2020-02-02 13:36:47
3	Connor Billings	1127	PHP	2019-12-30 17:33:08

#	User	Length	Language	Date
1	Andriy Zyevakov	420	Prolog	2018-11-11 22:55:43
2	Hakan Kjellerstrand	769	Prolog	2023-01-22 20:54:48

#	User	Length	Language	Date
1	Thomas Feld	129	Python 2	2019-08-26 13:57:21
2	Abdulselam Hassen	169	Python 2	2019-11-19 08:07:46
3	Andreas Björklund	171	Python 2	2019-03-25 06:31:01
4	Björn Magnusson	179	Python 2	2020-10-06 17:58:15
5	Lars Åström	181	Python 2	2018-11-15 20:38:44
6	Lim Hong Hui Eugene	191	Python 2	2019-04-09 12:51:30
7	Shakeel Samsudeen	200	Python 2	2020-06-10 23:00:51
8	Sigurður Jens Albertsson	212	Python 2	2019-11-22 18:05:10
9	Godmar Back	215	Python 2	2019-01-01 02:29:43
10	Ethan Arnold	219	Python 2	2018-11-08 23:28:38

#	User	Length	Language	Date
1	Clement Oh	92	Python 3	2023-05-22 18:48:15
2	Kevin Gomez	97	Python 3	2023-08-27 06:22:07
3	Russell Ng	100	Python 3	2025-07-29 20:06:03
4	Benjamin Z White	101	Python 3	2023-04-07 19:31:53
5	Błażej Dariusz Roszkowski	106	Python 3	2023-05-22 21:16:03
6	Hidden user	106	Python 3	2025-01-21 11:03:11
7	Ahmed Chamseddine	110	Python 3	2023-09-14 11:53:08
8	Oskar Haarklou Veileborg	127	Python 3	2020-01-28 13:29:49
9	Anderson Lizarazo Tellez	135	Python 3	2025-03-11 05:47:36
10	David Phillips	136	Python 3	2019-02-14 17:00:34

#	User	Length	Language	Date
1	Russell Ng	73	Ruby	2025-07-29 20:43:45
2	Thomas Feld	74	Ruby	2022-11-02 10:52:30
3	Patrick Elsen	88	Ruby	2022-09-11 14:28:32
4	Alexander Bilde Pedersen	104	Ruby	2023-04-10 22:45:50
5	Régis Hanol	116	Ruby	2022-01-09 16:36:27
6	Eugen Neagoe	141	Ruby	2023-03-22 01:48:19
7	Miorel Palii	160	Ruby	2018-11-04 17:17:11
8	Hidden user	180	Ruby	2019-02-16 17:03:09
9	Donald Dong	196	Ruby	2018-11-30 01:22:17
10	Lim Ming Yean	224	Ruby	2018-11-15 07:20:32

#	User	Length	Language	Date
1	Vincent Lagerros	265	Rust	2024-12-09 02:36:45
2	Artur Khuziakhmetov	380	Rust	2023-08-03 12:58:53
3	Thomas	539	Rust	2022-11-22 20:04:37
4	Florian ten Napel	542	Rust	2025-05-14 16:43:00
5	Oskar Strömberg	615	Rust	2020-10-23 01:28:22
6	Robert Janczewski	656	Rust	2020-02-05 15:02:54
7	Kok Dith	657	Rust	2021-08-01 14:04:09
8	Robert Dumitrescu	673	Rust	2018-12-13 12:56:36
9	Chaoyi Yin	681	Rust	2019-03-22 19:20:09
10	Gabriella	712	Rust	2025-04-15 15:13:22

Solution running time distribution