Leaderboard
China
China
Worldwide
Rank
Level
1
Jenny Wong
Region
97
2
fox
Region
96
3
User
Region
94
4
User
Region
93
5
User
Region
93
6
Yi Ke Hu
Zhejiang
91
7
User
Region
90
8
User
Shanghai
89
9
User
Region
89
10
James TSANG
Region
87
11
User
Region
83
12
User
Region
78
13
User
Hunan
77
14
HappyNewYear
Region
75
15
User
Region
70
16
User
Region
70
17
Felix Wong
Region
68
18
User
Region
68
19
User
Region
66
20
User
Region
66
21
User
Region
64
22
User
Region
63
23
Zhou Fan
Shanghai
63
24
User
Region
63
25
User
Region
62
26
User
Region
61
27
Josh Brookhart
Region
61
28
Ka Ming Sit
Region
58
29
User
Region
57
30
User
Region
55
31
K
Region
53
32
User
Region
53
33
User
Beijing
51
34
Ian Brookhart
Region
51
35
User
Region
49
36
Zhenglei Shi
Beijing
48
37
aa
Region
48
38
User
Region
47
39
User
Region
46
40
User
Region
46
41
User
Region
44
42
Matthew Lau
Region
43
43
User
Region
43
44
Nigel Jones
Shanghai
43
45
User
Region
42
46
User
Region
42
47
User
Region
42
48
User
Region
41
49
User
Region
41
50
User
Region
41
51
Wing Cheong Yip (Zero)
Region
41
52
Alistair Sexton
Shanghai
40
53
User
Guangdong
40
54
User
Region
40
55
Thane Rigwald
Region
40
56
User
Region
40
57
User
Region
39
58
User
Region
38
59
User
Region
38
60
shenglan zhang
Region
37
61
User
Region
36
62
User
Region
36
63
User
Shanghai
35
64
User
Region
35
65
User
Region
35
66
User
Region
34
67
User
Region
34
68
User
Region
34
69
James Chin
Region
34
70
User
Region
34
71
User
Region
34
72
User
Region
34
73
User
Region
34
74
User
Region
33
75
User
Region
33
76
User
Region
33
77
User
Region
33
78
User
Region
32
79
User
Region
31
80
User
Region
31
81
James Baghurst
Region
31
82
User
Region
31
83
User
Region
31
84
User
Region
31
85
Peter Wong
Guangdong
31
86
User
Region
30
87
User
Region
30
88
User
Region
30
89
User
Region
30
90
Matthijs De Lange
Region
30
91
User
Region
30
92
User
Region
30
93
Patrick Omey
Region
30
94
Павел Липаев
Region
30
95
abdelouahed benjelloun
Region
30
96
User
Region
29
97
User
Zhejiang
29
98
User
Region
28
99
User
Region
28
100
User
Region
28
101
User
Region
28
102
Aisling McCarron
Region
28
103
User
Region
27
104
Jino Lee
Region
27
105
Yuchan Shim
Region
27
106
User
Region
27
107
User
Region
27
108
User
Region
27
109
Ollie Wall
Region
26
110
User
Region
26
111
User
Region
26
112
Julius
Shanghai
26
113
User
Region
26
114
User
Region
26
115
User
Region
26
116
User
Region
26
117
User
Region
25
118
Rhys Ng
Region
25
119
User
Region
25
120
User
Region
25
121
User
Region
25
122
User
Region
25
123
User
Region
24
124
User
Region
24
125
User
Region
24
126
User
Region
24
127
bimal316
Region
24
128
User
Region
24
129
User
Region
24
130
User
Region
24
131
User
Jiangsu
23
132
User
Region
23
133
User
Region
23
134
User
Region
23
135
User
Region
23
136
User
Region
23
137
User
Region
22
138
Callista Ring
Region
22
139
User
Region
22
140
User
Region
22
141
Desmond Leung
Region
22
142
User
Region
22
143
User
Region
22
144
User
Region
22
145
User
Region
22
146
User
Region
22
147
User
Region
22
148
User
Region
22
149
User
Region
21
150
User
Region
21
151
Megan Tse
Region
21
152
User
Region
21
153
User
Region
21
154
User
Region
21
155
User
Region
21
156
User
Region
21
157
User
Region
21
158
User
Region
21
159
User
Region
20
160
User
Region
20
161
User
Region
20
162
User
Region
20
163
User
Region
20
164
User
Region
20
165
User
Region
20
166
User
Region
20
167
User
Region
19
168
User
Region
19
169
User
Shanghai
19
170
User
Region
19
171
User
Region
19
172
User
Region
19
173
User
Region
19
174
User
Region
19
175
User
Region
18
176
User
Region
18
177
User
Region
18
178
User
Region
18
179
User
Region
18
180
User
Region
18
181
User
Region
17
182
User
Region
17
183
User
Region
17
184
19605 ctsqn19605
Region
17
185
rdfyli@gmail.com
Region
16
186
User
Region
16
187
Jerome L Tan
Region
16
188
1C (10) Ng Sze Hon
Region
15
189
User
Region
15
190
User
Region
15
191
Kibaek Lee
Region
15
192
User
Region
15
193
User
Region
15
194
User
Region
15
195
User
Region
15
196
User
Region
15
197
User
Beijing
14
198
User
Region
14
199
TONY TIN-CIANG LO
Region
14
200
User
Region
14
201
User
Region
14
202
User
Region
14
203
User
Region
14
204
User
Region
14
205
User
Region
14
206
User
Region
14
207
User
Region
13
208
User
Region
13
209
User
Region
13
210
User
Region
13
211
User
Region
13
212
User
Region
13
213
User
Region
13
214
User
Region
13
215
User
Region
13
216
User
Region
13
217
User
Region
13
218
User
Region
13
219
User
Region
13
220
Angel Chen
Region
13
221
User
Region
12
222
User
Region
12
223
User
Region
12
224
User
Region
12
225
User
Shanghai
12
226
Henry Liu
Region
12
227
User
Region
12
228
User
Region
12
229
User
Region
12
230
JoyceKo
Region
12
231
User
Region
12
232
User
Region
12
233
User
Region
11
234
User
Region
11
235
User
Region
11
236
User
Region
11
237
amber
Region
11
238
User
Region
11
239
User
Region
11
240
User
Region
11
241
User
Region
11
242
User
Region
11
243
User
Region
11
244
St
Region
11
245
User
Region
11
246
User
Region
11
247
User
Region
11
248
User
Region
11
249
User
Region
11
250
User
Region
11
251
User
Region
11
252
User
Region
11
253
User
Region
10
254
User
Region
10
255
User
Region
10
256
User
Region
10
257
User
Region
10
258
User
Guangdong
10
259
User
Jiangsu
10
260
User
Region
10
261
User
Region
10
262
User
Region
10
263
User
Region
9
264
User
Region
9
265
User
Liaoning
9
266
Munisha Sharma
Region
9
267
Hugo So
Region
9
268
User
Region
9
269
User
Shanghai
9
270
User
Region
9
271
Seo Yun JEONG
Region
9
272
User
Region
9
273
User
Region
9
274
User
Region
9
275
asd
Region
9
276
User
Region
9
277
User
Region
9
278
User
Region
8
279
User
Region
8
280
User
Region
8
281
Daniel Cooper
Region
8
282
User
Region
8
283
User
Region
8
284
User
Region
8
285
User
Region
8
286
User
Region
8
287
User
Region
8
288
User
Region
8
289
Ian Brookhart
Region
8
290
User
Region
8
291
User
Region
8
292
User
Region
8
293
User
Region
8
294
User
Region
8
295
User
Region
8
296
User
Guangdong
8
297
User
Region
8
298
User
Shanghai
8
299
User
Region
7
300
User
Region
7
301
User
Region
7
302
User
Region
7
303
User
Region
7
304
User
Region
7
305
User
Region
7
306
User
Region
7
307
User
Region
7
308
User
Region
7
309
User
Region
7
310
Ailey Wong
Region
7
311
User
Region
7
312
Yangdon Sersang
Region
7
313
User
Region
7
314
User
Region
7
315
User
Region
7
316
User
Region
7
317
User
Region
7
318
User
Region
7
319
User
Region
7
320
User
Region
7
321
User
Region
6
322
User
Region
6
323
User
Region
6
324
User
Anhui
6
325
User
Region
6
326
User
Region
6
327
User
Region
6
328
User
Region
6
329
User
Region
6
330
User
Region
6
331
User
Region
6
332
User
Region
6
333
User
Region
6
334
User
Zhejiang
6
335
User
Region
6
336
User
Region
6
337
User
Region
6
338
User
Region
6
339
Amaia King
Region
6
340
User
Region
6
341
Ivan Lai
Region
6
342
User
Region
6
343
User
Region
6
344
User
Region
6
345
User
Region
6
346
User
Region
5
347
User
Region
5
348
User
Region
5
349
User
Region
5
350
User
Region
5
351
User
Region
5
352
User
Region
5
353
User
Region
5
354
User
Region
5
355
User
Region
5
356
User
Region
5
357
User
Region
5
358
User
Region
5
359
User
Region
5
360
User
Region
5
361
User
Region
5
362
User
Region
5
363
User
Region
5
364
User
Region
5
365
User
Region
4
366
User
Region
4
367
peper bubi
Region
4
368
User
Region
4
369
User
Region
4
370
User
Region
4
371
User
Region
4
372
User
Region
4
373
User
Region
4
374
User
Region
4
375
User
Shanghai
4
376
User
Jiangsu
4
377
User
Zhejiang
4
378
User
Shaanxi
4
379
User
Region
4
380
User
Region
4
381
User
Region
4
382
User
Region
4
383
User
Region
4
384
User
Region
4
385
User
Region
4
386
User
Region
4
387
Tan Thien Luong
Region
4
388
User
Region
4
389
User
Region
4
390
User
Region
4
391
User
Region
4
392
User
Region
4
393
User
Beijing
4
394
User
Region
4
395
User
Region
4
396
User
Shanghai
4
397
User
Region
4
398
User
Region
4
399
User
Region
3
400
User
Region
3
401
User
Region
3
402
User
Region
3
403
User
Region
3
404
User
Region
3
405
User
Region
3
406
User
Region
3
407
User
Region
3
408
User
Region
3
409
User
Region
3
410
User
Region
3
411
User
Region
3
412
User
Region
3
413
User
Region
3
414
User
Region
3
415
User
Zhejiang
3
416
User
Region
3
417
User
Zhejiang
3
418
User
Region
3
419
User
Region
3
420
User
Region
3
421
User
Region
3
422
User
Region
3
423
User
Region
3
424
Bernie Green
Region
3
425
User
Region
3
426
User
Region
3
427
User
Region
3
428
User
Yunnan
3
429
User
Region
3
430
User
Region
3
431
User
Region
3
432
User
Region
3
433
User
Region
3
434
User
Region
3
435
User
Region
3
436
User
Shanghai
3
437
User
Region
3
438
User
Region
3
439
User
Region
3
440
User
Region
3
441
User
Region
3
442
User
Region
3
443
User
Region
3
444
User
Region
3
445
User
Guangdong
3
446
User
Region
2
447
User
Region
2
448
User
Region
2
449
User
Beijing
2
450
User
Region
2
451
User
Region
2
452
User
Region
2
453
User
Region
2
454
User
Region
2
455
User
Region
2
456
User
Region
2
457
User
Region
2
458
User
Region
2
459
User
Zhejiang
2
460
User
Region
2
461
User
Region
2
462
janice
Region
2
463
User
Region
2
464
Karina
Region
2
465
User
Anhui
2
466
User
Region
2
467
User
Region
2
468
User
Region
2
469
User
Zhejiang
2
470
User
Region
2
471
User
Region
2
472
User
Shanghai
2
473
User
Region
2
474
User
Region
2
475
User
Region
2
476
User
Region
2
477
Jian Lee
Region
2
478
User
Region
2
479
User
Region
2
480
User
Region
2
481
User
Region
2
482
User
Region
2
483
User
Region
2
484
User
Region
2
485
User
Region
2
486
User
Region
2
487
User
Region
2
488
User
Region
2
489
User
Guangdong
2
490
User
Region
2
491
User
Region
2
492
User
Region
2
493
User
Region
2
494
User
Region
2
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User
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2
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User
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2
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User
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2
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User
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2
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User
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2
500
User
Region
2
501
User
Region
2
502
User
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1
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User
Region
1
504
User
Region
1
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User
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1
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User
Region
1
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User
Region
1
508
User
Region
1
509
User
Region
1
510
Ms. McCully
Region
1
511
User
Region
1
512
User
Shanghai
1
513
User
Region
1
514
User
Guangdong
1
515
User
Region
1
516
User
Region
1
517
User
Region
1
518
User
Region
1
519
User
Region
1
520
User
Region
1
521
User
Region
1
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User
Region
1
523
User
Chongqing
1
524
User
Region
1
525
User
Region
1
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User
Region
1
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User
Region
1
528
User
Region
1
529
User
Region
1
530
User
Region
1
531
User
Region
1
532
User
Region
1
533
User
Shanghai
1
534
User
Beijing
1
535
User
Region
1
536
Conor Watson
Beijing
1
537
User
Region
1
538
User
Region
1
539
Dani Majzoup
Region
1
540
Joseph Liu
Region
1
541
Mei Wong
Region
1
542
Samson Leung
Region
1

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A Web App for Mathematics Training

Do you want to be fast at mental math? Many people do, but the options for doing the necessary exercises are simply too cumbersome for all but the most dedicated of trainees. In physical fitness, many people are interested in training their bodies but allocating the time, energy, and money for it is a significant obstacle. Likewise, lugging around books and whatnot for math practice is a threshold that just doesn't meet the standards of modern life.

Training yourself to be skilled at mental math needs to be quick and convenient. mathtrainer.org is a web app that works in your browser rather than a program you have to download and install on your computer or phone. This allows users to try and use the app without having to install new software. As a web app, updates are also much simpler. There is no need to download endless updates—the website will always be the most current version.

You can access a web app from any device connected to the internet and equipped with a web browser, including smartphones, tablets, and desktop computers. Moreover, you are free to use whichever browser you prefer, including Google Chrome, Safari, Firefox, and others. Google Chrome is the recommended browser for the best maths training since it tends to lead the pack in supporting the latest web technologies.

Math Trainer is designed to offer a similar experience regardless of what you’re using to access it, whether it be Android, iOS, Windows, or another operating system. Though an on-screen touch keyboard will appear on mobile devices, you may prefer to use the app on a desktop with a keyboard. Hopefully the advantages of a web app for convenient mathematics training are apparent.

Another part of making the app easy to use is eliminating the need for signing up and logging in. Users can get started with their math training as soon as they click the start button on this page. After progressing to higher levels in the app, your progress is automatically saved so long as your return to the site through the same browser.


What's a Mental Math Tip?

A mental math tip is a sequence of steps that can be taken to solve a math problem in your head. Click the arrow below to see an example for the following problem:

÷
984
3
328

A tip like this one is available for every problem in Math Trainer, so there's always help if you get stuck. With enough practice, you'll be able to predict what the tips will say—you'll have learned mental math!


Get Better at Mental Math

The ability to quickly perform mental calculations offers advantages in certain circumstances. But even without applications, getting better at mental math is a great way to stimulate one’s mind. It develops better number sense and intuition for quantifying the world around us. Practicing mental calculation will strengthen your foundation for learning more advanced maths topics.

Nonetheless, the tangible benefits of improving at mental math are many. It is certainly expected that educated people are able to do simple arithmetic without having to pull out a calculator. An inability to do so may reflect poorly on you, while being well-practiced in mental calculation will leave your contemporaries impressed. In many scientific and technical circles, mental math ability is even more highly regarded.

For students, mental calculation speed will often have a direct impact on math and science test scores. At all grade levels, it is not sufficient to know how to solve math problems when tests have a time limit on them. The highest-scoring test takers are able to answer questions both correctly and efficiently. Improving mental math skills will only benefit a student’s academic career.

Calculating the solution to an arithmetic problem in your head is often faster than pulling out a device to tell you the answer. For example, figuring out how much to tip a server at a restaurant is a straightforward arithmetic problem that many people are unable to perform without a calculator. By training your brain to solve basic math problems, you can save time in situations like these.

Mental math can also be relied upon when calculation devices are not available. Even with the conveniences of modern life, we occasionally find ourselves without access to our cell phones or other capable devices. A mind skilled in mental math is always available to you.

Finally, getting better at mental math enables a quick estimate and sanity check on results obtained from calculators. While computers are extremely reliable at solving math problems, there is always the risk of incorrectly inputting the problem to the computer. By getting better at mental mathematics, you will develop an intuition for whether the results of calculators make sense.

In fact, the ability to estimate is often sufficient to avoid using calculators altogether. While the use of computers is widespread, estimation is an increasingly valued skill in many industries. There are many situations where complex math will eventually be required, but a preliminary estimate is needed quickly. A major boost to productivity!


Use a Math Trainer

Mental math ability is a lot like physical fitness training. You may be out of shape in the beginning, but with diligent training you can and will improve. Initially you might not enjoy the exercise, but you will reap significant rewards for your effort. As you become more fit, you’ll begin to enjoy the activity much more. If you are serious about it, your mental calculation fitness could become a source of energy, galvanizing you to face the challenges of life with enthusiasm.

In physical training, you break down the fibers in your muscles during a workout session. Your muscles actually sustain tiny tears during resistance training exercises. While you rest afterwards, your body repairs the damage, rebuilding the fibers thicker and stronger.

A similar process is believed to occur for cognitive tasks. A 2016 study found "extensive evidence that brain-training interventions improve performance on the trained tasks".1 Therefore you can expect training your brain to answer mental math questions will lead to improved performance over time.

In the context of physical fitness, a "trainer" often refers to a trained professional who guides the workout and recovery process. Personal trainers are tasked with assessing a trainee's level of ability, prescribing an exercise regimen, and offering feedback as the training goes along. The word "trainer" could also refer to a system that automates the role of a personal trainer. Many aerobic exercise machines today offer interactive training programs with feedback and analysis of a user's performance.

A math trainer is needed for optimal math fitness. Like in physical fitness, the trainer should be compatible with users at a variety of skill levels and should guide them to the next level. It should give an accurate assessment of a user's strengths and weakness, as well as offer helpful feedback on where to focus one's efforts. Learning the ropes of mental maths with a math trainer should be a seamless, rewarding journey to ever-greater abilities.


Mental Calculation

Mental calculation, or mental math, is performing arithmetical calculations without the aid of tools or supplies. As opposed to using a calculator or pencil and paper, mental math is performed entirely in one’s head.

People use mental calculation when computation aides are not available, when it is faster to do so, or when they wish to practice, show off, or participate in mental math competitions. Most people perform basic mental calculation using elementary arithmetic on a daily basis. An inability to calculate mentally is a serious obstacle to many common tasks.

In U.S. schools, mental calculation is taught only for the most elementary arithmetic, such as single-digit addition and multiplication of two numbers between 0 and 12. To solve addition problems involving multiple digits, you are taught to add columns of digits from right to left, carrying the tens digit if the column sum exceeds 9. For example, how would you approach this addition problem?

Example of two-digit
addition problem

If you were trained like many of us were, you’d add the right column to obtain 12. Since that’s two digits, you’d write the 2 under the right column and carry the 10 by writing a 1 above the left column. Finally, you’d add the two tens digits and the carried 1 to obtain the answer, 52.

To solve an addition problem mentally, it’s best to add the columns from left to right. In our example, you could add the tens digit of the second number, 30, to the first number, 14, to obtain 44. This is easier than the full problem because you’re just doing one mental calculation and tacking on the 4 from the 14 as the singles digit. Then you’d add the remaining ones digit of the second number, 8, to 44 to arrive at the answer, 52.

Which approach seems simpler to you? Can you do the first approach without pulling out a pencil and paper? It turns out the same advantages of left-to-right addition apply to much larger numbers as well. It’s unlikely that difficult addition problems can be solved right to left without needing to write it all out, which of course is more time consuming.

Mental math should be distinguished from the memorization of math facts such as multiplication tables. A foundation of memorized answers to simple math problems will make mental math easier, but performing maths in your head requires both memorized facts and the manipulation of numbers and operations to solve problems. This combination of skill and memory allows us to solve far more complex math questions than can be answered with readily-memorized math facts.

Many mental math tricks are specific to particular numbers or types of problems, usually dependent on the base of the number system used. In the decimal numeral system, for example, it is trivially easy to multiply by 10—just add a 0 to the end of the number. This mental math trick wouldn’t work in the hexadecimal numeral system, though, because the base is 16 instead of 10.

Therefore mental calculation is the ability to manipulate complex arithmetic problems in such a way that they can be resolved using simple memorized math facts.


Arithmetic

Arithmetic is the branch of mathematics concerning basic number operations: addition, subtraction, multiplication, and division. As kids, we are taught to do arithmetic because real-world math problems depend on a mastery of elementary arithmetic. Higher-level study of arithmetic and the integers, or whole numbers, is known as number theory.

Though the math kids initially study is arithmetic, the word is rarely used in this context anymore. Originally it comes from the Greek arithmos, meaning “number”. It has however been included in the “three Rs” of elementary Western education: reading, writing, and arithmetic.

There is evidence prehistoric humans were using arithmetic as hunter-gatherers. Archaeologists have uncovered a tally stick, believed to be over 20,000 years old, which may exhibit the earliest known sequences of prime numbers. An understanding of prime numbers, which are only divisible by themselves and the number 1, requires knowledge of the operation in arithmetic known as division.

From tally marks came base-10 numerals such as those used in Egypt over 5,000 years ago. Number systems based on 10 probably arose because humans have ten “digits” as fingers on their hands (or toes on their feet). A later advance in arithmetic was positional notation, which allowed the same symbols to represent different magnitudes depending on their position in the written number. These numeral systems allowed complex arithmetic to be communicated, recorded, and applied to the challenges faced by our ancestors.

The basic operation of arithmetic is addition. It combines two or more numbers into one, the sum of the terms. The terms can be added in any order, which is known as the commutative property of arithmetic. On a number line, the sum of two numbers is the total distance from zero covered by both numbers.

The inverse arithmetical operation of addition is subtraction. It finds the difference between two numbers. Subtraction is not commutative because the order of the numbers determines whether the answer is positive or negative. On a number line, the difference between two numbers is the distance between their positions.

A second basic operation of arithmetic is multiplication, which scales a number by another number. This second number is called a factor. Like addition, multiplication is commutative—you can change the order of the factors and still get the same answer. Multiplication on a number line can be viewed as adding the first number a total number of times equal to the second factor.

Finally, division is an arithmetical operation that is essentially the inverse of multiplication. Rather than scaling a number, it is divided into a number of pieces equal to the second number. Dividing by the number 0 is not defined in arithmetic because dividing something into zero pieces is impossible.

Basic arithmetic allows us to evaluate the answers to an unlimited number of mathematical expressions. Arithmetical expressions can be purely mathematical, as in 2 + 2, or they can represent quantities in the physical world, such as two items plus two more. Understanding the laws of arithmetic is tremendously powerful.


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