Base 10: Iteration Frequencies: Full Cycle

Radix Character Encoding
0	1	2	3	4	5	6	7	8	9

Color Key
Orange	Fixed Point	number that becomes itself after one iteration
Green	Final Numbers	all numbers eventually reached, from all cycles
Purple	Cycle Start	iterations include entry into cycle, assuming it repeats
Red	Full Cycle	iterations include entire cycle, proving it repeats
Blue	Start Numbers	subset (optimization) of all numbers; minimal for full coverage
Gray	No Results	any calculation that has no results

Digits

Average Steps
Full Cycle

1.90 step
avg

5.56 step
avg

4.27 step
avg

5.65 step
avg

6.65 step
avg

12.10 step
avg

13.80 step
avg

12.50 step
avg

19.11 step
avg

10.68 step
avg

11.97 step
avg

10.34 step
avg

10.42 step
avg

10.55 step
avg

10.24 step
avg

10.28 step
avg

10.98 step
avg

9.93 step
avg

11.69 step
avg

9.56 step
avg

11.65 step
avg

9.41 step
avg

11.21 step
avg

9.33 step
avg

10.43 step
avg

9.50 step
avg

9.67 step
avg

9.83 step
avg

9.13 step
avg

9.87 step
avg

8.90 step
avg

9.73 step
avg

8.70 step
avg

9.46 step
avg

8.70 step
avg

9.17 step
avg

8.71 step
avg

8.88 step
avg

8.67 step
avg

8.74 step
avg

8.55 step
avg

8.62 step
avg

8.35 step
avg

8.62 step
avg

8.15 step
avg

8.63 step
avg

7.98 step
avg

8.61 step
avg

7.91 step
avg

8.53 step
avg

7.82 step
avg

8.39 step
avg

7.84 step
avg

8.25 step
avg

7.84 step
avg

8.13 step
avg

7.83 step
avg

8.07 step
avg

7.77 step
avg

8.01 step
avg

7.68 step
avg

8.01 step
avg

7.59 step
avg

8.01 step
avg

7.50 step
avg

7.99 step
avg

7.47 step
avg

7.94 step
avg

7.43 step
avg

7.86 step
avg

7.43 step
avg

7.79 step
avg

7.44 step
avg

7.72 step
avg

7.42 step
avg

7.68 step
avg

7.40 step
avg

7.64 step
avg

7.35 step
avg

Step Frequency
Full Cycle

0s:
1s:
2s:
0×
1×
9×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
0×
1×
9×
0×
0×
3×
22×
20×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
0×
1×
39×
28×
54×
46×
34×
18×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
0×
1×
29×
34×
140×
129×
113×
153×
116×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
0×
1×
9×
78×
30×
432×
436×
354×
342×
242×
78×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
0×
1×
71×
68×
228×
24×
0×
0×
237×
463×
610×
428×
521×
468×
398×
472×
379×
378×
88×
166×
5×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
0×
1×
9×
0×
0×
0×
0×
0×
0×
622×
958×
1,136×
1,234×
956×
1,516×
2,088×
1,050×
930×
394×
320×
168×
58×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
0×
1×
86×
224×
464×
782×
1,103×
948×
775×
1,930×
2,721×
2,552×
1,803×
1,501×
1,167×
1,476×
1,373×
1,152×
947×
999×
757×
1,329×
220×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
0×
1×
201×
498×
984×
332×
298×
68×
46×
0×
0×
0×
0×
0×
0×
1,568×
4,024×
5,592×
3,936×
4,496×
6,542×
5,658×
6,074×
4,886×
1,992×
838×
538×
48×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
0×
1×
167×
856×
2,083×
5,413×
7,998×
7,780×
6,343×
6,653×
7,711×
7,572×
8,547×
7,058×
5,958×
5,639×
5,755×
4,399×
1,253×
933×
259×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
0×
1×
225×
786×
1,286×
1,638×
3,246×
8,252×
9,850×
11,628×
15,062×
20,536×
20,284×
20,882×
17,788×
10,878×
12,260×
8,146×
3,696×
872×
472×
172×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
0×
1×
278×
1,592×
4,448×
22,385×
27,921×
25,803×
28,749×
26,407×
25,248×
21,145×
19,754×
20,098×
16,126×
16,969×
18,871×
9,592×
4,583×
2,946×
933×
81×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
0×
1×
225×
1,506×
3,500×
7,068×
9,066×
31,156×
57,828×
74,098×
79,002×
80,710×
66,908×
35,328×
22,002×
10,766×
5,664×
5,208×
3,690×
2,546×
936×
166×
46×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
0×
1×
374×
4,172×
11,666×
69,910×
92,191×
74,102×
82,319×
73,286×
71,055×
40,965×
38,383×
37,612×
43,789×
40,721×
42,346×
28,041×
21,681×
13,855×
7,442×
6,758×
4,424×
3,812×
4,475×
2,012×
1,656×
98×
44×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
0×
1×
255×
1,938×
4,712×
8,932×
9,946×
80,724×
201,770×
189,220×
210,348×
229,882×
179,102×
112,152×
53,662×
16,964×
5,546×
1,770×
494×
86×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
0×
1×
536×
10,232×
39,939×
193,760×
251,498×
215,472×
196,354×
150,488×
164,216×
124,559×
88,321×
71,293×
85,474×
103,847×
117,683×
94,568×
57,004×
34,147×
11,869×
6,488×
4,166×
5,932×
6,316×
4,113×
2,123×
1,455×
1,049×
72×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
0×
1×
609×
12,944×
31,552×
19,600×
15,260×
154,978×
415,562×
372,838×
366,822×
428,270×
419,784×
334,586×
220,224×
154,372×
66,172×
59,094×
31,384×
14,368×
5,804×
248×
50×
28×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
0×
1×
890×
22,148×
72,961×
463,834×
678,548×
569,443×
467,625×
390,695×
358,476×
248,534×
200,898×
153,780×
154,298×
180,633×
224,421×
203,636×
109,632×
60,958×
39,478×
31,720×
13,250×
10,801×
6,864×
7,871×
4,962×
7,476×
2,447×
529×
16×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
0×
1×
1,121×
31,604×
87,436×
117,894×
186,540×
365,686×
681,414×
643,944×
583,828×
615,504×
602,348×
676,372×
697,564×
551,544×
440,808×
317,354×
187,006×
73,558×
32,584×
10,366×
1,302×
1,122×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
0×
1×
1,121×
39,862×
133,670×
1,004,163×
1,517,549×
1,395,229×
1,093,794×
891,448×
776,822×
547,788×
453,988×
379,855×
313,619×
243,931×
285,716×
330,737×
234,294×
157,074×
80,226×
41,544×
18,423×
14,365×
9,883×
8,489×
13,939×
12,724×
8,418×
4,359×
1,934×
40×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
0×
1×
1,663×
52,984×
155,020×
319,772×
779,016×
910,246×
1,211,620×
1,156,326×
1,252,826×
1,204,934×
1,116,928×
1,069,044×
1,167,810×
1,306,318×
1,220,948×
703,804×
401,426×
196,780×
56,542×
21,548×
1,564×
30×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
0×
1×
1,364×
68,626×
204,535×
1,946,778×
2,954,747×
2,580,146×
2,476,361×
2,010,552×
1,814,094×
1,453,477×
1,100,040×
716,124×
491,126×
403,384×
435,330×
428,154×
394,704×
273,808×
136,904×
99,901×
56,143×
28,297×
14,053×
9,442×
8,873×
14,037×
14,848×
2,889×
5,646×
7,900×
3,388×
2,222×
2,091×
90×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
0×
1×
2,913×
119,280×
362,800×
910,918×
2,226,124×
2,370,624×
2,396,476×
2,336,606×
2,193,952×
2,372,376×
2,105,360×
1,875,048×
1,937,210×
1,957,588×
2,024,258×
1,259,756×
877,356×
476,846×
142,308×
74,078×
22,700×
3,000×
972×
250×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
0×
1×
1,637×
109,126×
288,635×
3,751,224×
5,837,758×
4,741,946×
4,727,315×
3,822,516×
3,333,722×
3,248,582×
2,509,560×
1,596,729×
932,547×
664,678×
609,970×
559,984×
513,426×
418,718×
264,864×
217,969×
235,749×
57,982×
23,270×
14,986×
7,274×
9,905×
8,905×
5,773×
10,225×
14,023×
7,199×
5,455×
7,626×
2,735×
2,961×
2,101×
24×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
0×
1×
3,553×
201,692×
671,606×
2,278,874×
5,929,542×
5,178,796×
4,792,942×
5,163,648×
4,779,792×
4,486,554×
3,737,842×
3,035,776×
2,756,184×
2,810,900×
2,908,212×
1,549,674×
1,198,050×
596,316×
176,810×
119,132×
68,620×
5,614×
1,054×
72×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
0×
1×
2,279×
212,528×
671,721×
7,247,012×
10,693,188×
8,098,019×
7,862,234×
6,152,153×
4,988,474×
4,991,980×
4,780,865×
4,219,579×
3,220,018×
2,282,329×
1,398,976×
1,053,755×
798,219×
572,199×
427,302×
332,599×
287,444×
125,629×
49,774×
24,233×
20,949×
19,634×
11,019×
5,361×
8,832×
13,074×
11,018×
6,614×
8,098×
4,935×
2,141×
2,625×
650×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
0×
1×
4,769×
308,340×
1,007,310×
4,978,112×
13,327,232×
11,803,582×
9,926,820×
9,973,136×
9,224,296×
8,009,592×
6,002,322×
4,636,514×
3,595,656×
3,636,588×
3,559,880×
2,086,490×
1,111,106×
628,116×
161,454×
110,680×
45,780×
3,888×
1,328×
288×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
0×
1×
3,115×
362,506×
1,312,431×
13,199,446×
19,431,797×
14,505,839×
12,824,756×
8,902,417×
7,117,803×
6,364,789×
7,031,697×
7,329,687×
6,583,689×
4,822,509×
4,026,772×
3,741,517×
2,575,584×
1,375,696×
871,828×
806,122×
529,897×
283,102×
107,208×
65,726×
42,306×
32,175×
28,642×
21,907×
18,550×
23,111×
20,281×
11,321×
13,435×
3,916×
2,933×
9,085×
24×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
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0×
1×
6,201×
478,332×
1,647,394×
9,846,170×
26,169,786×
24,557,608×
19,549,036×
17,921,202×
15,565,066×
13,375,538×
9,322,316×
5,905,682×
4,642,542×
4,688,598×
4,531,198×
2,526,640×
1,254,564×
656,948×
181,580×
124,298×
53,260×
6,198×
1,452×
30×

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0×
1×
3,981×
562,092×
1,930,479×
23,054,054×
35,505,815×
24,989,129×
19,211,790×
13,981,097×
12,946,964×
11,239,339×
10,196,592×
9,700,783×
10,198,914×
10,810,337×
9,930,931×
6,283,105×
4,167,410×
2,227,753×
1,437,283×
1,183,850×
878,305×
486,256×
301,177×
133,239×
98,650×
132,648×
92,513×
44,702×
58,472×
50,041×
26,058×
20,096×
15,225×
6,552×
4,550×
3,859×
1,090×

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0×
1×
7,737×
723,172×
2,487,834×
18,527,174×
48,189,364×
41,171,780×
33,668,442×
29,417,248×
26,112,282×
23,253,832×
15,117,078×
9,751,364×
6,584,444×
6,024,578×
6,138,062×
3,539,580×
1,541,766×
788,334×
192,444×
140,146×
55,372×
4,914×
1,564×
368×

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0×
1×
5,600×
985,168×
3,287,095×
39,043,532×
62,220,014×
43,507,561×
29,231,419×
23,926,676×
22,074,966×
19,831,585×
15,633,762×
14,630,185×
16,436,405×
16,253,245×
14,409,714×
9,145,413×
7,651,206×
4,275,391×
2,221,037×
1,740,180×
1,257,745×
798,349×
671,829×
333,131×
181,559×
179,186×
152,634×
64,708×
64,478×
50,461×
24,434×
23,918×
16,817×
3,859×
4,517×
5,659×
126×

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0×
1×
9,303×
1,030,220×
3,341,304×
33,665,214×
85,149,598×
68,943,104×
55,486,168×
47,819,072×
38,864,848×
36,158,794×
25,486,894×
16,218,724×
9,698,246×
8,043,848×
8,603,762×
4,159,966×
1,719,460×
1,017,624×
255,930×
148,516×
62,854×
6,636×
1,694×
30×

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0×
1×
6,645×
1,478,100×
4,910,738×
64,733,754×
105,771,076×
72,895,750×
48,357,989×
42,990,352×
39,059,086×
32,224,337×
25,071,568×
21,825,890×
21,948,607×
21,932,506×
20,479,468×
12,668,093×
10,352,069×
5,496,127×
2,819,806×
2,221,953×
1,712,899×
1,240,057×
1,172,150×
677,816×
558,406×
550,948×
249,642×
119,988×
167,781×
82,354×
51,492×
48,280×
20,040×
10,920×
8,406×
5,371×
1,530×

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0×
1×
11,577×
1,638,656×
5,962,404×
59,109,874×
143,835,712×
111,358,868×
83,568,542×
69,452,540×
51,393,100×
48,619,116×
36,896,572×
30,580,856×
22,307,892×
18,325,660×
15,106,810×
6,238,610×
2,593,238×
1,400,786×
296,148×
160,706×
65,308×
5,202×
1,882×
448×

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0×
1×
8,266×
2,170,124×
6,840,395×
105,507,882×
177,446,415×
118,866,454×
79,066,790×
71,072,173×
65,763,955×
53,607,240×
38,560,482×
31,090,462×
28,754,688×
28,059,901×
24,837,056×
17,005,824×
12,400,140×
6,816,428×
3,928,890×
3,016,122×
2,844,538×
2,022,579×
1,732,275×
1,313,377×
886,453×
1,019,995×
608,463×
305,101×
212,511×
102,904×
66,706×
115,765×
78,705×
16,363×
11,255×
6,433×
24×

0s:
1s:
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0×
1×
14,521×
2,471,590×
8,903,256×
99,658,406×
234,425,794×
178,805,894×
128,914,318×
102,823,762×
73,250,874×
61,374,278×
47,606,126×
40,287,504×
34,872,760×
27,106,242×
25,458,154×
16,923,254×
11,402,436×
5,149,918×
1,284,044×
532,622×
389,828×
53,636×
7,082×
30×

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0×
1×
10,148×
3,169,146×
10,274,509×
165,197,584×
284,100,159×
197,597,121×
131,812,922×
115,743,007×
101,082,215×
81,565,469×
57,086,183×
42,426,341×
37,183,740×
36,121,769×
32,104,117×
21,575,279×
14,342,561×
7,886,096×
4,888,183×
3,807,354×
3,188,184×
2,831,621×
2,591,442×
1,743,279×
1,223,473×
1,088,880×
792,744×
424,939×
306,581×
147,900×
103,471×
120,969×
52,662×
26,916×
21,414×
8,796×
1,970×

0s:
1s:
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0×
1×
16,727×
3,379,392×
11,624,488×
162,611,706×
375,667,306×
273,383,808×
185,038,624×
147,868,852×
113,043,790×
94,400,902×
64,727,902×
48,247,972×
46,529,232×
47,743,166×
48,070,066×
28,300,328×
14,746,746×
7,514,340×
2,762,762×
891,382×
313,300×
217,316×
5,624×
908×

0s:
1s:
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0×
1×
12,170×
4,428,222×
13,670,396×
256,981,352×
448,651,226×
297,508,003×
196,938,901×
175,678,240×
155,213,692×
128,454,760×
84,416,363×
63,886,503×
51,796,007×
45,243,044×
41,284,077×
27,064,462×
17,740,834×
9,993,423×
7,123,981×
6,245,207×
4,422,765×
3,992,215×
3,746,058×
3,274,233×
2,197,802×
1,666,322×
1,046,637×
502,221×
452,914×
254,672×
208,620×
184,345×
79,622×
32,880×
42,513×
18,649×
1,125×
1,177×

0s:
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0×
1×
20,409×
4,998,402×
18,276,460×
258,250,736×
581,405,754×
412,864,944×
271,545,982×
221,191,570×
168,608,396×
137,504,386×
89,840,296×
63,930,414×
68,551,366×
67,633,210×
63,493,326×
31,583,242×
21,129,952×
13,892,872×
6,944,064×
2,284,792×
1,278,946×
177,824×
24,596×
1,582×
178×

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1s:
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0×
1×
14,222×
5,951,970×
17,307,802×
392,876,692×
689,369,950×
447,540,262×
298,191,439×
261,549,540×
217,721,600×
176,992,041×
128,375,084×
97,916,490×
70,634,241×
58,786,502×
55,645,520×
35,350,924×
22,936,710×
14,356,393×
10,316,839×
8,648,911×
6,008,927×
5,089,968×
4,384,374×
3,628,125×
3,747,667×
3,468,377×
2,083,055×
1,106,683×
759,817×
453,121×
456,635×
310,847×
119,902×
67,339×
82,947×
40,310×
9,302×
9,620×
2,201×

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0×
1×
23,609×
6,880,608×
24,931,730×
402,274,878×
892,106,028×
622,346,628×
394,516,260×
327,706,134×
254,679,052×
204,374,834×
125,474,330×
84,633,876×
82,489,216×
84,985,196×
81,611,704×
39,239,616×
25,861,584×
15,460,642×
5,772,062×
2,019,904×
1,477,940×
136,382×
64,038×
8,568×
580×

0s:
1s:
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0×
1×
17,027×
8,426,158×
27,272,757×
591,786,566×
1,031,142,013×
653,574,550×
432,800,112×
362,137,645×
278,798,131×
225,926,610×
172,655,448×
157,174,470×
123,261,338×
102,498,313×
89,019,090×
51,243,055×
30,421,449×
19,365,966×
14,707,607×
12,636,292×
8,728,498×
7,502,651×
6,029,487×
5,196,855×
5,296,396×
4,672,426×
2,985,493×
2,049,106×
1,551,388×
793,966×
611,217×
522,373×
262,010×
241,364×
159,939×
70,988×
22,654×
34,547×
14,890×
1,383×
1,321×

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0×
1×
27,385×
9,243,376×
31,883,756×
610,682,508×
1,340,923,870×
921,106,694×
576,773,896×
476,852,324×
373,508,884×
299,376,182×
171,365,100×
111,339,992×
100,435,804×
99,535,336×
93,255,396×
46,906,682×
29,216,184×
16,893,374×
4,995,012×
2,117,270×
1,355,946×
138,062×
3,196×
30×

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0×
1×
20,538×
11,535,688×
36,699,890×
875,127,224×
1,518,125,929×
947,886,781×
617,176,218×
511,430,845×
376,997,111×
283,710,475×
218,867,945×
195,414,387×
171,518,618×
136,739,661×
131,888,705×
94,069,831×
70,458,999×
47,142,110×
26,453,548×
19,167,186×
13,336,939×
11,626,459×
8,852,308×
7,083,292×
6,063,524×
5,358,191×
4,255,042×
3,321,017×
3,179,310×
1,722,823×
937,745×
717,744×
423,332×
494,533×
279,107×
130,352×
58,119×
77,041×
33,731×
7,724×
9,538×
2,489×

0s:
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0×
1×
31,761×
12,808,984×
45,104,512×
906,916,250×
1,968,338,994×
1,347,978,048×
831,060,386×
693,885,824×
533,985,366×
407,926,918×
233,943,688×
145,160,704×
121,835,884×
116,388,836×
105,480,658×
52,604,926×
26,672,910×
16,855,032×
4,840,006×
2,434,284×
1,525,696×
185,170×
2,874×
688×

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0×
1×
23,311×
15,033,046×
46,508,078×
1,273,024,648×
2,205,384,738×
1,349,693,979×
846,346,079×
701,153,850×
528,299,618×
397,440,620×
284,648,807×
223,894,265×
212,047,175×
219,325,552×
213,424,677×
154,148,950×
102,822,644×
54,929,737×
39,088,080×
32,087,369×
18,466,615×
15,485,438×
11,882,788×
9,358,559×
8,970,833×
8,329,885×
5,977,873×
5,716,843×
4,207,425×
3,468,223×
1,511,853×
1,306,027×
824,267×
582,988×
422,677×
202,480×
117,810×
152,697×
75,141×
24,924×
35,339×
13,728×
1,373×
1,465×

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0×
1×
36,369×
17,081,766×
56,448,580×
1,326,669,392×
2,838,129,558×
1,873,891,170×
1,136,733,462×
931,270,644×
758,903,500×
593,196,564×
341,324,474×
219,222,674×
159,371,400×
147,050,796×
132,102,744×
60,289,238×
30,938,402×
17,332,838×
4,960,272×
2,276,268×
1,597,708×
43,126×
2,974×
30×

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0×
1×
27,605×
20,376,944×
67,928,280×
1,820,726,046×
3,141,102,760×
1,915,431,490×
1,186,432,179×
987,110,560×
735,995,952×
554,027,867×
362,674,246×
281,503,428×
300,475,969×
277,029,476×
267,785,660×
169,371,316×
117,342,020×
90,415,027×
69,621,161×
52,266,727×
31,944,240×
24,541,802×
18,692,369×
13,015,791×
12,545,175×
11,332,986×
8,768,791×
7,076,469×
5,913,578×
4,433,200×
3,300,076×
2,393,486×
1,504,658×
747,144×
664,803×
323,206×
222,245×
270,117×
126,193×
60,627×
85,331×
40,971×
8,556×
11,956×
2,777×

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0×
1×
41,391×
22,189,382×
72,216,468×
1,911,633,338×
4,029,307,294×
2,611,222,938×
1,573,800,604×
1,296,472,014×
1,022,527,588×
777,066,272×
476,809,674×
308,894,502×
217,150,272×
176,794,800×
159,214,818×
69,489,906×
31,105,732×
18,226,188×
4,730,332×
2,440,426×
1,740,970×
63,590×
3,392×
768×

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0×
1×
31,453×
26,546,710×
87,973,120×
2,574,291,568×
4,449,223,821×
2,685,083,956×
1,631,117,570×
1,393,428,083×
1,025,800,633×
769,175,020×
494,584,020×
368,222,306×
365,402,766×
351,303,921×
332,878,262×
197,159,485×
137,461,419×
106,368,782×
76,683,123×
59,827,802×
43,231,248×
36,572,277×
28,901,189×
19,105,686×
15,854,248×
13,064,704×
10,475,770×
9,575,498×
9,329,649×
6,822,667×
4,789,740×
3,844,236×
2,994,319×
1,508,298×
1,108,030×
494,610×
381,438×
462,745×
223,683×
128,306×
166,407×
74,207×
27,588×
42,067×
17,956×
1,509×
1,609×

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0×
1×
46,737×
29,581,074×
98,563,972×
2,721,494,188×
5,633,515,970×
3,552,857,622×
2,121,548,160×
1,733,410,258×
1,263,450,602×
937,860,096×
585,809,360×
470,708,462×
365,442,338×
302,025,838×
273,919,946×
109,232,978×
46,968,612×
26,035,422×
7,952,834×
3,404,534×
2,588,870×
168,296×
4,940×
160×

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0×
1×
35,877×
33,922,142×
109,862,176×
3,594,673,260×
6,211,077,737×
3,749,356,971×
2,252,047,920×
1,898,661,807×
1,425,093,565×
1,064,232,907×
646,946,347×
476,347,481×
431,099,884×
427,968,319×
401,755,625×
231,657,859×
155,206,033×
123,591,386×
90,857,548×
66,954,556×
56,147,313×
43,483,837×
35,816,694×
24,970,342×
21,472,192×
20,237,337×
14,523,532×
12,661,852×
12,058,713×
9,586,312×
7,022,546×
6,288,061×
4,198,585×
2,666,528×
1,754,867×
779,859×
625,135×
781,843×
352,689×
239,563×
296,571×
146,203×
68,485×
95,185×
42,115×
9,388×
11,602×
3,065×

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0×
1×
53,265×
38,488,000×
128,333,654×
3,827,441,898×
7,778,766,570×
4,809,010,112×
2,870,194,366×
2,312,737,704×
1,636,266,830×
1,138,989,526×
746,664,678×
541,798,312×
459,344,972×
372,050,572×
356,286,660×
195,200,176×
150,873,420×
121,854,758×
29,673,320×
9,691,030×
8,868,734×
3,744,644×
2,841,628×
1,331,548×
77,594×
540×

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0×
1×
40,946×
43,923,904×
144,097,734×
4,943,621,066×
8,549,184,282×
5,181,270,477×
3,108,288,441×
2,612,877,780×
1,952,168,514×
1,400,020,730×
840,106,003×
584,812,443×
528,685,101×
490,137,136×
455,036,125×
257,845,048×
180,654,596×
138,341,559×
106,605,924×
82,310,939×
63,630,809×
53,635,092×
44,319,360×
34,321,365×
31,815,061×
29,276,453×
19,113,531×
17,532,069×
14,700,994×
12,701,170×
11,528,940×
12,761,494×
8,033,312×
4,151,255×
2,969,396×
1,525,790×
1,320,637×
1,185,029×
554,055×
418,992×
474,267×
231,389×
145,738×
188,825×
92,847×
30,252×
42,859×
16,752×
1,645×
1,753×

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0×
1×
59,055×
48,432,602×
157,346,726×
5,299,186,008×
10,612,622,726×
6,436,494,884×
3,759,726,940×
3,032,683,602×
2,161,790,842×
1,513,510,930×
943,616,286×
610,836,740×
548,291,556×
576,389,014×
556,813,924×
359,427,014×
217,467,020×
95,889,614×
48,025,258×
22,934,540×
9,913,020×
2,525,956×
146,396×
786×

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0×
1×
46,283×
55,617,780×
182,665,137×
6,749,559,532×
11,623,378,420×
6,890,610,802×
4,103,827,043×
3,407,155,506×
2,615,817,350×
1,926,679,981×
1,159,255,098×
852,414,868×
670,044,293×
580,303,596×
548,375,304×
297,224,676×
206,583,866×
163,577,159×
126,877,587×
109,131,871×
84,731,290×
72,490,596×
60,417,419×
43,923,725×
40,916,537×
36,032,060×
24,721,227×
25,820,447×
21,739,790×
15,488,175×
14,983,427×
14,332,303×
9,865,231×
6,215,151×
5,534,984×
3,085,213×
2,805,467×
1,742,180×
854,509×
671,577×
777,495×
394,925×
269,949×
333,109×
156,143×
73,571×
103,267×
49,775×
10,220×
14,292×
3,353×

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0×
1×
66,705×
62,620,478×
209,307,406×
7,251,789,084×
14,330,296,538×
8,600,911,604×
4,936,663,510×
4,030,213,558×
2,852,565,866×
2,001,409,456×
1,155,073,594×
771,103,436×
757,390,696×
714,150,360×
667,319,328×
368,765,454×
211,926,402×
167,836,244×
119,232,174×
36,690,802×
23,185,892×
10,886,884×
463,470×
180,976×
15,202×

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0×
1×
52,034×
69,203,306×
220,466,568×
9,118,654,088×
15,649,186,991×
9,140,256,810×
5,462,924,990×
4,521,656,637×
3,422,122,441×
2,446,866,880×
1,542,734,006×
1,136,282,034×
854,048,288×
708,032,311×
639,501,074×
356,812,503×
236,136,953×
195,500,640×
155,168,831×
132,369,108×
101,425,056×
92,329,325×
89,777,867×
62,038,236×
57,942,002×
49,930,250×
33,461,392×
34,889,344×
29,288,087×
26,378,457×
22,004,825×
15,855,321×
12,458,592×
9,399,621×
9,456,887×
4,724,467×
2,994,233×
3,031,297×
1,569,236×
1,504,312×
1,170,217×
600,851×
470,850×
566,617×
275,983×
154,948×
201,111×
90,729×
32,916×
50,131×
21,556×
1,781×
1,897×

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0×
1×
74,001×
78,715,022×
269,279,770×
9,819,934,818×
19,177,282,216×
11,415,877,292×
6,489,176,994×
5,304,425,032×
3,803,467,106×
2,646,005,420×
1,503,082,194×
971,161,516×
901,518,556×
883,487,516×
817,491,404×
381,320,758×
214,569,082×
174,174,222×
109,272,832×
35,991,842×
25,874,666×
10,722,928×
556,802×
23,164×
37,978×
5,060×
368×

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0×
1×
58,154×
88,274,592×
288,512,626×
12,222,328,344×
20,816,935,405×
12,009,602,241×
7,081,653,310×
5,844,379,003×
4,214,566,901×
2,847,260,887×
1,812,550,303×
1,555,286,813×
1,280,356,300×
1,083,298,255×
1,022,391,327×
516,304,469×
309,788,703×
241,265,274×
192,961,896×
164,214,368×
134,126,463×
128,547,177×
120,037,026×
83,822,598×
77,907,702×
65,983,673×
45,596,308×
41,428,502×
35,671,773×
29,383,910×
26,106,898×
22,327,790×
17,656,038×
13,518,473×
11,166,334×
8,068,994×
4,780,618×
4,384,378×
2,646,495×
2,615,394×
1,896,831×
1,009,525×
788,835×
882,349×
435,939×
289,625×
358,031×
178,741×
81,701×
113,329×
50,499×
11,052×
13,666×
3,641×

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0×
1×
81,873×
97,296,032×
322,266,376×
13,170,559,294×
25,437,639,904×
14,992,435,580×
8,549,383,184×
6,918,071,094×
4,982,257,800×
3,467,329,426×
1,940,922,040×
1,242,614,118×
1,062,851,560×
1,023,337,546×
921,411,486×
418,510,818×
226,453,108×
185,916,308×
96,757,964×
26,728,222×
23,317,388×
6,520,392×
279,172×
20,400×
38,606×
5,060×
368×

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0×
1×
65,492×
110,625,274×
362,660,583×
16,230,330,460×
27,506,083,188×
15,730,643,753×
9,189,895,419×
7,530,026,376×
5,269,973,852×
3,378,346,936×
2,230,290,715×
1,778,919,615×
1,568,578,841×
1,309,951,496×
1,197,928,279×
723,430,578×
628,462,010×
590,191,029×
302,165,416×
234,850,495×
182,842,911×
176,020,752×
163,113,358×
120,284,107×
103,344,391×
87,827,495×
62,642,495×
55,016,519×
52,345,244×
39,313,094×
31,709,040×
28,070,076×
23,668,459×
20,145,776×
16,600,751×
12,010,669×
8,065,758×
7,019,272×
4,850,218×
3,363,774×
2,813,944×
1,675,147×
1,834,874×
1,354,219×
688,039×
506,484×
572,469×
281,645×
173,690×
224,953×
112,341×
35,580×
50,379×
19,776×
1,917×
2,041×

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0×
1×
91,113×
121,986,532×
411,288,018×
17,452,263,236×
33,338,799,932×
19,595,166,726×
11,286,847,350×
9,175,729,306×
6,483,886,738×
4,454,053,948×
2,387,291,296×
1,437,134,946×
1,280,912,718×
1,147,040,370×
1,006,319,094×
420,212,174×
218,534,568×
176,323,244×
75,607,140×
22,121,966×
25,246,216×
6,213,938×
942,056×
123,982×
8,824×
2,082×

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0×
1×
72,092×
135,466,928×
438,613,943×
21,332,516,896×
36,006,955,104×
20,443,448,388×
11,724,413,251×
9,550,740,872×
6,678,689,228×
4,311,503,911×
2,787,401,478×
2,002,697,712×
1,794,994,915×
1,826,214,140×
1,746,702,882×
1,247,695,096×
828,525,318×
507,782,847×
366,864,379×
310,626,407×
229,754,618×
202,192,270×
215,071,285×
148,349,337×
130,017,243×
109,825,210×
85,395,857×
81,788,499×
71,665,760×
52,027,331×
41,193,557×
36,538,601×
27,483,451×
25,373,750×
23,588,011×
17,822,376×
15,605,010×
11,595,781×
7,440,966×
4,845,982×
3,839,611×
2,467,560×
3,192,747×
2,144,601×
1,046,571×
810,561×
935,275×
479,139×
322,219×
396,101×
187,993×
86,515×
121,203×
58,955×
11,884×
16,628×
3,929×

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0×
1×
99,945×
149,601,810×
497,489,738×
22,974,329,034×
43,386,730,262×
25,046,919,164×
14,290,787,808×
11,505,093,282×
8,390,685,356×
5,806,908,384×
3,192,030,840×
2,099,666,124×
1,599,802,564×
1,326,810,964×
1,165,727,310×
475,219,704×
248,805,746×
186,531,876×
71,340,054×
22,936,650×
23,516,342×
5,613,292×
28,534×
1,116×

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0×
1×
80,597×
168,849,276×
555,496,582×
27,848,369,944×
46,721,133,603×
26,277,235,360×
15,078,804,354×
12,308,576,231×
8,463,130,889×
5,563,938,852×
3,411,282,710×
2,513,778,138×
2,377,445,050×
2,153,010,147×
1,972,601,786×
1,277,253,681×
806,767,213×
719,236,068×
657,632,649×
379,923,674×
316,081,586×
287,449,367×
262,236,165×
203,730,396×
175,311,356×
142,504,042×
106,872,950×
101,948,166×
85,020,797×
66,496,347×
60,503,575×
56,389,007×
40,603,046×
33,069,625×
27,096,000×
22,781,992×
16,924,240×
18,550,820×
11,230,495×
8,182,665×
6,501,944×
4,343,415×
4,070,447×
3,023,899×
1,496,795×
1,250,938×
1,401,751×
724,111×
560,102×
673,251×
331,891×
182,866×
235,815×
106,975×
38,244×
58,195×
25,156×
2,053×
2,185×

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0×
1×
109,575×
181,185,524×
595,672,468×
30,014,871,922×
56,024,222,108×
31,973,838,650×
18,196,722,482×
14,733,962,072×
10,644,048,606×
7,115,071,238×
4,039,481,122×
2,720,105,822×
1,992,060,218×
1,651,523,982×
1,353,260,836×
534,656,018×
260,554,498×
208,695,152×
70,736,006×
25,515,668×
24,453,268×
3,863,682×
19,856×
1,676×

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0×
1×
88,784×
206,456,434×
696,845,031×
36,077,584,228×
60,225,811,333×
33,596,179,375×
19,255,781,996×
15,760,381,389×
10,816,012,457×
7,190,730,121×
4,396,471,465×
3,143,231,075×
2,793,204,290×
2,630,511,959×
2,408,014,431×
1,351,141,801×
862,153,919×
768,671,234×
642,566,698×
407,834,966×
367,318,221×
331,215,043×
308,979,332×
268,682,420×
227,446,236×
175,825,849×
140,367,232×
131,992,612×
105,125,283×
85,088,766×
82,328,354×
73,477,814×
51,226,492×
45,109,587×
36,738,098×
27,900,253×
24,525,935×
29,235,425×
18,058,788×
14,011,181×
10,123,398×
7,255,110×
4,960,537×
3,942,294×
2,142,501×
1,841,913×
2,061,505×
1,105,049×
900,063×
1,047,261×
520,017×
340,779×
419,867×
209,627×
94,917×
131,473×
58,883×
12,716×
15,730×
4,217×

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0×
1×
119,913×
222,988,506×
745,874,762×
38,881,030,162×
71,850,267,456×
40,605,614,002×
22,890,760,836×
18,392,921,536×
12,866,460,770×
8,096,031,326×
4,658,877,598×
3,618,273,436×
2,837,683,932×
2,438,837,986×
2,147,107,078×
844,705,904×
377,628,328×
269,140,098×
85,478,014×
35,330,154×
31,092,368×
4,036,878×
34,892×
1,264×

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0×
1×
97,547×
248,829,328×
831,450,493×
46,411,616,932×
77,110,968,116×
42,817,781,983×
24,533,943,127×
19,972,881,302×
13,792,576,566×
9,318,008,412×
5,463,815,993×
3,870,375,923×
3,278,032,405×
2,992,866,132×
2,703,870,339×
1,452,388,264×
935,735,256×
878,238,211×
670,290,772×
444,154,573×
411,744,545×
382,958,762×
353,470,222×
282,861,453×
266,767,431×
229,985,583×
184,490,105×
169,314,687×
151,508,770×
115,116,904×
101,887,470×
91,249,646×
69,008,221×
74,437,500×
57,573,305×
41,527,047×
42,421,717×
35,516,247×
25,800,731×
15,241,539×
14,846,479×
12,202,938×
7,673,831×
6,142,291×
2,931,520×
2,682,906×
2,842,639×
1,598,901×
1,419,174×
1,562,529×
813,367×
593,936×
670,395×
331,325×
201,642×
261,081×
129,711×
40,908×
57,899×
22,800×
2,189×
2,329×

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0×
1×
131,561×
270,765,812×
908,822,984×
50,061,553,312×
91,474,016,756×
51,241,635,616×
28,845,902,048×
23,033,158,050×
15,766,253,630×
9,474,878,520×
5,626,485,590×
3,944,077,968×
3,360,557,826×
2,785,037,938×
2,450,794,320×
1,216,610,252×
1,011,878,346×
1,009,862,036×
286,506,360×
129,664,606×
90,791,994×
36,137,362×
17,017,106×
8,717,756×
825,736×
4,414×

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0×
1×
107,723×
303,010,172×
1,013,908,049×
59,214,011,800×
97,843,238,504×
54,318,443,510×
31,462,719,045×
25,705,180,876×
17,470,288,400×
11,484,904,189×
6,496,899,996×
4,442,245,282×
3,901,528,479×
3,462,120,478×
3,009,710,850×
1,573,428,418×
988,777,878×
926,765,355×
698,789,879×
493,679,453×
494,558,906×
443,174,078×
406,346,165×
322,954,467×
318,355,867×
275,928,454×
233,817,789×
236,143,555×
203,856,294×
151,689,379×
142,203,735×
135,745,763×
91,164,169×
86,963,620×
66,766,929×
52,205,838×
44,881,728×
37,586,008×
30,633,087×
22,653,125×
24,911,228×
16,218,873×
11,843,582×
9,139,008×
4,449,947×
3,779,692×
3,998,409×
2,256,659×
2,090,907×
2,265,925×
1,217,971×
949,689×
1,093,463×
562,429×
372,925×
459,093×
217,647×
99,459×
139,139×
67,695×
13,548×
18,964×
4,505×

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0×
1×
142,471×
323,363,098×
1,086,091,200×
63,898,958,546×
115,764,072,628×
64,232,585,696×
35,812,701,336×
28,400,643,518×
19,359,470,002×
11,681,292,940×
6,831,633,900×
4,488,964,900×
3,894,531,990×
3,878,946,984×
3,470,347,752×
2,274,134,534×
1,452,650,806×
660,508,270×
316,480,578×
203,512,980×
82,330,412×
22,628,096×
774,626×
10,996×
5,938×
818×

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0×
1×
117,527×
363,098,938×
1,217,279,649×
75,141,747,626×
123,594,433,485×
67,692,105,598×
38,950,600,354×
31,380,125,801×
22,023,531,397×
14,500,332,436×
8,605,272,332×
6,113,990,088×
4,725,758,148×
3,976,943,621×
3,509,786,706×
1,710,906,953×
1,089,000,433×
1,054,312,522×
767,378,275×
572,635,896×
574,486,918×
512,864,475×
489,921,653×
398,947,184×
390,172,428×
353,157,126×
289,405,882×
286,380,896×
249,268,901×
189,789,885×
180,018,803×
162,971,077×
110,931,228×
97,325,549×
82,197,260×
67,212,808×
63,835,348×
51,080,108×
39,864,692×
32,487,972×
30,536,405×
24,373,202×
15,098,918×
12,436,840×
7,223,708×
6,812,054×
6,065,706×
3,158,727×
3,001,074×
3,286,943×
1,747,629×
1,467,584×
1,635,395×
850,355×
649,446×
778,201×
383,791×
209,220×
270,519×
123,529×
43,572×
66,259×
28,756×
2,325×
2,473×

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0×
1×
155,625×
393,044,710×
1,340,778,302×
81,153,224,932×
145,343,983,110×
80,017,115,720×
44,494,112,378×
35,297,038,198×
23,734,146,582×
14,704,453,794×
8,212,135,902×
5,596,422,458×
5,084,392,820×
4,504,856,580×
3,914,774,792×
2,288,377,704×
1,185,271,036×
1,031,929,190×
962,327,778×
298,051,380×
185,106,322×
106,402,070×
7,235,426×
782,606×
322,564×

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0×
1×
128,129×
430,587,708×
1,437,552,189×
94,787,624,556×
155,191,244,959×
84,417,461,759×
48,607,494,938×
39,083,056,281×
27,170,140,085×
17,399,153,385×
10,526,227,905×
7,547,751,547×
5,806,942,054×
4,762,693,479×
4,076,047,989×
1,968,979,663×
1,224,803,759×
1,181,747,460×
843,773,262×
637,791,388×
666,515,281×
600,021,315×
605,035,848×
484,902,374×
471,730,142×
454,187,161×
360,132,816×
347,965,592×
293,035,129×
237,387,430×
215,394,836×
194,076,840×
143,081,124×
133,642,427×
117,914,086×
81,603,103×
73,645,617×
65,957,493×
54,941,624×
43,911,034×
38,731,199×
30,942,649×
21,920,838×
19,836,567×
14,065,568×
11,091,790×
7,977,261×
4,341,576×
4,156,965×
4,758,899×
2,510,809×
2,157,757×
2,402,799×
1,290,985×
1,042,567×
1,209,229×
603,299×
390,461×
481,263×
242,437×
108,133×
149,617×
67,267×
14,380×
17,794×
4,793×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
0×
1×
168,937×
470,675,392×
1,629,819,154×
102,344,963,206×
181,606,979,414×
99,297,812,102×
55,244,895,032×
43,760,533,544×
29,416,836,828×
18,481,201,098×
10,244,942,018×
6,906,497,814×
5,808,609,028×
5,347,403,344×
4,605,484,560×
2,384,065,980×
1,271,062,336×
1,067,347,362×
901,579,754×
239,607,222×
207,240,548×
105,014,932×
7,389,948×
227,894×
2,792×