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Pi in Other Bases

Pi is an interesting number connected with the circle. It is usually written in base 10 notation: 3.14159265358979... Many people have wondered about it's universal significance and sought deeper meanings within it's unchanging digits. Some hold the belief that Pi is the "answer to the universe,". Perhaps the deeper meaning of Pi can be better seen in some other base?


Base 2
11.00100100001111

Base 3
10.01021101222201

Base 4
3.02100333122220

Base 5
3.03232214303343

Base 6
3.05033005141512

Base 7
3.06636514320361

Base 8
3.11037552421026

Base 9
3.12418812407442

Base 10
3.14159265358979

Base 11
3.16150702865A48

Base 12
3.184809493B9186

Base 13
3.1AC1049052A2C7

14
3.1DA75CDA813752

Base 15
3.21CD1DC46C2B7A

Base 16
3.243F6A8885A300


Base e
10.10100202000211

Simple Continued Fraction Expansion of Pi: Properties and Meanings

maths.org.uk/issue11/features/cfractions

One of the interesting things about the continued-fraction expansion of (irrational) numbers is that they are, in a sense, base-independent. Instead of endlessly repeating digits of the base in which we are representing the number (digits 0 - 9 in base ten), we get "whole" numbers: 1, 2, 3, etc. - as large as you wish. So we find a relatively large "292" fairly early in the simple continued fraction form of pi. What other large numbers might there be? How common are they?

3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1, 2, 3, 7, 1, 2, 1, 1, 12, 1, 1, 1, 3, 1, 1, 8, 1, 1, 2, 1, 6, 1, 1, 5, 2, 2, 3, 1, 2, 4, 4, 16, 1, 161, 45, 1, 22, 1, 2, 2, 1, 4, 1, 2, 24, 1, 2, 1, 3, 1, 2, 1, 1, 10, 2, 5, 4, 1, 2, 2, 8, 1, 5, 2, 2, 26, 1, 4, 1, 1, 8, 2, 42, 2, 1, 7, 3, 3, 1, 1, 7, 2, 4, 9, 7, 2, 3, 1, 57, 1, 18, 1, 9, 19, 1, 2, 18, 1, 3, 7, 30, 1, 1, 1, 3, 3, 3, 1, 2, 8, 1, 1, 2, 1, 15, 1, 2, 13, 1, 2, 1, 4, 1, 12, 1, 1, 3, 3, 28, 1, 10, 3, 2, 20, 1, 1, 1, 1, 4, 1, 1, 1, 5, 3, 2, 1, 6, 1, 4, 1, 120, 2, 1, 1, 3, 1, 23, 1, 15, 1, 3, 7, 1, 16, 1, 2, 1, 21, 2, 1, 1, 2, 9, 1, 6, 4, 127, 14, 5, 1, 3, 13, 7, 9, 1, 1, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 29, 3, 1, 1, 2, 2, 1, 3, 1, 1, 1, 3, 1, 1, 10, 3, 1, 3, 1, 2, 1, 12, 1, 4, 1, 1, 1, 1, 7, 1, 1, 2, 1, 11, 3, 1, 7, 1, 4, 1, 48, 16, 1, 4, 5, 2, 1, 1, 4, 3, 1, 2, 3, 1, 2, 2, 1, 2, 5, 20, 1, 1, 5, 4, 1, 436, 8, 1, 2, 2, 1, 1, 1, 1, 1, 5, 1, 2, 1, 3, 6, 11, 4, 3, 1, 1, 1, 2, 5, 4, 6, 9, 1, 5, 1, 5, 15, 1, 11, 24, 4, 4, 5, 2, 1, 4, 1, 6, 1, 1, 1, 4, 3, 2, 2, 1, 1, 2, 1, 58, 5, 1, 2, 1, 2, 1, 1, 2, 2, 7, 1, 15, 1, 4, 8, 1, 1, 4, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 9, 1, 4, 3, 15, 1, 2, 1, 13, 1, 1, 1, 3, 24, 1, 2, 4, 10, 5, 12, 3, 3, 21, 1, 2, 1, 34, 1, 1, 1, 4, 15, 1, 4, 44, 1, 4, 20776, 1, 1, 1, 1, 1, 1, 1, 23, 1, 7, 2, 1, 94, 55, 1, 1, 2, 1, 1, 3, 1, 1, 32, 5, 1, 14, 1, 1, 1, 1, 1, 3, 50, 2, 16, 5, 1, 2, 1, 4, 6, 3, 1, 3, 3, 1, 2, 2, 2, 5, 2, 2, 2, 28, 1, 1, 13, 1, 5, 43, 1, 4, 3, 5, 3, 1, 4, 1, 1, 2, 2, 1, 1, 19, 2, 7, 1, 72, 3, 1, 2, 3, 7, 11, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 33, 7, 19, 1, 19, 3, 1, 4, 1, 1, 1, 1, 2, 3, 1, 3, 2, 2, 2, 2, 4, 1, 1, 1, 4, 2, 3, 1, 1, 1, 1, 11, 1, 1, 2, 1, 2, 1, 2, 2, 1, 7, 2, 27, 1, 1, 6, 2, 1, 9, 6, 26, 1, 1, 3, 2, 1, 1, 1, 1, 1, 15, 1, 36, 4, 2, 2, 1, 22, 2, 1, 106, 2, 2, 1, 3, 1, 12, 10, 7, 1, 2, 1, 1, 1, 1, 8, 2, 4, 5, 3, 2, 1, 4, 23, 1, 18, 2, 10, 3, 1, 6, 6, 13, 8, 6, 2, 2, 2, 2, 1, 1, 1, 3, 1, 7, 17, 1, 1, 1, 2, 5, 5, 1, 1, 2, 11, 1, 6, 1, 6, 1, 29, 4, 29, 3, 5, 3, 1, 141, 1, 2, 7, 7, 2, 2, 7, 1, 1, 7, 1, 7, 1, 2, 4, 1, 1, 1, 30, 1, 12, 4, 18, 10, 2, 8, 1, 2, 2, 2, 4, 13, 1, 5, 4, 1, 6, 1, 1, 11, 2, 4, 2, 1, 1, 3, 3, 12, 1, 1, 39, 5, 1, 1, 16, 125, 1, 4, 1, 2, 1, 19, 1, 4, 1, 1, 2, 1, 4, 1, 10, 1, 4, 2, 1, 1, 1, 5, 10, 4, 14, 1, 13, 41, 1, 4, 1, 8, 1, 1, 2, 1, 3, 1, 6, 1, 3, 2, 2, 2, 1, 4, 1, 14, 1, 2, 8, 1, 8, 3, 3, 3, 1, 37, 4, 2, 4, 1, 3, 4, 25, 4, 27, 2, 7, 1, 1, 2, 6, 1, 1, 1, 12, 1, 2, 2, 2, 13, 12, 1, 3, 1, 6, 1, 1, 33, 1, 5, 3, 1, 5, 15, 8, 8, 47, 1, 3, 2, 12, 2, 12, 1, 12, 1, 2, 5, 3, 1, 1, 1, 1, 2, 3, 5, 4, 2, 1, 1, 5, 1, 9, 14, 1, 1, 3, 2, 1, 9, 3, 22, 13, 1, 1, 3, 20, 1, 1, 61, 1, 376, 2, 107, 1, 10, 3, 2, 2, 31, 1, 2, 10, 2, 2, 62, 2, 2, 7, 4, 5, 6, 1, 1, 1, 1, 2, 8, 2, 73, 3, 5, 42, 1, 3, 2, 1, 1, 59, 6, 1, 1, 1, 5, 1, 6, 1, 2, 6, 1, 1, 1, 1, 3, 2, 1, 3, 1, 8, 1, 4, 2, 5, 4, 7, 1, 4, 2, 2, 6, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 5, 1, 2, 1, 1, 10, 1, 6, 1, 129, 1, 4, 65, 2, 4, 4, 3, 2, 3, 1, 1, 5, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 4, 2, 1, 2, 27, 6, 2, 1, 193, 1, 3, 9, 1, 3, 35, 2, 1, 8, 1, 1, 1, 1, 9, 3, 56, 1, 6, 6, 2, 8, 1, 8, 1, 2, 3, 6, 3, 1, 3, 1, 1, 1, 2, 13, 1, 1, 1, 1, 13, 2, 1, 3, 1, 3, 15, 2, 1, 1, 2, 4, 1, 4, 5, 2, 2, 1, 2, 1, 6, 1, 4, 12, 1, 1, 1, 1, 13, 1, 3, 4, 1, 1, 1, 2, 9, 1, 7, 1, 1, 1, 1, 4, 1, 3, 4, 1, 1, 4, 3, 1, 39, 2, 1, 1, 1, 1, 1, 4, 7, 2, 2, 2, 1, 1, 1, 1, 2, 114, 12, 4, 1, 3, 2, 1, 19, 1, 1, 2, 1, 1, 3, 4, 1, 60, 3, 72, 2, 1, 1, 1, 50, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 4, 1, 7, 3, 1, 2, 1, 5, 1, 1, 1, 2, 6, 2, 21, 2, 6, 1, 6, 1, 1, 2, 1, 7, 1, 8, 1, 1, 5, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 11, 2, 4, 10, 2, 1, 1, 13, 1, 1, 7, 15, 1, 1, 1, 2, 3, 15, 8, 8, 2, 1, 13, 3, 5, 1, 2, 1, 6, 1, 10, 123, 3, 1, 4, 59, 4, 156, 88, 1, 5, 4, 1, 3, 1, 4, 2, 9, 1, 7, 4, 2, 1, 2, 3, 2, 1, 2, 11, 1, 13, 7, 7, 1, 63, 37, 12, 86, 1, 1, 1, 1, 2, 2, 4, 2, 18, 1, 1, 1, 41, 2, 1, 1, 12, 1, 2, 1, 1, 2, 10, 1, 1, 1, 5, 1, 1, 3, 1, 7, 5, 1, 9, 1, 2, 2, 7, 1, 1, 5, 2, 1, 3, 3, 5, 2, 1, 11, 3, 1, 3, 2, 1, 1, 2, 1, 14, 5, 2, 2, 1, 1, 1, 1, 3, 1, 3, 3, 2, 2, 1, 3, 2, 1, 2, 1, 4, 1, 14, 1, 1, 58, 7, 1, 2, 1, 1, 5, 1, 2, 1, 5, 18, 1, 4, 3, 1, 1, 1, 4, 1, 1, 2, 5, 1, 148, 1, 9, 2, 1, 2, 1, 5, 4, 93, 1, 1, 2, 4, 1, 2, 73, 1, 1, 3, 1, 1, 1, 1, 2, 1, 34, 1, 5, 6, 1, 2, 1, 3, 4, 1, 16, 28, 17, 2, 5, 5, 26, 1, 1, 4, 12, 1, 3, 2, 1, 5, 1, 2, 9, 3, 2, 41, 1, 16, 2, 2, 20, 1, 17, 1, 6, 16, 3, 3, 2, 2, 2, 18, 15, 1, 1, 51, 4, 9, 5, 2, 2, 1, 2, 1, 45, 3, 1, 1, 3, 1, 2, 1, 3, 1, 1, 3, 5, 1, 2, 3, 8, 2, 47, 2, 3, 1, 1, 1, 15, 9, 1, 8, 2, 1, 4, 2, 4, 14, 1, 12, 2, 1, 161, 1, 26, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 18, 528, 12, 4, 1, 5, 16, 3, 1, 1, 1, 1, 1, 5, 1, 2, 1, 63, 1, 97, 1, 4, 4, 10, 5, 9, 5, 2, 3, 2, 5, 7, 1, 32, 13, 1, 5, 4, 1, 7, 1, 3, 12, 1, 3, 9, 1, 7, 1, 102, 53, 1, 1, 1, 3, 4, 2, 15, 2, 8, 2, 2, 3, 1, 2, 4, 1, 1, 3, 2, 3, 1, 1, 2, 3, 1, 1, 6, 1, 1, 14, 1, 80, 11, 1, 1, 1, 1, 22, 1, 2, 3, 1, 3, 26, 2, 24, 2, 2, 4, 3, 1, 1, 1, 1, 3, 1, 63, 1, 1, 1, 25, 1, 1, 1, 8, 1, 3, 3, 1, 10, 5, 6, 2, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 2, 8, 12, 1, 53, 1, 2, 1, 1, 5, 1, 1, 3, 1, 39, 1, 12, 1, 3, 14, 18, 9, 3, 2, 2, 2, 1, 1, 3, 1, 4, 4, 7, 1, 17, 1, 14, 1, 1, 1, 1, 3, 1, 1, 10, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 12, 1, 3, 44, 2, 10, 1, 14, 1, 2, 1, 43, 4, 1, 7, 3, 4, 1, 1, 2, 2, 1, 34, 1, 2, 5, 8, 3, 2, 1, 2, 13, 4, 3, 2, 1, 1, 1, 1, 25, 1, 5, 1, 94, 2, 4, 3, 4, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 41, 1, 5, 1, 4, 4, 1, 155, 1, 8, 1, 1, 1, 1, 4, 1, 1, 2, 9, 2, 1, 2, 1, 1, 1, 6, 23, 1, 2, 3, 5, 2, 1, 1, 1, 1, 7, 67, 5, 7, 1, 23, 3, 3, 1, 6, 1, 11, 1, 57, 1, 4, 1, 5, 1, 1, 8, 1, 1, 2, 5, 2, 10, 1, 1, 2, 1, 1, 3, 1, 2, 1, 3, 1, 11, 2, 10, 1, 4, 18, 1, 2, 3, 1, 1, 6, 3, 6, 4, 31, 3, 4, 1, 18, 3, 9, 7, 5, 1, 2, 2, 1, 7, 1, 23, 2, 217, 1, 2, 1, 4, 1, 54, 2, 196, 10, 3, 1, 32, 1, 40, 55, 1, 5, 1, 3, 3, 1, 2, 2, 1, 3, 6, 3, 16, 1, 31, 1, 5, 6, 1, 4, 42, 4, 1, 10, 1, 3, 1, 3, 3, 1, 2, 1, 1, 1, 4, 1, 13, 1, 88, 1, 1, 1, 14, 3, 27, 3, 1, 1, 16, 4, 1, 2, 4, 1, 4, 1, 1, 17, 2, 4, 1, 1, 9, 2, 1, 1, 3, 1, 1, 30, 1, 1, 3, 2, 2, 1, 1, 4, 10, 1, 7, 1, 6, 1, 35, 1, 1, 2, 3, 6, 1, 1, 2, 4, 4, 24, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 2, 1, 6, 6, 2, 1, 1, 10, 6, 4, 2, 1, 3, 9, 1, 2, 16, 1, 5, 1, 1, 1, 1, 6, 5, 1, 13, 5, 4, 1, 2, 3, 1, 1, 1, 3, 1, 30, 2, 5, 1, 1, 1, 1, 2, 3, 1, 2, 3, 1, 1, 1, 1, 1, 6, 5, 3, 65, 48, 3, 3, 6, 1, 9, 2, 1, 5, 6, 2, 1, 1, 1, 1, 620, 8, 1, 1, 4, 8, 1, 6, 1, 5, 8, 1, 5, 1, 4, 9, 47, 3, 1, 6, 1, 25, 1, 3, 425, 2, 3, 3, 17, 1, 2, 3, 2, 3, 1, 1, 1, 5, 2, 1, 41, 1, 1, 1, 1, 3, 1, 5, 1, 1, 6, 256, 17, 1, 14, 1, 2, 3, 1, 2, 2, 2, 4, 9, 7, 3, 3, 18, 1, 33, 1, 5, 2, 4, 25, 1, 2, 1, 6, 1, 3, 4, 16, 4, 2, 2, 7, 3, 1, 14, 2, 1, 2, 1, 3, 3, 1, 4, 1, 59, 1, 121, 9, 1, 2, 1, 11, 1, 20, 1, 9, 2, 1, 3, 391, 1, 2, 8, 3, 4, 1, 1, 3, 13, 1, 95, 2, 2, 4, 21, 1, 21, 2, 8, 13, 3, 1, 1, 1, 5, 1, 8, 1, 15, 1, 252, 3, 4, 2, 15, 1, 1, 1, 5, 2, 6, 11, 1, 10, 41, 1, 4, 2, 2, 1, 1, 1, 5, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 24, 8, 21, 3, 3, 9, 14, 9, 1, 9, 3, 1, 2, 3, 2, 2, 2, 9, 1, 5, 3, 7, 1, 2, 1, 6, 1, 1, 3, 6, 1, 1, 1, 1, 1, 1, 1, 15, 2, 4, 1, 1, 7, 1, 2, 1, 1, 15, 2, 1, 5, 1, 1, 13, 1, 2, 1, 1, 1, 5, 2, 21, 1, 1, 1, 1, 13, 1, 1, 10, 1, 6, 2, 11, 1, 2, 7, 1, 7, 1, 16, 1, 4, 3, 1, 2, 1, 7, 1, 3, 1, 4, 9, 2, 1, 1, 1, 1, 23, 1, 1, 4, 1, 4, 3, 1, 2, 2, 2, 1, 3, 1, 1, 5, 1, 1, 1, 6, 106, 1, 1, 1, 7, 2, 18, 1, 1, 1, 4, 1, 2, 4, 20, 2, 1, 3, 1, 5, 1, 3, 1, 50, 1, 2, 14, 2, 1, 1, 2, 1, 2, 2, 1, 1, 3, 3, 1, 1, 4, 1, 1, 1, 13, 8, 3, 2, 1, 8, 5, 1, 6, 1, 50, 1, 2, 3, 8, 1, 3, 5, 2, 1, 8, 8, 1, 1, 10, 2, 1, 1, 1, 2, 13, 1, 4, 10, 1, 1, 1, 1, 26, 2, 22, 3, 7, 6, 1, 2, 3, 28, 3, 17, 3, 1, 1, 1, 4, 1, 5, 2, 4, 5, 1, 2, 1, 1, 1, 4, 1, 2, 5, 1, 1, 1, 4, 1, 2, 5, 2, 193, 2, 1, 47, 1, 4, 1, 6, 1, 4, 1, 6, 23, 4, 1, 20, 2, 3, 32, 1, 6, 1, 4, 1, 3, 1, 10, 1, 3, 1, 1, 2, 5, 2, 1, 1, 1, 93, 1, 1, 11, 8, 1, 1, 1, 1, 2, 15, 4, 1, 7, 1, 3, 2, 1, 1, 1, 9, 10, 1, 6, 1, 4, 5, 3, 1, 11, 1, 6, 5, 1, 1, 1, 1, 3, 1, 152, 3, 1, 4, 3, 7, 1, 473, 1, 1, 1, 3, 108, 2, 1, 3, 3, 3, 6, 1, 1, 1, 18, 1, 51, 2, 2, 5, 2, 2, 1, 1, 15, 6, 10, 1, 6, 1, 1, 6, 8, 2, 33, 1, 6, 2, 5, 3, 1, 13, 1, 2, 1, 2, 3, 2, 1, 5, 1, 2, 1, 2, 1, 10, 4, 2, 1, 2, 6, 23, 4, 1, 3, 1, 5, 1, 3, 5, 3, 1, 3, 2, 5, 8, 1, 4, 5, 1, 1, 18, 6, 1, 1, 43, 1, 8, 1, 22, 1, 9, 5, 1, 2, 1, 15, 16, 1, 1, 5, 4, 3, 7, 1, 1, 1, 4, 1, 1, 3, 3, 1, 2, 16, 2, 7, 1, 17, 3, 28, 5, 15, 5, 1, 8, 3, 1, 141, 1, 9, 7, 2, 5, 1, 1, 7, 5, 30, 1, 6, 2, 2, 6, 1, 4, 3, 3, 10, 22, 14, 1, 2, 3, 21, 4, 1, 1, 1, 12, 1, 9, 4, 2, 1, 7, 1, 1, 1, 10, 1, 3, 1, 1, 1, 1, 1, 1, 6, 1, 10, 1, 7, 8, 2, 1, 1, 1, 5, 8, 5, 9, 37, 4, 1, 17, 1, 2, 1, 3, 1, 5, 2, 1, 4, 15, 2, 2, 5, 1, 1, 1, 6, 1, 1, 20, 48, 1, 5, 17, 2, 7, 7, 1, 16, 1, 37, 3, 2, 1, 2, 5, 1, 1, 1, 4, 3, 2, 3, 16, 1, 2, 18, 2, 1, 1, 1, 1, 1, 4, 1, 3, 5, 1, 2, 23, 2, 3, 1, 4, 13, 7, 1, 5, 1, 2, 1, 1, 30, 1, 7, 4, 1, 1, 1, 15, 1, 17, 1, 4, 1, 1, 1, 2, 188, 1, 5, 2, 2, 19, 2, 1, 2, 1, 70, 1, 2, 1, 2, 3, 1, 4, 1, 1, 1, 4, 1, 3, 1, 1, 2, 1, 1, 5, 5, 2, 1, 2, 7, 2, 2, 1, 1, 2, 2, 1, 31, 8, 1, 1, 3, 1, 1, 1, 1, 3, 15, 2, 1, 3, 1, 1, 3, 24, 4, 1, 1, 7, 2, 12, 4, 2, 2, 1, 15, 1, 1, 1, 1, 2, 1, 9, 1, 2, 2, 3, 1, 2, 9, 1, 1, 3, 1, 1, 7, 1, 12, 1, 3, 1, 2, 1, 3, 6, 6, 1, 1, 1, 1, 10, 2, 10, 1, 2, 2, 2, 5, 12, 1, 2, 3, 4, 10, 1, 1, 3, 2, 4, 1, 37, 1, 4, 2, 1, 1, 67, 1, 1, 6, 2, 1, 2, 2, 3, 1, 2, 2, 1, 5, 2, 2, 1, 1, 6, 2, 1, 1, 47, 57, 1, 1, 1, 1, 2, 2, 7, 5, 2, 2, 2, 3, 7, 1, 4, 1, 1, 6, 1, 4, 1, 3, 1, 1, 1, 4, 16, 49, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 38, 2, 3, 2, 3, 25, 6, 1, 1, 12, 3, 5, 3, 4, 7, 1, 1, 2, 7, 1, 9, 1, 5, 2, 1, 1, 1, 33, 2, 6, 3, 1, 10, 1, 1, 2, 43, 2, 1, 1, 2, 3, 1, 4, 310, 2, 7, 2, 53, 211, 2, 2, 2, 1, 1, 3, 7, 1, 1, 8, 2, 3, 2, 2, 1, 2, 1, 2, 1, 9, 3, 11, 1, 2, 1, 2, 4, 1, 1, 1, 1, 5, 2, 2, 1, 17, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 4, 3, 3, 11, 23, 2, 1, 5, 12, 21, 2, 1, 2, 3, 6, 5, 1, 1, 1, 1, 1, 210, 15, 1, 1, 16, 3, 1, 2, 4, 1, 2, 20, 3, 3, 3, 3, 3, 1, 23, 29, 1, 23, 24, 1, 2, 3, 1, 2, 7, 1, 5, 80, 1, 2, 4, 2, 2, 32, 2, 4, 16, 3, 46, 2, 5, 1, 113, 4, 1, 6, 1, 1, 2, 1, 1, 1, 16, 1, 2, 1, 5, 4, 7, 1, 1, 5, 1, 31, 1, 2, 1, 3, 1, 14, 3, 1, 2, 5, 1, 1, 17, 3, 2, 3, 1, 2, 10, 2, 2, 1, 1, 325, 1, 85, 3, 1, 4, 55, 3, 1, 3, 14, 1, 5, 1, 6, 4, 6, 30, 3, 1, 11, 1, 1, 1, 1, 1722, 1, 87, 24, 5, 1, 1, 16, 1, 15, 23, 8, 3, 3, 15, 1, 1, 292, 2, 6, 2, 1, 98, 3, 1, 2, 4, 1, 5, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 8, 1, 2, 33, 3, 3, 2, 3, 9, 6, 4, 4, 5, 7, 1, 13, 7, 1, 2, 2, 21, 4, 1, 8, 3, 19, 7, 1, 1, 50, 1, 3, 1, 1, 17, 1, 4, 5, 2, 3, 1, 2, 2, 1, 18, 4, 38, 1, 33, 4, 2, 1, 57, 1, 1, 6, 1, 1, 4, 1, 2, 104, 3, 5, 8, 1, 1, 7, 1, 4, 1, 52, 1, 5, 1, 5, 1, 4, 84, 1, 2, 8, 8, 2, 1, 1, 1, 1, 2, 1, 111, 1, 12, 1, 1, 18, 4, 2, 3, 1, 9, 2, 1, 40, 1, 1, 1, 1, 2, 1, 1, 1, 9, 1, 5, 1, 3, 2, 2, 2, 1, 1, 204, 36, 1, 1, 4, 118, 1, 8, 3, 2, 1, 12, 1, 1, 1, 2, 1, 31, 1, 4, 5, 1, 11, 2, 55, 1, 17, 1, 1, 1, 6, 6, 1, 4, 5, 8, 1, 5, 1, 14, 1, 1, 3, 2, 5, 1, 1, 1, 3, 1, 1, 2, 1, 2, 5, 1, 1, 5, 20, 11, 1, 1, 2, 1, 1, 2, 1, 3, 4, 46, 2, 4, 1, 1, 1, 10, 2, 1, 5, 1, 2, 4, 22, 2, 7, 1, 1, 1, 10, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 10, 11, 7, 3, 1, 1, 1, 7, 1, 1, 8, 1, 8, 1, 2, 2, 3, 6, 2, 36, 1, 2, 1, 4, 3, 1, 1, 1, 1, 1, 4, 2, 3, 1, 7, 3, 4, 4, 1, 1, 1, 2, 54, 16, 1, 7, 19, 2, 4, 1, 1, 1, 2, 7, 1, 1, 5, 3, 4, 1, 4, 18, 1, 1, 1, 1, 1, 8, 3, 1, 8, 1, 2, 1, 1, 4, 1, 1, 1, 2, 3, 7, 6, 1, 1, 8, 2, 3, 2, 13, 1, 1, 1, 1, 7, 1, 3, 1, 10, 2, 1, 3, 2, 5, 1, 1, 1, 2, 142, 2, 1, 1, 1, 3, 7, 1, 16, 4, 1, 84, 1, 14, 1, 39, 1, 1, 33, 1, 1, 1, 1, 5, 1, 2, 2, 6, 1, 1, 5, 1, 1, 1, 4, 2, 2, 1, 4, 5, 1, 2, 1, 3, 1, 1, 1, 10, 3, 2, 1, 9, 2, 10, 1, 6, 1, 1, 1, 1, 2, 2, 14, 3, 1, 5, 2, 4, 1, 3, 29, 2, 2, 2, 4, 1, 18, 1, 4, 1, 1, 2, 3, 3, 4, 1, 3, 2, 1, 1, 1, 2, 4, 1, 1, 1, 1, 46, 1, 1, 3, 4, 3, 212, 3, 1, 2, 1, 1, 4, 8, 1, 74, 1, 2, 1, 5, 1, 1, 9, 1, 1, 1, 1, 3, 80, 2, 1, 3, 1, 1, 2, 2, 4, 4, 1, 2159, 5, 8, 4, 1, 1, 4, 2, 2, 5, 1, 5, 2, 2, 2, 44, 1, 1, 1, 23, 2, 1, 6, 1, 1, 1, 13, 46, 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6, 1, 1, 1, 3, 2, 1, 1, 2, 3, 19, 11, 20, 5, 22, 1, 1, 2, 1, 6, 1, 1, 9, 1, 1, 1, 1, 1, 4, 1, 25, 2, 3, 1, 1, 2, 62, 1, 1, 3, 1, 6, 32, 1, 3, 1, 2, 1, 4, 2, 1, 1, 1, 14, 2, 1, 1, 7, 44, 1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 8, 1, 4, 44, 1, 4, 1, 2, 15, 1, 2, 164, 2, 4, 1, 5, 1, 2, 1, 1, 1, 11, 5, 1, 1, 1, 3, 1, 2, 3, 1, 10, 3, 1, 5, 3, 4, 1, 32, 1, 62, 11, 1, 5, 1, 5, 2, 12, 5, 44, 4, 1, 6, 1, 7, 1, 5, 3, 12, 6, 5, 2, 1, 1, 3, 1, 2, 1, 1, 10, 2, 2, 1, 7, 18, 13, 4, 24, 2, 1, 5, 56, 3, 3, 1, 4, 1, 1, 15, 3, 42, 1, 4, 4, 4, 2, 6, 65, 1, 1, 1, 5, 1, 12, 2, 4, 1, 3, 1, 2, 17, 2, 1, 5, 28, 2, 24, 5, 12, 2, 2, 3, 1, 2, 1, 1, 1, 23, 3, 4, 1, 1, 24, 6, 2, 1, 1, 4, 1, 2, 1, 1, 2, 3, 1, 3, 1, 2, 1, 1, 2, 1, 3, 12, 8, 2, 15, 1, 11, 2, 3, 1, 2, 1, 1, 1, 14, 1, 15, 1, 1, 13, 3, 1, 2, 12, 1, 2, 4, 1, 6, 1, 3, 2, 8, 5, 2, 3, 2, 2, 1, 2, 7, 1, 1, 4, 1, 2, 8, 1, 2, 16, 1, 3, 5, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 23, 16, 1, 5, 1, 7, 2, 1, 3, 2, 1, 1, 80, 6, 4, 5, 10, 1, 7, 1, 5, 2, 5, 1, 3, 2, 31, 2, 3, 1, 4, 2, 2, 2, 5, 2, 1, 4, 1, 1, 1, 1, 30, 3, 16, 2, 4, 1, 25, 1, 3, 1, 1, 95, 1, 3, 1, 7, 1, 1, 11, 1, 1, 1, 7, 1, 3, 5, 1, 1, 1, 1, 1, 1, 3, 1, 39, 1, 2, 2, 1, 1, 7, 5, 1, 1, 1, 2, 4, 1, 1, 3, 1, 16, 4, 1, 6, 7, 3, 1, 1, 231, 3, 29, 9, 1, 3, 3, 3, 1, 2, 2, 1, 1, 1, 1, 2, 9, 1, 4, 1, 5, 2, 10, 9, 7, 1, 1, 1, 5, 30, 2, 39, 1, 2, 2, 1, 9, 1, 1, 1, 1, 1, 2, 4, 1, 5, 3, 1, 30, 3, 3, 7, 181, 10, 1, 1, 14, 5, 2, 1, 2, 20, 27, 1, 5, 1, 4, 3, 1, 2, 10, 3, 1, 6, 1, 18, 1, 1, 1, 4, 70, 7, 2, 1, 10, 1, 58, 13, 1, 1, 5, 3, 1, 31, 4, 1, 3, 3, 2, 5, 1, 2, 22, 2, 7, 1, 4, 1, 1, 2, 4, 2, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 18, 10, 3, 8, 217, 1, 1, 1, 6, 4, 2, 4, 8, 1, 1, 2, 2, 2, 9, 17, 1, 10, 2, 8, 1, 3, 1, 3, 7, 1, 2, 1, 3, 1, 1, 2, 5, 10, 9, 2, 1, 5, 3, 3, 2, 3, 1, 1, 3, 1, 1, 9, 1, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 6, 6, 1, 1, 5, 2, 11, 16, 1, 3, 1, 1, 1, 5, 1, 133, 1, 1, 6, 1, 3, 4, 4, 58, 1, 2, 1, 1, 4, 14, 1, 6, 1, 1, 1, 11, 1, 1, 5, 1, 1, 2, 2, 75, 2, 50, 1, 5, 2, 6, 1, 1, 1, 1, 1, 17, 3, 4, 4, 2, 3, 2, 3, 1, 7, 7, 1, 6, 1, 10, 1, 2, 3, 5, 4, 1, 1, 3, 2, 8, 1, 2, 1, 7, 1, 6, 1, 2, 3, 5, 2, 16, 3, 3, 49, 1, 6, 1, 1, 6, 17, 5, 1, 16, 2, 11, 2, 2, 1, 1, 4, 2, 3, 10, 2, 4, 2, 2, 3, 7, 1, 27, 2, 2, 1, 6, 1, 11, 3, 1, 4, 2, 2, 2, 2, 1, 3, 1, 12, 2, 9, 31, 1, 17, 6, 2, 1, 1, 1, 2, 1, 1, 10, 5, 3, 2, 2, 3, 107, 1, 10, 9, 1, 21, 108, 2, 2, 1, 34, 3, 9, 2, 2, 11, 2, 1, 1, 3, 11, 1, 3, 35, 1, 13, 5, 7, 6, 1, 1, 3, 4, 3, 2, 10, 1, 3, 3, 1, 10, 1, 1, 1, 3, 9, 2, 3, 1, 2, 1, 2, 3, 2, 2, 4, 1, 1, 22, 1, 3, 10, 1, 1, 2, 1, 184, 32, 4, 1, 1, 3, 19, 4, 13, 6, 1, 1, 1, 91, 1, 12, 1, 1, 5, 1, 1, 3, 1, 12, 5, 1, 12, 2, 2, 1, 52, 1, 8, 1, 1, 3, 3, 2, 22, 5, 7, 2, 2, 1, 1, 1, 5, 1, 5, 1, 2, 1, 2, 1, 16, 4, 30, 2, 1, 13, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 3, 2, 1, 1, 2, 7, 6, 1, 1, 3, 1, 8, 1, 17, 1, 94, 4, 1, 1, 2, 11, 1, 4, 1, 2, 1, 69, 1, 4, 13, 2, 4, 1, 1, 1, 6, 4, 4, 1, 7, 4, 9, 1, 1, 5, 1, 1, 9, 16, 1, 2, 1, 1, 2, 1, 1, 16, 16, 1, 2, 2, 7, 14, 1, 2, 3, 13, 6, 2, 2, 6, 2, 6, 1, 1, 35, 1, 3, 10, 1, 1, 1, 1, 1, 544, 1, 6, 46, 1, 5, 67, 1, 4, 9, 1, 2, 1, 2, 6, 3, 12, 4, 3, 1, 5, 2, 5, 1, 2, 1, 75, 22, 1, 1, 21, 1, 5, 9, 1, 1, 2, 3, 6, 14, 1, 2, 3, 3, 2, 2, 756, 26, 1, 3, 2, 1, 4, 1, 1, 265, 4, 2, 2, 37, 6, 1, 1, 13, 5, 2, 1, 6, 2, 1, 6, 6, 46, 15, 1, 1, 1, 1, 2, 1, 2, 2, 1, 5, 2, 21, 4, 1, 8, 4, 2, 6, 3, 1, 4, 7, 2, 1, 7, 3, 7, 4, 2, 2, 2, 6, 2, 1, 1, 1, 5, 5, 1, 94, 1, 2, 2, 3, 11, 1, 1, 7, 1, 16, 2, 1, 4, 1, 1, 1, 5, 1, 1, 2, 1, 6, 1, 7, 1, 2, 2, 1, 16, 1, 10, 7, 2, 3, 1, 2, 3, 1, 5, 6, 11, 2, 40, 7, 1, 1, 29, 3, 2, 534, 6, 1, 3, 2, 2, 1, 2, 2, 1, 9, 1, 3, 3, 6, 1, 1, 6, 4, 55, 45, 3, 1, 8, 2, 3, 17, 1, 5, 1, 88, 2, 1, 1, 1, 1, 2, 2, 1, 13, 1, 3, 5, 2, 2, 2, 21, 1, 1, 11, 9, 2, 2, 26, 1, 1, 1, 1, 76, 2, 2, 1, 1, 3, 1, 7, 109, 3, 1, 3, 5, 1, 1, 2, 3, 1, 1, 7, 1, 1, 6, 8, 3, 2, 2, 1, 1, 3, 1, 2, 55, 1, 14, 3, 1, 2, 1, 3, 1, 3, 3, 7, 1, 1, 8, 1, 2, 7, 1, 1, 12, 1, 1, 16, 1, 1, 1, 3, 24, 4, 2, 4, 2, 2, 1, 7, 1, 2, 22, 8, 1, 6, 182, 1, 1, 4, 5, 12, 4, 1, 2, 5, 1, 7, 2, 29, 3, 13, 8, 1, 6, 14, 1, 1, 4, 4, 59, 1, 27, 4, 4, 2, 7, 2, 3, 1, 1, 4, 3, 2, 8, 4, 3, 4, 3, 1, 1, 3, 1, 3, 1, 1, 7, 1, 31, 11, 1, 1, 8, 1, 1, 8, 2, 1, 1, 1, 2, 1, 7, 1, 4, 28, 1, 8, 1, 7, 1, 4, 2, 1, 2, 1, 3, 1, 8, 1, 6, 2, 632, 1, 1, 1, 5, 10, 1, 6, 5, 1, 5, 1, 1, 1, 1, 1, 1, 1, 97, 2, 2, 1, 3, 1, 3, 1, 1, 72, 58, 1, 2, 1, 1, 1, 21, 19, 1, 8, 3, 1, 1, 1, 2, 41, 1, 22, 4, 1, 1, 1, 1, 6, 8, 1, 1, 18, 1, 33, 2, 537, 3, 1, 2, 4, 10, 2, 53, 2, 4, 1, 6, 1, 3, 13, 1, 1, 50, 2, 1, 1, 2, 3, 1, 3, 6, 1, 29, 1, 2, 1, 1, 5, 1, 6, 2, 2, 1, 2, 3, 1, 11, 2, 1, 4, 12, 1, 1, 1, 1, 4, 1, 1, 2, 3, 2, 3, 2, 1, 4, 1, 17, 1, 3, 2, 2, 1, 1, 1, 2, 2, 2, 1, 7, 6, 1, 4, 1, 1, 2, 1, 2, 1, 4, 1, 4, 4, 1, 1, 1, 3, 2, 8, 5, 134, 11, 2, 1, 12, 3, 2, 4, 1, 13, 2, 2, 2, 25, 25, 4, 1, 2, 14, 1, 1, 1, 9, 1, 1, 3, 1, 4, 2, 1, 1, 1, 1, 1, 2, 6, 1, 69, 100, 1, 5, 4, 2, 1, 54, 1, 15, 12, 16, 3, 1, 1, 7, 1, 1, 2, 4, 1, 2, 1, 1, 11, 1, 6, 2, 9, 1, 2, 3, 6, 1, 1, 4, 1, 2, 1, 62, 1, 6, 4, 1, 24, 8, 3, 2, 10, 26, 1, 8, 1, 1, 12, 1, 6, 3, 1, 2, 2, 19, 2, 1, 2, 1, 4, 11, 5, 1, 1, 2, 1, 8, 24, 2, 14, 5, 14, 14, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 4, 1, 6, 3, 1, 8, 1, 1, 2, 1, 1, 4, 2, 1, 3, 5, 2, 1, 5, 3, 5, 2, 138, 1, 9, 2, 1, 2, 1, 9, 1, 2, 1, 1, 1, 4, 1, 1, 2, 4, 27, 2, 1, 7, 2, 1, 9, 1, 1, 1, 1, 2, 2, 1, 2, 3, 1, 3, 2, 1, 4, 5, 1, 3, 1, 5, 2, 1, 1, 1, 6, 1, 4, 2, 1, 1, 5, 1, 1, 1, 5, 1, 3, 5, 1, 2, 3, 3, 1, 1, 3, 1, 1, 7, 2, 1, 1, 5, 2, 3, 5, 1, 2, 1, 7, 2, 1, 2, 1, 1, 5, 1, 5, 1, 3, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 14, 3, 2, 5, 3, 1, 3, 1, 3, 7, 2, 11, 10, 1, 1, 1, 1, 6, 4, 4, 1, 17, 10, 1, 1, 2, 7, 2, 1, 1, 1, 3, 2, 1, 2, 4, 1, 4, 55, 1, 5, 1, 1, 3, 1, 5, 2, 8, 1, 2, 2, 1, 11, 1, 3, 2, 1, 4, 8, 3, 2, 1, 1, 1, 2, 3, 1, 15, 2, 4, 7, 1, 16, 2, 1, 7, 1, 6, 1, 3, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 42, 2, 1, 13, 1, 1, 1, 626, 5, 2, 2, 7, 2, 4, 1, 102, 2, 12, 1, 1, 2, 1, 1, 2, 5, 1, 3, 1, 2, 3, 1, 2, 1, 6, 1, 1, 1, 1, 15, 1, 1, 2, 4, 1, 1, 4, 3, 10, 2, 9, 4, 1, 211, 3, 1, 34, 1, 4, 2, 1, 1, 1, 4, 1, 12, 1, 3, 1, 2, 4, 2...

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