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SA Editor: Anil Bhoot
P emmaraju V.R.Rayudu, BE, M.Tech, a former Senior Scientist and Deputy Director of Defense Research and Development Laboratory of Government of India, has been studying, researching, and practicing Hindu Astrology for the last four decades. Member of the AFA and author of the much acclaimed ‘How to Read A Horoscope’ & ‘How to Match Horoscopes’ is known for his authentic work in rare areas like Nadi Astrology. Though 70 yrs old & busy in his spiritual life his love for Saptarishis Astrology is there right from its inception stage.
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he aim of this article is to find the link between the varga charts and nadi amshas and to prepare a nadi chart and interpret it vis-à-vis birth chart. Varga charts are Divisional charts of the birth chart, dividing into different parts. The divisions are 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/16, 1/20, 1/24, 1/27, 1/30, 1/40, 1/45, 1/60, 1/81, 1/108, 1/150. They are given nomenclature as D- charts as D-1 (birth chart), D-2 (Hora), D-3 (Drekkana), D-7 (Saptamsha), D-9 (Navamsha), D-10 (Dashamsha) etc. Each of these varga charts represent a particular life aspect such as D-3 coborns, D-7 Children, D-9 partner, D-10 profession etc. Nadi amsha is 1/150 division and its division chart is called nadi chart. Nadi amshas are of uniform duration or of nonuniform duration. Non-uniform nadi amshas are preferred since for change of
each nadi amsha, one or more of the varga charts change, indicating a difference in life pattern of that particular varga chart. Rectification of birth time up to seconds is necessary since small changes in time would change the nadi amsha and nadi chart, consequently change the varga charts showing a different life pattern.
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he rectification of birth time is to be done as per Tatwa/ Antartatwa Siddhantha given by my Guru Late Shri DV Subbarao in his Telugu language book published in 1970 (out of print now). I have published the English translation of this in the Times of Astrology magazine, New Delhi and also included in the Articles published by Saptarishai Astrology.com. Basically the method is based on selecting a particular time for male/ female birth depending on the particular lagna (ascendant) movable/ fixed/dual, Moon star, day of birth, tatwa etc. This method gives rectification upto 24 seconds. Readers are requested to refer to my article since it would be too big to include it here.
The methodology for preparation of various varga charts and the life aspects they represent are described in any standard astrology text book and they are easily given gi ven in many astrology software programmes.
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adi amsha is the 1/150 part of each rashi of 30 degrees. When uniformly divided, each nadi amsha would be 12 minutes in arc amounting to approximately 48 seconds in time. The 1st nadi amsha called Vasudha is from 00-00-00 to 00-12-00 and the 2nd nadi amsha called Vaishnavi is from 00-12-00 to 00-24-00 etc. The duration of D60 chart is for 30 minutes in arc and for the 1st and 2nd uniform nadi amshas all the varga charts including the D-60 would be the same indicating same life patterns for two persons born in the different uniform nadi amshas. Hence it is not practical to consider uniform nadi amshas. The list of names and durations of uniform nadi amshas are given in the book Chandrakala Nadi by Shri R. Santhanam Santhanam published by Sagar Publications, New Delhi.
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he list of non-uniform nadi amshas names and durations for movable/ fixed/ dual rashis is given in the book Nadi Astrology by Shri C. S. Patel published by Sagar Publications, New Delhi (this book is out of print now). It is not known how this list is prepared. For example the 1st nadi amsha called Vasudha is from 00-00-00 to 00-30-00 in movable rashis (Aries, Cancer, Libra, Capricorn), 29-30-00 to 30-00-00 in fixed rashis(Taurus, Leo, Scorpio, Aquarius) and from 15-00-00 to 15-20-00 in dual rashis (Gemini, Virgo, Sagittarius, Pisces) and the 2 nd nadi amsha called Vaishnavi is from 00-30-00 to 00-4000 in movable rashis, 29-20-00 to 29-30-00 in fixed rashis and from 15-20-00 to 15-30-00 in dual rashis. Since the 1st nadi amsha changes after 30 minutes arc and since the D-60 chart is for 30 minutes arc duration, when the 1st nadi amsha changes to 2 nd, the D-60 chart changes showing different D-charts for two persons born in different nadi amshas. For example, for Aries rashi, for nadi no.1 from 00-00-00 to 00-30-00 all the varga charts including D-60 will be in Aries and when the nadi changes to nadi no.2 from 00-30-00 to 00-40-00, all the varga charts except D-60 will be in Aries and the D-60 changes to Taurus. The biggest nadi amsha is 00-30-00 amounting to about 2 minutes in time and the smallest nadi amsha is 00-01-40 amounting to about 7 seconds in time. Hence non-uniform nadi amshas are preferred. If the nadi amshas are further divided into four equal parts as indicated in Chandrakala Nadi book by Shri R. Santhanam, the time interval may come to about 2 seconds and this is not discussed here and it can be taken up as a separate research project. The list of the non-uniform nadi amshas is given in Table 1 in the Appendix. In Aries, the variation of rashis in varga charts for each nadi number is given in Table 3. Similarly the tables for Taurus to Pisces can be prepared to see the variation of rashis in varga charts for each nadi number. The numbers 1 to 12 in the Table indicate Aries to Pisces respectively.
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he methodology to prepare the nadi chart is given in my article Nadi chart published in the Times of Astrology magazine, New Delhi and also included in the link Articles-Nadi astrology- Nadi chart published by SaptarishiAstrology.com.
Readymade tables are given as Table 1 and Table 2 in the Appendix to prepare the nadi chart easily. Note down the longitude of lagna/ planet in the birth chart in movable/ fixed/ dual rashi. For that longitude find out the duration of nadi amsha, nadi name and nadi number
from Table 1. For example if the longitude in birth chart of lagna in Aries (movable rashi) is 03-07-34, then it falls in the nadi duration 03-00-00 to 03-20-00 in Table 1 with the name Kutila and nadi no.16. Then go to the Table 2, for this nadi number and name, under the birth chart rashi against the nadi number find the nadi chart rashi. For example, for nadi no. 16, under 1 (Aries), you find no.4 which is Cancer and place the lagna in Cancer in nadi chart. In the Table 2, the numbers 1 to 12 indicate Aries to Pisces respectively. Similarly in the birth chart if Saturn is at 05-27-00 in Aquarius (fixed rashi), then see in Table1 that it falls in the nadi duration of 05-20-00 to 05-30-00 in the fixed column with the nadi name Ambuja and nadi number 124. Now go to Table 2, against nadi no.124, under no.11 which is Aquarius in birth chart, see no.12 which is Pisces and place Saturn in Pisces in nadi chart. Similarly for the longitudes of lagna and all the planets in the birth chart, a nadi chart can be prepared.
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he rules given by my Guru Late Shri DV Subbarao in his Telugu language book published in 1970 can be followed for interpretation of varga charts. The main rule is that the lordships of houses should not be considered in varga charts. The placement of lagna lord in the varga chart is important. The placement, associations and aspects can be taken. The English translation of these rules are published in Saptarishi Astrology Emagazine in July 2012 with a title “16 secrets of varga charts”. It is not repeated here for want of space. For example the placement of lagna lord / planet in 6th, 8tth or 12th house from lagna in the varga chart would not give good results for the life aspect represented by that varga. Since Nadi chart is also a varga chart of minutest division, the same rules are to be applied. The benefic/ malefic planets in the varga charts are to be found.
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he Three “S” analogy of Seed, Soil, Season is applied to understand the link between the nadi chart and birth chart. If the Seed is good, even if the Soil &/ Season may not be good, still the plant may survive and give good results to some extent. If the Seed is bad, even if the Soil &/ Season are good, the results may not be good. If all the Seed, Soil & Season are good, the results would be very satisfactory. Here we consider the nadi chart as Seed since it is the minutest division, the birth chart with other varga charts as Soil and the Gochara (transits) as Season. If a planet is malefic in the nadi chart, even if it is benefic in birth and varga charts and in Gochara, it may not produce good
results. If a planet is benefic in the nadi chart, even if it is malefic in birth chart it may still give good results to some extent. If a planet is benefic in the nadi and birth & varga charts, it would give very good results during its Dasa periods. The benefic/ malefic analysis can be done qualitatively as per the placements, associations, aspects etc. to check how far the nadi chart would support the birth chart. The benefic and malefic analysis of planets can be calculated quantitatively also as given in my book “ How to read a Horoscope- A Scientific model of predictions based on benefic and malefic analysis of planets and bhavas as per Hindu astrology ” published by M/s Motilal Banarsidas Publishers, New Delhi.
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ate of birth 7 September 1938, Place of birth Vizianagaram, Andhra Pradesh, India (Lat 18N7, Long 83E25), Time of birth 08-56-16 (rectified as per Tatwa/Antartatwa Siddhanta), Lahiri ayanamsha, Goravani astrology software version 2.26
Lagna ( ascendant) libra 05-53-34; sun leo 20-50-54; mars leo 06-32-50; mercury leo 05-58-38; moon Capricorn 20-09-30; Jupiter aquarius 02-07-05; venus libra 07-04-16; Saturn pisces 23-5123; rahu libra 27-16-03; ketu aries 27-16-03
Lagna scorpio; venus Sagittarius; ketu Capricorn; Jupiter & sun aquarius; moon pisces; Saturn Gemini; rahu cancer; mercury virgo; mars libra
Lagna pisces; mars pisces; moon aries; ketu cancer; venus virgo; Jupiter & Saturn scorpio; mercury Sagittarius; rahu Capricorn; sun aquarius The benefic/ malefic analysis of Jupiter is as follows as per my book (the points are given in brackets)
: if natural benefic (1); if in functional friend Saturn sign (1); if in lordship benefic Saturn sign (2); if in lordship benefic mars star (2); if aspected by lordship benefic mercury (2); if aspected by lordship benefic mars (2); as natural benefic not in12th bhava (1); Total 11 points
: if lordship malefic (1); if in natural malefic Saturn sign (1); if in natural malefic mars star (1); if functional enemy of lagna lord Venus ( 2); if aspected by functional enemy mercury (1); if aspected by lordship malefic sun (2); if aspected by natural malefic mars (1); if aspected by natural malefic sun (1); if aspected by natural malefic mercury (1); as lordship malefic not in 6th, 8th or 12th bhava ( 2); Total 13 points Benefic 11+Malefic 13=24 points; Benefic 11 divided by 24 and multiplied by100=45.83 %; Malefic 54.17%
: if natural benefic (1); as natural benefic not in 12 th bhava (1); total 2 points : if lagna lord I 12th (1); if in functional Saturn sign (1); if in natural malefic Saturn sign (1); if in association with functional enemy sun (1); if in association with natural malefic sun(1); total 5 Benefic 2+Malefic 5=7 points Benefic 28.57%; Malefic 71.43%
: if natural benefic (1); if lagna lord (1); as natural benefic not in 12 th bhava (1); as lordship benefic not in 6th, 8th, or 12th bhava (2); total 5 points : if in natural malefic mars sign (1); if in association with functional enemy Saturn (1); if in association with natural malefic Saturn (1); total 3 points Benefic 5+Malefic 3= 8 points Benefic 62.5%; Malefic 37.5% Though Jupiter is malefic in birth & Dasamsha charts, Jupiter is benefic in nadi chart. So Jupiter has given benefic results for profession in Jupiter dasa (period) from 24/1/1966 to 24/1/1981 such as promotions, position in profession etc Similarly for Saturn in birth chart benefic 61.1%, malefic 38.9%; dashamsha chart benefic 45.45%, malefic 54.55%; nadi chart benefic 27.3%, malefic 72.7%.
Though Saturn is benefic in birth chart, Saturn is malefic in D-10 chart and nadi chart. So Saturn has not given benefic results for profession in Saturn dasa from 24/1/1982 to 24/1/2001 such as no promotions, no position, loss of job by voluntary retirement, professional worries etc. If the nadi chart is not prepared and analyzed, it would have been inferred that Jupiter would give bad results and Saturn would give benefic results based on birth chart analysis.
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his is only a research project for preparing and analyzing nadi chart and to study the variation of varga charts whenever a nadi amsha changes. It is not claimed that it is right .Readers and scholars are requested to further study it and improve this methodology. Thanks to Mr. Kamesh Pemmaraju (USA) and Mr. Shrinivas Gramopadhyaye (Miraj, India) for participating in discussions and preparing the required tables. Hope that the youngsters with interest in astrology research would decipher these secrets of our ancient treasures of knowledge. My God bless all of us.
Nadi Amsha 1 2 3 4 5 6 7
Vasudhaa Vaishnavi Braahmi Kaalakoota Shaankari Sudhaakari Samaa
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Saumyaa Suraa Maayaa Manoharaa Maadhavi Manjuswanaa Ghoraa Kumbhini Kutilaa Prabhaa Paraa Payasvini Maalaa Jagati Jarjharaa Dhruvaa Musalaa Mudgaraa Paashaa Champakaa Daamakaa Mahi Kalusha Kamalaa Kaantaa Kaalaa Karikaraa Kshamaa Durdharaa Durbhagaa Vishwaa Visheernaa Vikataa Avilaa Vibhramaa Sukhadaa Snigdhaa
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Sodaraa Surasundari Amritaplaavini Kaaraa Kaamadhruk Karaveerani Gahvaraa Kundini Raudraa Vishaakhyaa Vishanaashini Nirmadaa Sheetalaa Nimnaa Preetaa Priyavardhini Maanaghnaa Durbhagaa Chitraa Chitrini Chiranjeevini Bhoopaa Gadaharaa Naalaa Nalini Nirmalaa Nadi Sudhaamritaamshu Kalushankuraa Trailokyamohankari Mahaamaari Susheetalaa Sukhadaa Suprabhaa Shobhaa Shobhanaa Shivadaa
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Shivaa Balaa Jwaalaa Gadaa Gaadhaa Nootanaa Sumanoharaa Somavalli Somalataa Mangalaa Mudrikaa Shudhaa Mokshaapavargaa Valayaa Navaneeta Nishaachari Nivrutti Nigadaa Saraa Sangeetaa Saamadaa Samaa Viwhwambharaa Kumaari Kokilaa Kunjaraakriti Aindraa Swaahaa Swaraa Brahmi Preetaa Rakshajalaaplavaa Vaaruni Madiraa Maitri Haarini Harini
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Maruta Dhananjyaa Dhanakari Dhanadaa Kachchhapa Ambuja Manshani Shoolini Raudri Shivaa Shivakari Kalaa Kundaa Mukundaa Bharataa Hasitaa Kadalee Smaraa Kandalaa Kokilaa Paapaa Kaamini Kalashodk-bhavaa Veeraprasoo Sangaraa Shatayagnaa Shataavari Prahavi Patalini Naagaa Pankajaa Parameshwari
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23:45:00 24:00:00 24:22:30 24:26:40 24:30:00 24:40:00 24:45:00 25:00:00 25:20:00 25:30:00 25:33:20 25:42:51 26:00:00 26:15:00 26:30:00 26:40:00 27:00:00 27:20:00 27:30:00 27:45:00 27:46:40 28:00:00 28:07:30 28:30:00 28:40:00 28:45:00 28:53:20 29:00:00 29:15:00 29:20:00 29:30:00 30:00:00
6:15:00 6:00:00 5:37:30 5:33:20 5:30:00 5:20:00 5:15:00 5:00:00 4:40:00 4:30:00 4:26:40 4:17:08 4:00:00 3:45:00 3:30:00 3:20:00 3:00:00 2:40:00 2:30:00 2:15:00 2:13:20 2:00:00 1:52:30 1:30:00 1:20:00 1:15:00 1:06:40 1:00:00 0:45:00 0:40:00 0:30:00 0:00:00
6:30:00 6:15:00 6:00:00 5:37:30 5:33:20 5:30:00 5:20:00 5:15:00 5:00:00 4:40:00 4:30:00 4:26:40 4:17:08 4:00:00 3:45:00 3:30:00 3:20:00 3:00:00 2:40:00 2:30:00 2:15:00 2:13:20 2:00:00 1:52:30 1:30:00 1:20:00 1:15:00 1:06:40 1:00:00 0:45:00 0:40:00 0:30:00
8:40:00 8:45:00 8:53:20 9:00:00 9:20:00 9:22:30 9:30:00 9:45:00 10:00:00 10:30:00 10:40:00 11:00:00 11:06:40 11:15:00 11:20:00 11:30:00 12:00:00 12:13:20 12:30:00 12:40:00 12:45:00 12:51:25 13:00:00 13:07:30 13:20:00 13:30:00 13:45:00 14:00:00 14:15:00 14:26:40 14:30:00 14:40:00
8:45:00 8:53:20 9:00:00 9:20:00 9:22:30 9:30:00 9:45:00 10:00:00 10:30:00 10:40:00 11:00:00 11:06:40 11:15:00 11:20:00 11:30:00 12:00:00 12:13:20 12:30:00 12:40:00 12:45:00 12:51:25 13:00:00 13:07:30 13:20:00 13:30:00 13:45:00 14:00:00 14:15:00 14:26:40 14:30:00 14:40:00 15:00:00
Nadi Amsha 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
1
2
3
4
5
6
7
8
9
10 11 12
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8
6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11
4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2
7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2
7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2
12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5
10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5
10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5
3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8
33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9
10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10
12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1
3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3
3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3
4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4
6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6
6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6
7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7
9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106
10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10
9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9
1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1
12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12
4 5 6 7 8 9 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10
4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4
3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3
7 8 9 10 11 12 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1
7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7
6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6
10 11 12 1 2 3 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4
107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143
11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8
8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8
2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2
11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11
11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11
5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5
2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2
2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2
8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8
5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5
5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5
144 145 146 147 148 149 150
12 1 2 3 4 5 6
7 9 3 10 12 6 10 4 9 1 5 11 5 8 2 4 12 6 7 3 3 1 7 6 4 2 2 8 5 5 1 3 9 4 6
6 7 8 9 10 11 12
1 12 11 10 9 8 7
3 9 4 4 10 3 5 11 2 6 12 1 7 1 12 8 2 11 9 3 10
6 7 8 9 10 11 12
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 2 3
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 12 12 11 11 11 11 11 11
1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5
5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 9 10 10
1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 11 11 11 11 11 11 11 11
1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 5 5 5 6 6 6 6 7 7 7 8 8 8 8 8 9 9 9
1 1 2 2 2 2 2 3 3 3 4 4 4 4 5 5 6 6 6 7 7 7 7 8 8 8 9 9 9 9 10 10 10
1 2 2 2 3 3 3 3 4 4 5 5 5 6 6 7 7 8 8 9 9 9 10 10 11 11 11 12 12 12 1 1 2
1 2 2 3 3 4 4 4 5 6 6 7 7 7 8 9 10 10 11 11 12 1 1 2 3 3 3 4 4 5 5 6 7
1 2 3 3 4 5 5 5 6 7 8 9 9 10 10 11 12 12 1 2 3 4 4 4 5 6 7 7 7 8 9 10 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
1 2 1 2 1 2 1 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4
2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5
3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5
11 11 11 11 11 11 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 8
3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6
4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8
5 5 5 5 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 10 10
10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3 3 4
7 7 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9 9 10 10 10 10 11 11 11 11 11 12 12 12 12 12 12 12 1 1 1
11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
9 10 10 10 11 11 11 12 12 12 12 12 12 1 1 1 1 2 2 3 3 3 3 4 4 4 5 5 5 5 6 6 6 6 6 7 7
11 11 11 12 12 12 1 1 1 1 2 2 2 2 3 3 3 3 4 4 5 5 5 5 6 6 7 7 7 8 8 8 8 8 9 9 9
2 2 3 3 4 4 5 5 6 6 6 6 6 7 7 7 8 8 9 10 10 11 11 11 11 12 1 1 2 2 2 2 3 3 3 4 4
7 7 8 9 10 11 11 12 12 1 1 1 2 2 3 3 3 4 5 6 6 7 8 8 9 10 11 11 12 12 12 1 1 2 2 3 3
12 12 1 2 2 3 4 5 6 6 7 7 8 8 8 9 9 10 11 12 1 2 2 3 3 4 5 6 7 8 8 8 9 9 10 11 12
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 9 9 9 9 9 9 9
4 4 4 4 4 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6
5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7
5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8
8 8 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6
6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9
8 8 8 8 8 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 12 12 12 12 12
10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3
4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 9 9 10
1 1 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 6 6 6 6 7 7 7 7 7 7 8 8
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
7 8 8 8 8 9 9 9 9 10 10 10 11 11 11 11 11 12 12 12 12 1 1 1 2 2 2 2 3 3 4 4 4 4 5 5 5
10 10 10 10 11 11 12 12 12 12 1 1 1 2 2 2 2 2 3 3 3 4 4 5 5 5 5 6 6 7 7 7 7 8 8 8 8
5 5 5 6 6 7 7 8 8 8 9 9 10 10 10 11 11 11 11 12 12 1 2 2 2 2 3 3 4 5 5 6 6 6 7 7 7
4 5 5 5 6 7 7 8 8 9 9 10 11 11 12 12 12 12 1 2 2 3 4 4 4 5 5 6 6 7 7 8 8 8 9 9 9
12 1 2 2 3 4 5 6 6 7 8 9 10 10 11 11 12 12 1 1 2 3 4 5 6 6 7 8 9 10 11 12 12 1 2 2 3
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
7 7 7 7 7 7 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7
6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8
7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9
8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10
6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3
9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12
12 12 12 12 12 12 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4
3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 8 8
10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 12 12 12 12 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 3
8 8 8 8 8 9 9 9 9 9 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 1 1 1 1 1 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
5 5 5 7 6 6 8 8 8 9 9 9 9 10 10 10 10 10 11 11 11 12 12 12 12 1 1 1 1 2 2 3 3 3 3 4 4
9 9 9 9 10 10 10 11 11 11 12 12 12 1 1 1 1 2 2 2 3 3 3 3 4 4 4 5 5 6 6 6 6 7 7 7 8
7 7 8 8 9 9 10 10 11 11 11 12 12 1 1 1 2 2 2 3 3 4 4 4 5 5 6 6 7 7 8 8 8 9 9 10 10
9 9 10 10 11 12 12 1 2 2 3 3 4 4 5 5 6 7 7 7 7 8 9 9 10 10 10 11 11 12 12 1 2 2 3 4 5
3 3 4 4 5 6 7 8 9 10 10 11 12 1 2 2 2 3 3 4 5 5 6 7 8 9 9 10 10 11 12 1 1 2 2 3 4
1 1 1 1 1 1
4 4 4 4 4 4
9 9 9 9 9 9
10 10 10 10 10 10
5 5 5 5 5 5
6 6 6 6 6 6
7 7 7 7 7 7
8 8 8 8 8 8
9 9 9 9 9 9
10 10 10 10 10 10
3 3 3 3 3 3
12 12 12 12 12 12
4 4 4 4 4 4
8 8 8 8 8 8
4 4 4 4 4 4
2 3 3 3 3 3
7 7 7 7 7 7
4 4 4 5 5 5
8 8 8 8 9 9
10 10 11 11 11 12
5 5 6 7 7 7
5 5 6 6 7 7
