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THE

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WORK DAYS OF GOD

Herbert W Morris D.D.circa 1883

Page 22

"As all the words in the English language are composed out of the twenty-six letters of the alphabet,.."

 

 

LIGHT AND LIFE

Lars Olof Bjorn 1976

Page 197

"By writing the 26 letters of the alphabet in a certain order one may put down almost any message (this book 'is written with the same letters' as the Encyclopaedia Britannica and Winnie the Pooh, only the order of the letters differs). In the same way Nature is able to convey with her language how a cell and a whole organism is to be constructed and how it is to function. Nature has succeeded better than we humans; for the genetic code there is only one universal language which is the same in a man, a bean plant and a bacterium."

"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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"BY WRITING THE 26 LETTERS OF THE ALPHABET IN A CERTAIN ORDER

ONE MAY PUT DOWN ALMOST ANY MESSAGE"

 

 

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A

HISTORY OF GOD

Karen Armstrong

The God of the Mystics

Page 250

"(The Book of Creation). There is no attempt to describe the creative process realistically; the account is unashamedly symbolic and shows God creating the world by means of language as though he were writing a book. But language has been entirely transformed and the message of creation is no longer clear. Each letter of the Hebrew alphabet is given a numerical value; by combining the letters with the sacred numbers, rearranging them in endless configurations, the mystic weaned his mind away from the normal connotations of words."  

 

 

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THERE IS NO ATTEMPT MADE TO DESCRIBE THE CREATIVE PROCESS REALISTICALLY

THE ACCOUNT IS SYMBOLIC AND SHOWS GOD CREATING THE WORLD BY MEANS OF LANGUAGE

AS THOUGH WRITING A BOOK BUT LANGUAGE ENTIRELY TRANSFORMED

THE MESSAGE OF CREATION IS CLEAR EACH LETTER OF

THE

ALPHABET

IS

GIVEN

A

NUMERICAL

VALUE BY COMBINING THE LETTERS WITH THE SACRED NUMBERS

REARRANGING THEM IN ENDLESS CONFIGURATIONS

THE MYSTIC WEANED THE MIND AWAY FROM THE NORMAL CONNOTATIONS OF WORDS

 

 

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FINGERPRINTS OF THE GODS

A QUEST FOR THE BEGINNING AND THE END

Graham Hancock 1995

Chapter 32

Speaking to the Unborn

Page 285

"It is understandable that a huge range of myths from all over the ancient world should describe geological catastrophes in graphic detail. Mankind survived the horror of the last Ice Age, and the most plausible source for our enduring traditions of flooding and freezing, massive volcanism and devastating earthquakes is in the tumultuous upheavals unleashed during the great meltdown of 15,000 to 8000 BC. The final retreat of the ice sheets, and the consequent 300-400 foot rise in global sea levels, took place only a few thousand years before the beginning of the historical period. It is therefore not surprising that all our early civilizations should have retained vivid memories of the vast cataclysms that had terrified their forefathers.
Much harder to explain is the peculiar but distinctive way the myths of cataclysm seem to bear the intelligent imprint of a guiding hand.l Indeed the degree of convergence between such ancient stories is frequently remarkable enough to raise the suspicion that they must all have been 'written' by the same 'author'.
Could that author have had anything to do with the wondrous deity, or superhuman, spoken of in so many of the myths we have reviewed, who appears immediately after the world has been shattered by a horrifying geological catastrophe and brings comfort and the gifts of civilization to the shocked and demoralized survivors?
White and bearded, Osiris is the Egyptian manifestation of this / Page 286 / universal figure, and it may not be an accident that one of the first acts he is remembered for in myth is the abolition of cannibalism among the primitive inhabitants of the Nile Valley.2 Viracocha, in South America, was said to have begun his civilizing mission immediately after a great flood; Quetzalcoatl, the discoverer of maize, brought the benefits of crops, mathematics, astronomy and a refined culture to Mexico after the Fourth Sun had been overwhelmed by a destroying deluge.
Could these strange myths contain a record of encounters between scattered palaeolithic tribes which survived the last Ice Age and an as yet unidentified high civilization which passed through the same epoch?
And could the myths be attempts to communicate?

A message in the bottle of time"

'Of all the other stupendous inventions,' Galileo once remarked,

what sublimity of mind must have been his who conceived how to communicate his most secret thoughts to any other person, though very distant either in time or place, speaking with those who are in the Indies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years? And with no greater difficulty than the various arrangements of two dozen little signs on paper? Let this be the seal of all the admirable inventions of men.3

If the 'precessional message' identified by scholars like Santillana, von Dechend and Jane Sellers is indeed a deliberate attempt at communication by some lost civilization of antiquity, how come it wasn't just written down and left for us to find? Wouldn't that have been easier than encoding it in myths? Perhaps.
Nevertheless, suppose that whatever the message was written on got destroyed or worn away after many thousands of years? Or suppose that the language in which it was inscribed was later forgotten utterly (like the enigmatic Indus Valley script, which has been studied closely for more than half a century but has so far resisted all attempts at decoding)? It must be obvious that in such circumstances a written / Page 287 / legacy to the future would be of no value at all, because nobody would be able to make sense of it.
What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them - and the city of Teotihuacan may be the calling-card of a lost civilization written in the eternal language of mathematics.
Geodetic data, related to the exact positioning of fixed geographical points and to the shape and size of the earth, would also remain valid and recognizable for tens of thousands of years, and might be most conveniently expressed by means of cartography (or in the construction of giant geodetic monuments like the Great Pyramid of Egypt, as we shall see).
Another 'constant' in our solar system is the language of time: the great but regular intervals of time calibrated by the inch-worm creep of precessional motion. Now, or ten thousand years in the future, a message that prints out numbers like 72 or 2160 or 4320 or 25,920 should be instantly intelligible to any civilization that has evolved a modest talent for mathematics and the ability to detect and measure the almost imperceptible reverse wobble that the sun appears to make along the ecliptic against the background of the fixed stars..."

"What one would look for, therefore, would be a universal language, the kind of language that would be comprehensible to any technologically advanced society in any epoch, even a thousand or ten thousand years into the future. Such languages are few and far between, but mathematics is one of them"

"WRITTEN IN THE ETERNAL LANGUAGE OF MATHEMATICS"

 

 

 

 

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www.bibliotecapleyades.net/hamlets_mill/hamlet

HAMLET'S MILL

AN ESSAY INVESTIGATING THE ORIGINS OF HUMAN KNOWLEDGE

AND ITS TRANSMISSION THROUGH MYTH

Giorgio De Santillana and Hertha Von Dechend 1969

Intoduction

Page 1 (number omitted)

"The unbreakable fetters which bound down the Great Wolf Fenrir had been cunningly forged by Loki from these: the footfall of a cat, the roots of a rock, the beard of a woman, the breath of a fish, the spittle of a bird. The Edda

Toute vue des choses qui n'est pas estrange est fausse. VALERY


THIS IS meant to be only an essay. It is a first reconnaissance of a realm well-nigh unexplored and uncharted. From whichever way onc enters it, one is caught in the same bewildering circular complexity, as in a labyrinth, for it has no deductive order in the abstract sense, but instead resembles an organism tightly closed in itself, or even better, a monumental "Art of the Fugue."

The figure of Hamlet as a favorable starting point came by chance. Many other avenues offered themselves, rich in strange symbols and beckoning with great images, but the choice went to Hamlet because he led the mind on a truly inductive quest through a familiar landscape-and one which has the merit of its literary setting. Here is a character deeply present to our awareness, in whom ambiguities and uncertainties, tormented self-questioning and dispassionate insight give a presentiment of the modern mind. His personal drama was that he had to be a hero, but still try to avoid the role Destiny assigned him. His lucid intellect remained above the conflict of motives-in other words, his was and is a truly con­/ Page 2 / temporary consciousness. And yet this character whom the poet made one of us, the first unhappy intellectual, concealed a past as a legendary being, his features predetermined, preshaped by long­standing myth. There was a numinous aura around him, and many clues led up to him. But it was a surprise to find behind the mask an ancient and all-embracing cosmic power-the original master of the dreamed-of first age of the world.
Yet in all his guises he remained strangely himself. The original Amlodhi, * as his name was in Icelandic legend, shows the same characteristics of melancholy and high intellect. He, too, is a son dedicated to avenge his father, a speaker of cryptic but inescapable truths, an elusive carrier of Fate who must yield once his mission is accomplished and sink once more into concealment in the depths of time to which he belongs: Lord of the Golden Age, the Once and Future King.

This essay will follow the figure farther and farther afield, from the Northland to Rome, from there to Finland, Iran, and India; he will appear again unmistakably in Polynesian legend. Many other Dominations and Powers will materialize to frame him within the proper order.

Amlodhi was identified, in the crude and vivid imagery of the Norse, by the ownership of a fabled mill which, in his own time, ground out peace and plenty. Later, in decaying times, it ground out salt; and now finally, having landed at the bottom of the sea, it is grinding rock and sand, creating a vast whirlpool, the Maelstrom (i.e., the grinding stream, from the verb mala, "to grind"), which is supposed to be a way to the land of the dead. This imagery stands, as the evidence develops, for an astronomical process, the secular shifting of the sun through the signs of the zodiac which determines world-ages, each numbering thousands of years. Each age brings a World Era, a Twilight of the Gods. Great structures collapse; pillars topple which supported the great fabric; floods and cataclysms herald the shaping of a new world.
The image of the mill and its owner yielded elsewhere to more / Page 3 / sophisticated ones, more adherent to celestial events. In Plato's powerful mind, the figure stood out as the Craftsman God, the Demiurge, who shaped the heavens; but even Plato did not escape the idea he had inherited, of catastrophes and the periodic rebuilding of the world.

Tradition will show that the measures of a new world had to be procured from the depths of the celestial ocean and tuned with the measures from above, dictated by the "Seven Sages," as they are often cryptically mentioned in India and elsewhere. They turn out to be the Seven Stars of Ursa, which are normative in all cosmological alignments on the starry sphere. These dominant stars of the Far North are peculiarly but systematically linked with those which are considered the operative powers of the cosmos, that is, the planets as they move in different placements and configurations along the zodiac. The ancient Pythagoreans, in their conventional language, called the two Bears the Hands of Rhea (the Lady of Turning Heaven), and called the planets the Hounds of Persephone, Queen of the Underworld. Far away to the south, the mysterious ship Argo with its Pilot star held the depths of the past; and the Galaxy was the Bridge out of Time. These notions appear to have been common doctrine in the age before history-all over the belt of high civilizations around our globe. They also seem to have been born of the great intellectual and technological revolution of the late Neolithic period.

The intensity and richness, the coincidence of details, in this cumulative thought have led to the conclusion that it all had its origin in the Near East. It is evident that this indicates a diffusion of ideas to an extent hardly countenanced by current anthropology. But this science, although it has dug up a marvelous wealth of details, has been led by its modern evolutionary and psychological bent to forget about the main source of myth, which was astronomy -the Royal Science. This obliviousness is itself a recent turn of events-barely a century old. Today expert philologists tell us that Saturn and Jupiter are names of vague deities, subterranean or atmospheric, superimposed on the planets at a "late" period; they neatly sort out folk origins and "late" derivations, all unaware that planetary periods, sidereal and synodic, were known and rehearsed / Page 4 / in numerous ways by celebrations already traditional in archaic times. If a scholar has never known those periods even from elementary science, he is not in the best position to recognize them when they come up in his material.

Ancient historians would have been aghast had they been told that obvious things were to become unnoticeable. Aristotle was proud to state it as known that the gods were originally stars, even if popular fantasy had later obscured this truth. Little as he believed in progress, he felt this much had been secured for the future. He could not guess that W. D. Ross, his modern editor, would condescendingly annotate: "This is historically untrue." Yet we know that Saturday and Sabbath had to do with Saturn, just as Wednesday and Mercredi had to do with Mercury. Such names are as old as time; as old, certainly, as the planetary heptagram of the Har­ranians. They go back far before Professor Ross' Greek philology. The inquiries of great and meticulous scholars such as Ideler, Lep­sius, Chwolson, BoIl and, to go farther back, of Athanasius Kircher and Petavius, had they only been read carefully, and noted, would have taught several relevant lessons to the historians of culture, but interest shifted to other goals, as can be seen from current anthro­pology, which has built up its own idea of the "primitive" and what came after.

One still reads in that most unscientific of records, the Bible, that God disposed all things by number, weight and measure; ancient Chinese texts say that "the calendar and the pitch pipes have such a close fit, that you could not slip a hair between them." People read it, and think nothing of it. Yet such hints might reveal a world of vast and firmly established complexity, infinitely different from ours. But the experts now are benighted by the current folk fantasy, which is the belief that they are beyond all this-critics without nonsense and extremely wise.

In 1959 I wrote:
The dust of centuries had settled upon the remains of this great world-wide archaic construction when the Greeks came upon the scene. Yet something of it survived in traditional rites, in myths and fairy tales no longer understood. Taken verbally, it matured the / Page 5 / bloody cults intended to procure fertility, based on the belief in a dark universal force of an ambivalent nature, which seems now to monopolize our interest. Yet its original themes could flash out again, preserved almost intact, in the later thought of the Pythagoreans and of Plato.

But they are tantalizing fragments of a lost whole. They make one think of those "mist landscapes" of which Chinese painters are masters, which show here a rock, here a gable, there the tip of a tree, and leave the rest to imagination. Even when the code shall have yielded, when the techniques shall be known, we cannot expect to gauge the thought of those remote ancestors of ours, wrapped as it is in its symbols.

Their words are no more heard again Through lapse of many ages. . .

We think we have now broken part of that code. The thought behind these constructions of the high and far-off times is also lofty, even if its forms are strange. The theory about "how the world began" seems to involve the breaking asunder of a harmony, a kind of cosmogonic "original sin" whereby the circle of the ecliptic (with the zodiac) was tilted up at an angle with respect to the equator, and the cycles of change came into being.

This is not to suggest that this archaic cosmology will show any great physical discoveries, although it required prodigious feats of concentration and computing. What it did was to mark out the unity of the universe, and of man's mind, reaching out to its farthest limits. Truly, man is doing the same today.

Einstein said: "What is inconceivable about the universe, is that it should be at all conceivable." Man is not giving up. When he discovers remote galaxies by the million, and then those quasi-stellar radio sources billions of light-years away which confound his speculation, he is happy that he can reach out to those depths. But he pays a terrible price for his achievement. The science of astro­physics reaches out on a grander and grander scale without losing its footing. Man as man cannot do this. In the depths of space he loses himself and all notion of his significance. He is unable to fit himself into the concepts of today's astrophysics short of schizophrenia. Modern man is facing the nonconceivable. Archaic man, however, kept a firm grip on the conceivable by framing within his cosmos / Page 6 / an order of time and an eschatology that made sense to him and reserved a fate for his soul. Yet it was a prodigiously vast theory, with no concessions to merely human sentiments. It, too, dilated the mind beyond the bearable, although without destroying man's role in the cosmos. It was a ruthless metaphysics.

Not a forgiving universe, not a world of mercy. That surely not. Inexorable as the stars in their courses, miserationis parcissimae, the Romans used to say. Yet it was a world somehow not unmindful of man, one in which there was an accepted place for everything, rightfully and not only statistically, where no sparrow could fall unnoted, and where even what was rejected through its own error would not go down to eternal perdition; for the order of Number and Time was a total order preserving all, of which all were members, gods and men and animals, trees and crystals and even absurd errant stars, all subject to law and measure.

This is what Plato knew, who could still speak the language of archaic myth. He made myth consonant with his thought, as he built the first modern philosophy. We have trusted his clues as landmarks even on occasions when he professes to speak "not quite seriously." He gave us a first rule of thumb; he knew what he was talking about.

Behind Plato there stands the imposing body of doctrine attributed to Pythagoras, some of its formulation uncouth, but rich with the prodigious content of early mathematics, pregnant with a sci­ence and a metaphysics that were to flower in Plato's time. From it come such words as "theorem," "theory," and "philosophy." This in its turn rests on what might be called a proto-Pythagorean phase, spread all over the East but with a focus in Susa. And then there was something else again, the stark numerical computing of Baby­Ion. From it all came that strange principle: "Things are numbers."

Once having grasped a thread going back in time, then the test of later doctrines with their own historical developments lies in their congruence with tradition preserved intact even if half under­stood. For there are seeds which propagate themselves along the jetstream of time.

Page 7

And universality is in itself a test when coupled with a firm design. When something found, say, in China turns up also in Babyionian astrological texts, then it must be assumed to be relevant, for it reveals a complex of uncommon images which nobody could claim had risen independently by spontaneous generation.

Take the origin of music. Orpheus and his harrowing death may be a poetic creation born in more than one instance in diverse places. But when characters who do not play the lyre but blow pipes get themselves flayed alive for various absurd reasons, and their identical end is rehearsed on several continents, then we feel we have got hold of something, for such stories cannot be linked by internal sequence. And when the Pied Piper turns up both in the medieval German myth of Hamelin and in Mexico long before Columbus, and is linked in both places with certain attributes like the color red, it can hardly be a coincidence. Generally, there is little that finds its way into music by chance.

Again, when one finds numbers like 108, or 9 x 13, reappearing under several multiples in the Vedas, in the temples of Angkor, in Babylon, in Heraclitus' dark utterances, and also in the Norse Valhalla, it is not accident.

There is one way of checking signals thus scattered in early data, in lore, fables and sacred texts. What we have used for sources may seem strange and disparate, but the sifting was considered, and it had its reasons. Those reasons will be given later in the chapter on method. I might call it comparative morphology. The reservoir of myth and fable is great, but there are morphological "markers" for what is not mere storytelling of the kind that comes naturally. There is also wonderfully preserved archaic material in "secondary" primitives, like American Indians and West Africans. Then there are courtly stories and annals of dynasties which look like novels: the Feng Shen Yen I, the Japanese Nihongi, the Hawaiian Kumulipo. These are not merely fantasy-ridden fables.

In hard and perilous ages, what information should a well-born man entrust to his eldest son? Lines of descent surely, but what else? The memory of an ancient nobility is the means of preserving the / Page 8 / arcana imperii, the arcana legis and the arcana mundi, just as it was in ancient Rome. This is the wisdom of a ruling class. The Polynesian chants taught in the severely restricted Whare-wananga were mostly astronomy. That is what a liberal education meant then.

Sacred texts are another great source. In our age of print one is tempted to dismiss these as religious excursions into homiletics, but originally they represented a great concentration of attention on material which had been distilled for relevancy through a long period of time and which was considered worthy of being committed to memory generation after generation. The tradition of Celtic Druidism was delivered not only in songs, but also in tree-lore which was much like a code. And in the East, out of complicated games based on astronomy, there developed a kind of shorthand which became the alphabet.

As we follow the clues-stars, numbers, colors, plants, forms, verse, music, structres-a huge framework of connections is re­vealed at many levels. One is inside an echoing manifold where everything responds and everything has a place and a time assigned to it. This is a true edifice, something like a mathematical matrix, a World-Image that fits the many levels, and all of it kept in order by strict measure. It is measure that provides the countercheck, for there is much that can be identified and redisposed from rules like the old Chinese saying about the pitch pipes and the calendar. When we speak of measures, it is always some form of Time that provides them, starting from two basic ones, the solar year and the octave, and going down from there in many periods and intervals, to actual weights and sizes. What modern man attempted in the merely conventional metric system has archaic precedents of great complexity. Down the centuries there comes an echo of Al-Biruni's wondering a thousand years ago, when that prince of scientists discovered that the Indians, by then miserable astronomers, calculated aspects and events by means of stars-and were not able to show him anyone star that he asked for. Stars had become items for them, as they were to become again for Leverrier and Adams, who never troubled to look at Neptune in their life although they had computed and discovered it in 1847. The Mayas and the Aztecs in their / Page 9 / unending calculations seem to have had similar attitudes. The connections were what counted. Ultimately so it was in the archaic universe, where all things were signs and signatures of each other, inscribed in the hologram, to be divined subtly. And Number dominated them all (appendix # I ).

This ancient world moves a little closer if one recalls two great transitional figures who were simultaneously archaic and modern in their habits of thought. The first is Johannes Kepler, who was of the old order in his unremitting calculations and his passionate devotion to the dream of rediscovering the "Harmony of the Spheres." But he was a man of his own time, and also of ours, when this dream began to prefigure the polyphony that led up to Bach. In somewhat the same way, our strictly scientific world view has its counterpart in what John Hollander, the historian of music, has described as "The Untuning of the Sky." The second transitional figure is no less a man than Sir Isaac Newton, the very inceptor of the rigorously scientific view. There is no real paradox in mentioning Newton in this connection. John Maynard Keynes, who knew Newton as well as many of our time, said of him:

Newton was not the first of the Age of Reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual world rather less than 10,000 years ago. . . Why do I call him a magician? Because he looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher's treasure hunt to the esoteric brother­hood. He believed that these clues were to be found partly in the evidence of the heavens and in the constitution of elements (and that is what gives the false suggestion of his being an experimental natural philosopher), but also partly in certain papers and traditions handed down by the brethren in an unbroken chain back to the original cryptic revelation in Babylonia. He regarded the universe as a cryptogram set by the Almighty-just as he himself wrapt the discovery of the calculus in a cryptogram when he communicated with Leibniz. By pure thought, by concentration of mind, the riddle, he believed, would be revealed to the initiate.1

Page 10

Lord Keynes' appraisal, written ca. 1942, remains both unconventional and profound. He knew, we all know, that Newton failed. Newton was led astray by his dour sectarian preconceptions. But his undertaking was truly in the archaic spirit, as it begins to appear now after two centuries of scholarly search into many cul­tures of which he could have had no idea. To the few clues he found with rigorous method, a vast number have been added. Still, the wonder remains, the same that was expressed by his great predecessor Galileo:

But of all other stupendous inventions, what sublimity of mind must have been his who conccived how to communicate his most secret thoughts to any othcr person, though very far distant either in time or place, speaking with those who are in the In dies, speaking to those who are not yet born, nor shall be this thousand or ten thousand years) And with no greater difficulty than the various arrangement of two dozcn little signs upon paper? Let this be the seal of all the admirable inventions of man.

'Way back in the 6th century A.D., Gregoire de Tours was writing: "The mind has lost its cutting edge, we hardly understand the Ancicnts." So much more today, despite our wallowing in mathematics for the million and in sophisticated technology.
It is undeniable that, notwithstanding our Classics Departments' labors, the wilting away of classical studies, the abandonment of any living familiarity with Greek and Latin has cut the ompha­loessa, the umbilical cord which connected our cultUre-at least at its top level-with Greece, in the same manner in which men of the Pythagorean and Orphic tradition were tied up through Plato and a few others with the most ancient Near East. It is beginning to appear that this destruction is leading into a very up-to-date Middle Ages, much worse than the first. People will sneer: "Stop the World, I want to get off." It cannot be changed, however; this is the way it goes when someone or other tampers with the reserved knowledge that science is, and was meant to represent.
But, as Goethe said at the very onset of the Progressive Age, "Noch ist es Tag, da ruhre sich der Mann! Die Nacht tritt ein, wo niemand wirken kann." ("It is still day, let men get up and / Page 11 / going-the night creeps in, when there is nothing doing.") There might come once more some kind of "Renaissance" out of the hopelessly condemned and trampled past, when certain ideas come to life again, and we should not deprive our grandchildren of a last chance at the heritage of the highest and farthest-off times. And if, as looks infinitely probable, even that last chance is passed up in the turmoil of progress, why then one can still think with Poliziano, who was himself a master humanist, that there will be men whose minds find a refuge in poetry and art and the holy tradition "which alone make men free from death and turn them to eternity, so long as the stars will go on, still shining over a world made for­ever silent." Right now, there is still left some daylight in which to undertake this first quick reconnaissance. It will necessarily leave out great and significant areas of material, but even so, it will in­vestigate many unexpected byways and crannies of the past."

Page 2 Note *. The indulgence of specialists is asked for the form of certain transliterations throughout the text; for example, Amlodhi instead of Amlodi, Grotte instead of Grotti, etc. (Ed.)

Page 9 Note 1 1 "Newton the Man," in The Royal Society. Newton Tercentenary Celebrations (1947), p. 29.

 

 

-
CODE
-
-
-
2
CO
18
9
9
2
DE
9
9
9
4
CODE
27
18
18
-
-
2+7
1+8
1+8
4
CODE
9
9
9

 

 

THE

FAR YONDER SCRIBE

AND OFT TIMES SHADOWED SUBSTANCES WATCHED IN FINE AMAZE

THE

ZED ALIZ ZED

IN SWIFT REPEAT SCATTER STAR DUST AMONGST THE LETTERS OF THEIR PROGRESS

AT THE THROW OF THE NINTH RAM WHEN IN CONJUNCTION SET

THE

FAR YONDER SCRIBE

MADE RECORD OF THEIR FALL

 

 

NUMBER

9

THE SEARCH FOR THE SIGMA CODE

Cecil Balmond 1998

Cycles and Patterns

Page 165

Patterns

"The essence of mathematics is to look for patterns.

Our minds seem to be organised to search for relationships and sequences. We look for hidden orders.

These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac!

Searching out patterns is a pure delight.

Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden.

And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."

 

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

A
-
J
-
S
-
-
-
-
-
--
1
-
1
-
1
+
=
3
-
=
3
A
-
J
-
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
B
-
K
-
T
-
-
-
-
-
--
2
-
2
-
2
+
=
6
-
=
6
B
-
K
-
T
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
C
-
L
-
U
-
-
-
-
-
--
3
-
3
-
3
+
=
9
-
=
9
C
-
L
-
U
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
D
-
M
-
V
-
-
-
-
-
--
4
-
4
-
4
+
=
12
1+2
=
3
D
-
M
-
V
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
E
-
N
-
W
-
-
-
-
-
--
5
-
5
-
5
+
=
15
1+5
=
6
E
-
N
-
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
F
-
O
-
X
-
-
-
-
-
--
6
-
6
-
6
+
=
18
1+8
=
9
F
-
O
-
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
G
-
P
-
Y
-
-
-
-
-
--
7
-
7
-
7
+
=
21
2+1
=
3
G
-
P
-
Y
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
H
-
Q
-
Z
-
-
-
-
-
--
8
-
8
-
8
+
=
24
2+4
=
6
H
-
Q
-
Z
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
I
-
R
-
-
-
-
-
-
-
--
9
-
9
-
-
+
=
18
1+8
=
9
I
-
R
-
-
-
-
-
-
-
--
-
-
-
-
-
-
-
126
-
-
54
-
-
-
-
-
-
-
1+2+6
-
-
5+4
-
-
-
-
-
-
-
9
-
-
9

 

 

3
3
-
A+B+C
6
6
6
2
-
2
D+E
9
9
9
3
3
-
F+G+H
21
21
3
1
-
1
I
9
9
9
3
3
J+K+L
33
6
6
2
-
2
M+N
27
9
9
2
2
-
O+P
31
13
4
3
-
3
QRS
54
18
9
3
-
3
TUV
63
9
9
3
-
3
WXY
72
18
9
1
1
-
Z
26
8
8
26
12
14
First Total
351
126
81
2+6
1+2
1+4
Add to Reduce
3+5+1
1+2+6
8+1
8
3
5
Reduce to Deduce
9
9
9

 

 

3
A+B+C
6
6
6
-
D+E
-
-
-
3
F+G+H
21
21
3
-
I
-
-
-
3
J+K+L
33
6
6
-
M+N
-
-
-
2
O+P
31
13
4
-
QRS
-
-
-
-
TUV
-
-
-
-
WXY
-
-
-
1
Z
26
8
8
12
First Total
117
54
27
2+6
Add to Reduce
1+1+7
5+4
2+7
8
Reduce to Deduce
9
9
9

 

 

-
A+B+C
-
-
-
2
D+E
9
9
9
-
F+G+H
-
-
-
1
I
9
9
9
-
J+K+L
-
-
-
2
M+N
27
9
9
-
O+P
-
-
-
3
QRS
54
18
9
3
TUV
63
9
9
3
WXY
72
18
9
-
Z
-
-
-
14
First Total
234
72
54
1+4
Add to Reduce
2+3+4
7+2
5+4
5
Reduce to Deduce
9
9
9

 

 

-

4

ZERO

64

28

1
1
3

ONE
34
16
7
2
3

TWO
58
13
4
3
5

THREE
56
29
2
4
4

FOUR
60
24
6
5
4

FIVE
42
24
6
6
3

SIX
52
16
7
7
5

SEVEN
65
20
2
8
5

EIGHT
49
31
4
9
4

NINE
42
24
6
45
40
-
522
225
45
4+5
4+0
-
5+2+2
2+2+5
4+5
9
4
-
9
9
9

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
-
7
-
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
-
7
-
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
-
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
-
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
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
+
=
351
3+5+1
=
9
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
-
9
-
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
-
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
-
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

-
RAINBOW
-
-
-
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
7
RAINBOW
82
37
28
-
-
8+2
3+7
2+8
7
RAINBOW
10
10
10
-
-
1+0
1+0
1+0
7
RAINBOW
1
1
1

 

 

-
BE-A-RAINBOW
-
-
-
-
BE
7
7
7
-
A
1
1
1
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
9
BE-A-RAINBOW
90
45
36
-
-
9+0
4+5
3+6
9
BE-A-RAINBOW
9
9
9

 

 

1
B-RAINBOW
-
-
-
1
B
2
2
2
1
R
18
9
9
1
A
1
1
1
1
I
9
9
9
4
N+B+O+W
54
18
9
-
B-RAINBOW
-
-
-

 

 

-
BRAIN+BODY
-
-
-
-
B
2
2
2
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N
14
5
5
-
BODY
46
19
1
9
BRAIN+BODY
90
45
27
-
-
9+0
4+5
2+7
9
BRAIN+BODY
9
9
9

 

 

-
HEAD+BRAIN+BODY
-
-
-
4
HEAD
18
18
9
5
BRAIN
44
26
8
4
BODY
46
19
1
13
HEAD+BRAIN+BODY
108
63
18
1+3
-
1+0+8
6+3
1+8
4
HEAD+BRAIN+BODY
9
9
9

 

 

-
RAINBOW
-
-
-
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
7
RAINBOW
82
37
28
-
-
8+2
3+7
2+8
7
RAINBOW
10
10
10
-
-
1+0
1+0
1+0
7
RAINBOW
1
1
1

 

 

-
R-IN-A-BOW
-
-
-
-
R
18
9
9
-
IN
1
1
1
-
A
1
1
1
-
B+O+W
40
13
4
7
R-IN-A-BOW
82
37
28
-
-
8+2
3+7
2+8
7
R-IN-A-BOW
10
10
10
-
-
1+0
1+0
1+0
7
R-IN-A-BOW
1
1
1

 

 

-
RA-IN-BOW
-
-
-
-
R+A
19
10
1
-
I+N
23
14
5
-
B+O+W
40
13
4
7
RA-IN-BOW
82
37
28
-
-
8+2
3+7
2+8
7
RA-IN-BOW
10
10
10
-
-
1+0
1+0
1+0
7
RA-IN-BOW
1
1
1

 

 

--
7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
9
5
-
-
6
-
+
=
36
3+6
=
9
=
9
=
9
-
`-
-
-
-
9
14
-
-
15
-
+
=
81
8+1
=
9
=
9
=
9
--
7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
9
1
-
-
-
-
2
-
5
+
=
32
3+2
=
5
=
5
=
5
-
`-
18
1
-
-
-
-
2
-
23
+
=
85
8+5
=
14
1+4
5
=
5
--
7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
`-
18
1
-
9
14
-
2
15
23
+
=
82
8+2
=
10
1+0
1
=
1
-
-
9
1
-
9
5
-
2
6
5
+
=
37
3+7
=
10
1+0
1
=
1
-
7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
-
9
-
-
-
-
-
-
-
9
occurs
x
2
=
37
1+8
9
22
7
R
A
-
I
N
-
B
O
W
-
-
23
-
-
7
-
37
-
19
2+2
-
9
-
-
9
-
-
-
-
-
-
-
2+3
-
-
-
-
3+7
-
1+9
4
7
R
A
-
I
N
-
B
O
W
-
-
5
-
-
7
-
10
-
10
-
-
9
1
-
9
5
-
2
6
5
-
-
-
-
-
-
-
1+0
-
1+0
4
7
R
A
-
I
N
-
B
O
W
-
-
5
-
-
7
-
1
-
1

 

HURRAH FOR RAH FOR RAH HURRAH

 

7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
5
-
-
6
-
+
=
36
3+6
=
9
=
9
=
9
`-
-
-
-
9
14
-
-
15
-
+
=
81
8+1
=
9
=
9
=
9
7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
-
9
1
-
-
-
-
2
-
5
+
=
32
3+2
=
5
=
5
=
5
`-
18
1
-
-
-
-
2
-
23
+
=
85
8+5
=
14
1+4
5
=
5
7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
--
-
-
-
-
`-
18
1
-
9
14
-
2
15
23
+
=
82
8+2
=
10
1+0
1
=
1
-
9
1
-
9
5
-
2
6
5
+
=
37
3+7
=
10
1+0
1
=
1
7
R
A
-
I
N
-
B
O
W
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
5
-
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
-
9
-
-
9
-
-
-
-
-
-
-
9
occurs
x
2
=
37
1+8
9
7
R
A
-
I
N
-
B
O
W
-
-
23
-
-
7
-
37
-
19
-
9
-
-
9
-
-
-
-
-
-
-
2+3
-
-
-
-
3+7
-
1+9
7
R
A
-
I
N
-
B
O
W
-
-
5
-
-
7
-
10
-
10
-
9
1
-
9
5
-
2
6
5
-
-
-
-
-
-
-
1+0
-
1+0
7
R
A
-
I
N
-
B
O
W
-
-
5
-
-
7
-
1
-
1

 

 

--
7
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
-
-
9
5
-
6
-
+
=
36
3+6
=
9
=
9
=
9
-
`-
-
-
9
14
-
15
-
+
=
81
8+1
=
9
=
9
=
9
--
7
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
9
1
-
-
2
-
5
+
=
32
3+2
=
5
=
5
=
5
-
`-
18
1
-
-
2
-
23
+
=
85
8+5
=
14
1+4
5
=
5
--
7
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
`-
18
1
9
14
2
15
23
+
=
82
8+2
=
10
1+0
1
=
1
-
-
9
1
9
5
2
6
5
+
=
37
3+7
=
10
1+0
1
=
1
-
7
R
A
I
N
B
O
W
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
occurs
x
2
=
37
1+8
9
22
7
R
A
I
N
B
O
W
-
-
23
-
-
7
-
37
-
19
2+2
-
9
-
9
-
-
-
-
-
-
2+3
-
-
-
-
3+7
-
1+9
4
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
10
-
10
-
-
9
1
9
5
2
6
5
-
-
-
-
-
-
-
1+0
-
1+0
4
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
1
-
1

 

 

7
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
-
-
9
5
-
6
-
+
=
36
3+6
=
9
=
9
=
9
`-
-
-
9
14
-
15
-
+
=
81
8+1
=
9
=
9
=
9
7
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
-
9
1
-
-
2
-
5
+
=
32
3+2
=
5
=
5
=
5
`-
18
1
-
-
2
-
23
+
=
85
8+5
=
14
1+4
5
=
5
7
R
A
I
N
B
O
W
-
-
-
-
-
--
-
-
-
-
`-
18
1
9
14
2
15
23
+
=
82
8+2
=
10
1+0
1
=
1
-
9
1
9
5
2
6
5
+
=
37
3+7
=
10
1+0
1
=
1
7
R
A
I
N
B
O
W
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
5
-
-
5
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
6
-
-
-
6
occurs
x
1
=
6
=
6
-
9
-
9
-
-
-
-
-
-
9
occurs
x
2
=
37
1+8
9
7
R
A
I
N
B
O
W
-
-
23
-
-
7
-
37
-
19
-
9
-
9
-
-
-
-
-
-
2+3
-
-
-
-
3+7
-
1+9
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
10
-
10
-
9
1
9
5
2
6
5
-
-
-
-
-
-
-
1+0
-
1+0
7
R
A
I
N
B
O
W
-
-
5
-
-
7
-
1
-
1

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

-
RAINBOW
-
-
-
1
BRAIN
44
26
8
4
OW
54
18
9
7
RAINBOW
82
37
28
-
-
8+2
3+7
3+7
7
RAINBOW
10
10
10
-
-
1+0
1+0
1+0
7
RAINBOW
1
1
1

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
-
8
-
-
-
-
9
14
-
15
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
--
--
--
--
--
--
--
--
--
--
--
--
--
--
-
-
4
FOUR
4
-
-
-
-
-
--
--
--
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
4
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
-
1+5
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
4
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
4
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
8
-
-
-
-
9
14
-
15
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
--
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
1+5
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
6
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
9
5
-
6
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
8
-
-
-
9
14
-
15
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
2
-
5
9
1
-
-
2
-
5
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
20
-
5
18
1
-
-
2
-
23
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
20
8
5
18
1
9
14
2
15
23
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
2
8
5
9
1
9
5
2
6
5
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
-
-
-
-
2
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
--
-
5
-
-
-
5
-
-
5
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
15
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
1+5
-
-
-
9
-
9
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
6
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
2
8
5
9
1
9
5
2
6
5
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
6
T
H
E
R
A
I
N
B
O
W
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
-
8
-
-
14
-
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
-
1
-
4
-
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
-
20
18
21
20
-
-
1
-
4
-
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
-
1
14
4
-
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-T
-
2
9
3
2
8
-T
1
5
4
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
6
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
-
1+2
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
-
2
9
3
2
8
-
1
5
4
-
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
8
-
-
14
-
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
-
1
-
4
-
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
20
18
21
20
-
-
1
-
4
-
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
-
1
14
4
-
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-
2
9
3
2
8
-T
1
5
4
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
1+2
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
2
9
3
2
8
-
1
5
4
-
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
5
-
-
9
-
8
-
+
=
30
3+0
=
3
=
3
=
3
-
-
-
-
-
8
-
14
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
=
3
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
2
9
3
2
-
1
-
4
3
-
7
-
2
+
=
33
3+3
=
6
-
6
=
6
-
20
18
21
20
-
1
-
4
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
=
6
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
20
18
21
20
8
1
14
4
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
=
9
-
2
9
3
2
8
1
5
4
3
9
7
8
2
+
=
63
6+3
=
9
-
9
=
9
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
2
-
-
2
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
3
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
--
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
12
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
1+2
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
3
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
2
9
3
2
8
1
5
4
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
3
T
R
U
T
H
A
N
D
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

-
-
-
-
-
LIGHT
-
-
-
-
-
-
-
4
LIGH
36
27
9
-
-
-
-
1
T
20
2
2
L
=
3
-
5
LIGHT
56
29
11
-
-
1+0
-
-
-
5+6
2+9
1+1
-
-
1
-
9
LIGHT
11
11
7
-
-
1+0
-
-
-
1+1
1+1
-
-
-
1
-
9
LIGHT
2
2
2

 

 

-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
+
=
12
1+2
=
3
=
3
-
3
-
-
12
-
7
-
20
+
=
39
3+9
=
12
1+2
3
-
3
-
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
+
=
56
5+6
=
11
1+1
2
-
2
-
-
3
9
7
8
2
+
=
29
2+9
=
11
1+1
2
-
2
-
5
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
--
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
16
5
L
I
G
H
T
-
-
29
-
1
5
-
29
-
29
1+6
-
-
9
-
-
-
-
-
2+9
-
-
-
-
2+9
-
2+9
7
5
L
I
G
H
T
-
-
11
-
1
5
-
11
-
11
-
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
7
5
L
I
G
H
T
-
-
2
-
-
5
-
2
-
2

 

 

5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
+
=
12
1+2
=
3
=
3
-
3
-
12
-
7
-
20
+
=
39
3+9
=
12
1+2
3
-
3
5
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
12
9
7
8
20
+
=
56
5+6
=
11
1+1
2
-
2
-
3
9
7
8
2
+
=
29
2+9
=
11
1+1
2
-
2
5
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
--
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
5
L
I
G
H
T
-
-
29
-
1
5
-
29
-
29
-
-
9
-
-
-
-
-
2+9
-
-
-
-
2+9
-
2+9
5
L
I
G
H
T
-
-
11
-
1
5
-
11
-
11
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
5
L
I
G
H
T
-
-
2
-
-
5
-
2
-
2

 

 

L
=
3
-
6
LIVING
73
37
1
H
=
8
-
4
HEAT
34
16
7
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
-
163
82
10
-
-
1+4
-
1+5
-
1+6+3
8+2
1+0
-
-
5
-
6
-
10
10
1
-
-
-
-
-
-
1+0
1+0
-
-
-
5
-
6
-
1
1
9

 

 

L
=
3
-
6
LOVING
79
34
7
H
=
8
-
4
HEAT
34
16
7
L
=
3
-
5
LIGHT
56
29
2
-
-
14
-
15
-
169
79
16
-
-
1+4
-
1+5
-
1+6+9
7+9
1+6
-
-
5
-
6
-
16
10
7
-
-
-
-
-
-
1+6
1+0
-
-
-
5
-
6
-
7
7
7

 

 

P
=
7
-
4
PARTICLES
103
40
4
O
=
6
-
1
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
16
-
10
-
180
81
9
-
-
1+6
-
1+0
-
1+8+0
8+1
-
-
-
7
-
1
-
9
9
9

 

 

9
PARTICLES
103
40
4
2
OF
21
12
3
5
LIGHT
56
29
2
16
Add to Reduce
180
81
9
1+6
Reduce to Deduce
1+8+0
8+1
-
7
Essence of Number
9
9
9

 

 

-T
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-T
`-
-
-
-
-
9
-
-
-
1
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
-
`-
-
-
-
-
9
-
-
-
19
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
-
6
-
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
-
`-
16
1
18
20
-
3
12
5
-
-
-
6
-
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
-
15
6
-
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
-
7
1
9
2
9
3
3
5
1
-T
6
6
-T
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
-
7
1
9
2
9
3
-
5
1
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
-
9
-
-
-
1
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
-
9
-
-
-
19
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
-
6
-
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
`-
16
1
18
20
-
3
12
5
-
-
-
6
-
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
-
15
6
-
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
7
1
9
2
9
3
3
5
1
-T
6
6
-T
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
9
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
7
1
9
2
9
3
-
5
1
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
-
9
-
-
-
1
6
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
-
9
-
-
-
19
15
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
6
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
=
3
`-
16
1
18
20
-
3
12
5
-
-
6
12
-
7
-
20
+
=
120
1+2+0
=
3
=
3
=
3
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
15
6
12
9
7
8
20
+
=
180
1+8+0
=
9
=
9
=
9
-
7
1
9
2
9
3
3
5
1
6
6
3
9
7
8
2
+
=
81
8+1
=
9
=
9
=
9
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
3
3
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
--
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
7
1
9
2
9
3
-
5
1
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
16
P
A
R
T
I
C
L
E
S
O
F
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

-
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
1
+
=
18
1+8
=
9
=
9
=
9
-
`-
-
9
-
8
-
-
-
-
-
-
19
+
=
36
3+6
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
-
`-
12
-
7
-
20
-
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
-
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
3
9
7
8
2
-T
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
6
10
L
I
G
H
T
-
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
-
1+0
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
-
3
9
7
8
2
-
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
-
1
+
=
18
1+8
=
9
=
9
=
9
`-
-
9
-
8
-
-
-
-
-
-
19
+
=
36
3+6
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
-
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
`-
12
-
7
-
20
-
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
-
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
3
9
7
8
2
-T
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
L
I
G
H
T
-
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
1+0
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
3
9
7
8
2
-
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
1
L
I
G
H
T
-
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

10
L
I
G
H
T
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
-
-
-
-
-
1
+
=
18
-
=
9
=
9
=
9
`-
-
9
-
8
-
-
-
-
-
19
+
=
38
-
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-
-
-
-
-
-
-
-
-
-
-
3
-
7
-
2
5
1
4
5
-
+
=
27
2+7
=
9
=
9
=
9
`-
12
-
7
-
20
23
1
22
5
-
+
=
90
7+5
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
23
1
22
5
19
+
=
126
1+2+6
=
9
=
9
=
9
-
3
9
7
8
2
5
1
4
5
1
+
=
45
4+5
=
9
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
10
L
I
G
H
T
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
1+0
-
9
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
1
L
I
G
H
T
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
3
9
7
8
2
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
1
L
I
G
H
T
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

5
WAVES
70
16
7
9
PARTICLES
103
40
4

 

 

4
WAVE
51
15
6
9
PARTICLES
103
40
4
13
First Total
154
55
10
1+3
Add to Reduce
1+5+4
5+5
1+0
4
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
4
Essence of Number
1
1
1

 

 

W
=
5
4
WAVE
51
15
6
P
=
7
8
PARTICLE
84
39
3
-
-
12
12
Add to Reduce
135
54
9
-
-
1+2
1+2
Reduce to Deduce
1+3+5
5+4
-
-
-
3
3
Essence of Number
9
9
9

 

 

-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+4
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
5
1
4
5
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
=
9
=
9
-
23
1
22
5
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
23
1
22
5
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
=
9
=
9
-
5
1
4
5
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
=
9
=
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
5
-
-
5
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
12
W
A
V
E
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+2
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
3
W
A
V
E
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
5
1
4
5
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
3
W
A
V
E
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

S
=
1
-
5
SPEED
49
22
4
O
=
6
-
2
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
10
-
12
-
126
63
9
-
-
1+0
-
1+2
-
1+2+6
6+3
-
-
-
1
-
3
-
9
9
9

 

 

-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
6
-
-
-
9
-
8
-
+
=
24
2+4
=
6
=
6
=
6
-
-
19
-
-
-
-
-
15
-
-
-
9
-
8
-
+
=
51
5+1
=
6
=
6
=
6
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
7
5
5
4
-
-
6
-
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
16
5
5
4
-
-
6
-
12
-
7
-
20
+
=
75
7+5
=
12
1+2
3
=
3
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
19
16
5
5
4
-
15
6
-
12
9
7
8
20
+
=
126
1+2+6
=
9
=
9
=
9
--
-
1
7
5
5
4
-T
6
6
-T
3
9
7
8
2
+
=
63
6+3
=
9
=
9
=
9
-
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
--
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
27
=
9
45
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
45
-
1
12
-
81
-
36
4+5
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+2
-
8+1
-
3+4
9
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
1
3
-
9
-
9
-
-
1
7
5
5
4
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
-
3
-
9
-
9

 

 

-
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
6
-
-
9
-
8
-
+
=
24
2+4
=
6
=
6
=
6
-
-
19
-
-
-
-
15
-
-
9
-
8
-
+
=
51
5+1
=
6
=
6
=
6
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
7
5
5
4
-
6
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
-
-
-
16
5
5
4
-
6
12
-
7
-
20
+
=
75
7+5
=
12
1+2
3
=
3
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
19
16
5
5
4
15
6
12
9
7
8
20
+
=
126
1+2+6
=
9
=
9
=
9
--
-
1
7
5
5
4
6
6
3
9
7
8
2
+
=
63
6+3
=
9
=
9
=
9
-
12
S
P
E
E
D
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
--
-
7
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
27
=
9
45
12
S
P
E
E
D
O
F
L
I
G
H
T
-
-
45
-
1
12
-
81
-
36
4+5
1+2
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+2
-
8+1
-
3+4
9
3
S
P
E
E
D
O
F
L
I
G
H
T
-
-
9
-
1
3
-
9
-
9
-
-
1
7
5
5
4
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
3
S
P
E
E
D
O
F
L
I
G
H
T
-
-
9
-
-
3
-
9
-
9

 

 

16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
1
-
9
-
-
-
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
19
-
9
-
-
-
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
2
-
4
1
3
-
-
6
-
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
`-
-
6
5
-
20
-
22
1
12
-
-
6
-
12
-
7
-
20
+
=
111
1+1+1
=
3
=
3
=
3
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
6
5
19
20
9
22
1
12
-
15
6
-
12
9
7
8
20
+
=
171
1+7+1
=
9
=
9
=
9
-
-
6
5
1
2
9
4
1
3
-T
6
6
-T
3
9
7
8
2
+
=
72
7+2
=
9
=
9
=
9
16
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
3
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
6
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
15
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
45
-
1
15
-
72
-
54
4+5
1+5
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+5
-
7+2
-
5+4
9
6
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
9
-
1
6
-
9
-
9
-
-
6
5
1
2
9
4
1
3
-T
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
6
F
E
S
T
I
V
A
L
-
O
F
-
L
I
G
H
T
-
-
9
-
-
6
-
9
-
9

 

 

16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
-
-
1
-
9
-
-
-
6
-
-
9
-
8
-
+
=
33
3+3
=
6
=
6
=
6
`-
-
-
-
19
-
9
-
-
-
15
-
-
9
-
8
-
+
=
60
6+0
=
6
=
6
=
6
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
2
-
4
1
3
-
6
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
=
3
`-
-
6
5
-
20
-
22
1
12
-
6
12
-
7
-
20
+
=
111
1+1+1
=
3
=
3
=
3
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
`-
-
6
5
19
20
9
22
1
12
15
6
12
9
7
8
20
+
=
171
1+7+1
=
9
=
9
=
9
-
-
6
5
1
2
9
4
1
3
6
6
3
9
7
8
2
+
=
72
7+2
=
9
=
9
=
9
16
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
3
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
5
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
-
6
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
6
occurs
x
3
=
18
1+8
9
7
--
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
45
15
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
45
-
1
15
-
72
-
54
4+5
1+5
-
-
-
-
9
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+5
-
7+2
-
5+4
9
6
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
9
-
1
6
-
9
-
9
-
-
6
5
1
2
9
4
1
3
6
6
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
9
6
F
E
S
T
I
V
A
L
O
F
L
I
G
H
T
-
-
9
-
-
6
-
9
-
9

 

THE LIGHT IS RISING RISING IS THE LIGHT

 

 

T
=
2
-
3
THE
33
15
6
P
=
7
-
6
PEOPLE
69
33
6
T
=
2
-
4
THAT
49
13
4
W
=
5
-
6
WALKED
56
20
2
I
=
9
-
2
IN
23
14
5
D
=
4
-
8
DARKNESS
91
28
1
H
=
8
-
4
HAVE
36
18
9
S
=
1
-
4
SEEN
43
16
7
A
=
1
-
1
A
1
1
1
G
=
7
-
5
GREAT
51
24
6
L
=
3
-
5
LIGHT
56
29
2
-
-
49
4
48
First Total
508
211
49
-
-
4+9
-
4+8
Add to Reduce
5+0+8
2+1+1
4+9
Q
-
13
-
12
Second Total
13
4
13
-
-
1+3
-
1+2
Reduce to Deduce
1+3
-
1+3
-
-
4
4
3
Essence of Number
4
4
4

 

 

T
=
2
-
4
THEY
58
22
4
T
=
2
-
4
THAT
49
13
4
D
=
4
-
5
DWELL
56
20
23
T
=
2
-
2
IN
23
14
5
T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LAND
31
13
4
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SHADOW
70
25
7
O
=
6
-
2
OF
21
12
3
D
=
4
-
5
DEATH
38
20
2
U
=
3
3
4
UPON
66
21
3
T
=
2
4
4
THEM
46
19
1
H
=
8
4
4
HATH
37
19
1
T
=
2
3
3
THE
33
15
6
L
=
3
4
5
LIGHT
56
29
2
S
=
1
4
6
SHINED
59
32
5
-
-
60
4
66
First Total
730
316
64
-
-
6+0
-
6+6
Add to Reduce
7+3+0
3+1+6
6+4
Q
-
6
-
12
Second Total
10
10
10
-
-
-
-
1+2
Reduce to Deduce
1+0
1+0
1+0
-
-
6
4
3
Essence of Number
1
1
1

 

 

T
=
2
-
3
THE
33
15
6
P
=
7
-
6
PEOPLE
69
33
6
T
=
2
-
4
THAT
49
13
4
W
=
5
-
6
WALKED
56
20
2
I
=
9
-
2
IN
23
14
5
D
=
4
-
8
DARKNESS
91
28
1
H
=
8
-
4
HAVE
36
18
9
S
=
1
-
4
SEEN
43
16
7
A
=
1
-
1
A
1
1
1
G
=
7
-
5
GREAT
51
24
6
L
=
3
-
5
LIGHT
56
29
2
T
=
2
-
4
THEY
58
22
4
T
=
2
-
4
THAT
49
13
4
D
=
4
-
5
DWELL
56
20
23
T
=
2
-
2
IN
23
14
5
T
=
2
-
3
THE
33
15
6
L
=
3
-
4
LAND
31
13
4
O
=
6
-
2
OF
21
12
3
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SHADOW
70
25
7
O
=
6
-
2
OF
21
12
3
D
=
4
-
5
DEATH
38
20
2
U
=
3
3
4
UPON
66
21
3
T
=
2
4
4
THEM
46
19
1
H
=
8
4
4
HATH
37
19
1
T
=
2
3
3
THE
33
15
6
L
=
3
4
5
LIGHT
56
29
2
S
=
1
4
6
SHINED
59
32
5
-
-
109
4
114
First Total
1238
527
113
-
-
1+0+9
-
1+1+4
Add to Reduce
1+2+3+8
5+2+7
1+1+3
Q
-
10
-
6
Second Total
14
14
5
-
-
1+0
-
-
Reduce to Deduce
1+4
1+4
-
-
-
1
4
6
Essence of Number
5
5
5

 

 

-
THE RAINBOW LIGHT
-
-
-
3
THE
33
15
6
7
RAINBOW
82
37
1
5
LIGHT
56
29
2
15
THE RAINBOW LIGHT
171
81
9
1+5
-
1+7+1
8+1
-
6
THE RAINBOW LIGHT
9
9
9

 

 

15
THE RAINBOW LIGHT
-
-
-
-
THE
33
15
6
-
R
18
9
9
-
A
1
1
1
-
I
9
9
9
-
N+B+O+W
54
18
9
-
L
12
3
3
-
I
9
9
9
-
G+H+T
35
17
8
15
THE RAINBOW LIGHT
171
81
54
1+5
-
1+7+1
8+1
5+4
6
THE RAINBOW LIGHT
9
9
9

 

 

-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
--
-
-
-
-
-
8
-
-
-
-
9
5
-
6
-
-
-
9
-
8
-
+
+
45
4+5
=
9
=
9
=
9
-
-
-
8
-
-
-
-
9
14
-
15
-
-
-
9
-
8
-
+
+
63
6+3
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
--
-
--
-
-
--
-
2
-
5
-
9
1
-
-
2
-
5
-
3
-
7
-
14
+
+
36
3+6
=
9
=
9
=
9
-
-
20
-
5
-
18
1
-
-
2
-
23
-
12
-
7
-
20
+
+
108
1+0+8
=
9
=
9
=
9
-
15
T
H
E
--
R
A
I
N
B
O
W
--
L
I
G
H
T
-
-
-
-
-
--
-
--
-
-
-
-
20
8
5
-
18
1
9
14
2
15
23
-
12
9
7
8
20
+
+
171
1+7+1
=
9
=
9
=
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
+
+
81
8+1
=
9
=
9
=
9
-
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
-
-
--
-
-
2
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
--
-
-
-
-
-
-
-
--
--
--
--
--
--
--
--
4
--
--
--
--
--
--
--
-
-
-
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
-
-
-
-
--
--
--
--
--
--
--
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
9
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
2+7
9
4
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
41
-
-
15
-
81
-
45
-
-
-
-
5
-
-
-
-
5
-
-
5
-
-
-
-
-
-
-
-
4+1
-
-
1+5
-
8+1
-
4+5
4
15
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9
-
-
2
8
5
-
9
1
9
5
2
6
5
-
3
9
7
8
2
-
-
-
-
-
--
-
-
-
-
4
5
T
H
E
-
R
A
I
N
B
O
W
-
L
I
G
H
T
-
-
5
-
-
6
-
9
-
9

 

 

-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
`-
-
-
-
-
8
-
-
5
-
-
-
9
-
8
-
+
=
30
3+0
=
3
-
3
-
3
-
`-
-
-
-
-
8
-
-
14
-
-
-
9
-
8
-
+
=
39
3+9
=
12
1+2
3
-
3
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
2
9
3
2
-
-
1
-
4
-
3
-
7
-
2
+
=
33
3+3
=
6
-
6
-
6
-
`-
20
18
21
20
-
-
1
-
4
-
12
-
7
-
20
+
=
123
1+2+3
=
6
-
6
-
6
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
`-
20
18
21
20
8
-
1
14
4
-
12
9
7
8
20
+
=
162
1+6+2
=
9
-
9
-
9
-T
-
2
9
3
2
8
-T
1
5
4
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
-
9
-
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
2
-
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
-
-
-
-
3
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
2
=
6
=
6
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
--
-
-
1
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
18
1+8
9
6
12
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
39
-
1
12
-
54
-
45
-
1+2
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
3+9
-
-
1+2
-
5+4
-
4+5
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
12
-
1
3
-
9
-
9
-
-
2
9
3
2
8
-
1
5
4
-
3
9
7
8
2
-
-
1+2
-
-
-
-
-
-
-
6
3
T
R
U
T
H
-
A
N
D
-
L
I
G
H
T
-
-
3
-
-
3
-
9
-
9

 

 

-
-
-
1
-
LIGHT
-
-
-
-
-
-
-
4
LIGH
36
27
9
-
-
-
1
1
T
20
2
2
L
=
3
1
5
LIGHT
56
29
11
-
-
1+0
-
-
-
5+6
2+9
1+1
1
1
1
1
9
-
11
11
2
-
-
1+0
-
-
-
1+1
1+1
-
-
-
1
-
9
-
2
2
2

 

 

-
5
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
`-
-
9
-
8
-
+
=
17
1+7
=
8
-
8
-
8
-
5
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
3
-
7
-
2
+
=
12
1+2
=
3
=
3
-
3
-
`-
12
-
7
-
20
+
=
39
3+9
=
12
1+2
3
-
3
-
5
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
`-
12
9
7
8
20
+
=
56
5+6
=
11
1+1
2
-
2
-
-
3
9
7
8
2
+
=
29
2+9
=
11
1+1
2
-
2
-
5
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
--
-
-
7
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
9
=
9
16
5
L
I
G
H
T
-
-
29
-
1
5
-
29
-
29
1+6
-
-
9
-
-
-
-
-
2+9
-
-
-
-
2+9
-
2+9
7
5
L
I
G
H
T
-
-
11
-
1
5
-
11
-
11
-
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
7
5
L
I
G
H
T
-
-
2
-
-
5
-
2
-
2

 

 

P
=
7
-
4
PARTICLES
103
40
4
O
=
6
-
1
OF
21
12
3
L
=
3
-
5
LIGHT
56
29
2
-
-
16
-
10
-
180
81
9
-
-
1+6
-
1+0
-
1+8+0
8+1
-
-
-
7
-
1
-
9
9
9

 

 

-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
`-
-
-
-
-
9
-
-
-
1
-
6
-
-
-
9
-
8
-
+
=
33
3+3
=
6
-
6
-
6
-
`-
-
-
-
-
9
-
-
-
19
-
15
-
-
-
9
-
8
-
+
=
60
6+0
=
6
-
6
-
6
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
7
1
9
2
-
3
3
5
-
-
-
6
-
3
-
7
-
2
+
=
48
4+8
=
12
1+2
3
-
3
-
`-
16
1
18
20
-
3
12
5
-
-
-
6
-
12
-
7
-
20
+
=
120
1+2+0
=
3
-
3
-
3
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
`-
16
1
18
20
9
3
12
5
19
-
15
6
-
12
9
7
8
20
+
=
180
1+8+0
=
9
-
9
-
9
-
-
7
1
9
2
9
3
3
5
1
-T
6
6
-T
3
9
7
8
2
+
=
81
8+1
=
9
-
9
-
9
-
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
3
3
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
--
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
3
=
27
=
9
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
41
-
1
16
-
81
-
45
-
-
-
-
9
-
9
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+1
-
-
1+6
-
8+1
-
4+5
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
1
7
-
9
-
9
-
-
7
1
9
2
9
3
-
5
1
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
4
16
P
A
R
T
I
C
L
E
S
-
O
F
-
L
I
G
H
T
-
-
5
-
-
7
-
9
-
9

 

 

-T
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
--
-
-
-
-
-
`-
-
9
-
8
-
-
-
-
-
-
1
+
=
18
-
=
9
-
9
-
9
-
`-
-
9
-
8
-
-
-
-
-
-
19
+
=
38
-
=
9
-
9
-
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-
-
-
-
-
--
-
-
-
-
-
-
3
-
7
-
2
-
5
1
4
5
-
+
=
27
2+7
=
9
-
9
-
9
-
`-
12
-
7
-
20
-
23
1
22
5
-
+
=
90
7+5
=
9
-
9
-
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
`-
12
9
7
8
20
-
23
1
22
5
19
+
=
126
1+2+6
=
9
-
9
-
9
-
-
3
9
7
8
2
-T
5
1
4
5
1
+
=
45
4+5
=
9
-
9
-
9
-
10
L
I
G
H
T
-
W
A
V
E
S
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
5
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
--
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
=
9
6
10
L
I
G
H
T
-
W
A
V
E
S
-
-
39
-
1
12
-
45
-
36
-
1+0
-
9
-
-
-
-
-
-
-
-
-
-
-
3+9
-
-
1+2
-
4+5
-
3+6
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
12
-
1
3
-
9
-
9
-
-
3
9
7
8
2
-
5
1
4
5
1
-
-
1+2
-
-
-
-
-
-
-
6
1
L
I
G
H
T
-
W
A
V
E
S
-
-
3
-
-
3
-
9
-
9

 

 

5
WAVES
70
16
7
9
PARTICLES
103
40
4

 

 

4
WAVE
51
15
6
9
PARTICLES
103
40
4
13
First Total
154
55
10
1+3
Add to Reduce
1+5+4
5+5
1+0
4
Second Total
10
10
1
-
Reduce to Deduce
1+0
1+0
-
4
Essence of Number
1
1
1

 

 

W
=
5
4
WAVE
51
15
6
P
=
7
8
PARTICLE
84
39
3
-
-
12
12
Add to Reduce
135
54
9
-
-
 1+2 1+2
Reduce to Deduce
1+3+5
5+4
-
-
-
3
3
Essence of Number
9
9
9

 

 

-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
+
=
9
-
=
9
-
9
-
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
5
1
4
5
-
7
1
9
2
-
3
3
5
+
=
45
4+5
=
9
-
9
-
9
-
-
23
1
22
5
-
16
1
18
20
-
3
12
5
+
=
126
1+2+6
=
9
-
9
-
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
23
1
22
5
-
16
1
18
20
9
3
12
5
+
=
135
1+3+5
=
9
-
9
=
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
+
=
54
5+4
=
9
-
9
=
9
-
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
-
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
-
6
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
5
-
-
5
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
14
12
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
31
-
-
12
-
54
-
36
1+4
1+2
-
-
-
-
-
-
-
9
-
9
-
-
-
-
-
3+1
-
-
1+2
-
5+4
-
3+6
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9
-
-
5
1
4
5
-
7
1
9
2
9
3
3
5
-
-
-
-
-
-
-
-
-
-
5
3
W
A
V
E
-
P
A
R
T
I
C
L
E
-
-
4
-
-
3
-
9
-
9

 

 

S
=
1
5
SPEED
49
22
4
O
=
6
2
OF
21
12
3
L
=
3
5
LIGHT
56
29
2
-
-
10
12
-
126
63
9
-
-
1+0
1+2
-
1+2+6
6+3
-
-
-
1
3
-
9
9
9

 

 

12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
`-
1
-
-
-
-
-
6
-
-
-
9
-
8
-
+
=
24
2+4
=
6
-
6
-
6
`-
19
-
-
-
-
-
15
-
-
-
9
-
8
-
+
=
51
5+1
=
6
-
6
-
6
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
-
-
-
--
-
-
-
-
-
-
7
5
5
4
-
-
6
-
3
-
7
-
2
+
=
39
3+9
=
12
1+2
3
-
3
`-
-
16
5
5
4
-
-
6
-
12
-
7
-
20
+
=
75
7+5
=
12
1+2
3
-
3
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
`-
19
16
5
5
4
-
15
6
-
12
9
7
8
20
+
=
126
1+2+6
=
9
-
9
-
9
-
1
7
5
5
4
-T
6
6
-T
3
9
7
8
2
+
=
63
6+3
=
9
-
9
-
9
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
5
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
--
-
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
9
occurs
x
1
=
27
=
9
12
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
45
-
1
12
-
81
-
36
1+2
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
4+5
-
-
1+2
-
8+1
-
3+4
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
1
3
-
9
-
9
-
1
7
5
5
4
-
6
6
-
3
9
7
8
2
-
-
-
-
-
-
-
-
-
-
3
S
P
E
E
D
-
O
F
-
L
I
G
H
T
-
-
9
-
-
3
-
9
-
9

 

 

-
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
6
+
=
5
-
=
6
=
6
-
6
-
-
-
-
-
24
+
=
24
2+4
=
6
=
6
-
6
-
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
6
3
3
-
+
=
12
1+2
=
3
=
3
-
3
-
-
6
12
21
-
+
=
39
3+9
=
12
1+2
3
-
3
-
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
6
12
21
24
+
=
72
7+2
=
9
=
9
-
9
-
-
6
3
3
6
+
=
18
1+8
=
9
=
9
-
9
-
4
F
L
U
X
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
36
4
F
L
U
X
-
-
9
-
-
4
-
18
-
9
3+6
-
-
-
-
-
-
-
`-
-
-
-
-
1+8
-
`-
9
4
F
L
U
X
-
-
9
-
-
4
-
9
-
9

 

 

4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
+
=
5
-
=
6
=
6
-
6
-
-
-
-
24
+
=
24
2+4
=
6
=
6
-
6
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
6
3
3
-
+
=
12
1+2
=
3
=
3
-
3
-
6
12
21
-
+
=
39
3+9
=
12
1+2
3
-
3
4
F
L
U
X
-
-
-
-
-
--
-
-
-
-
-
6
12
21
24
+
=
72
7+2
=
9
=
9
-
9
-
6
3
3
6
+
=
18
1+8
=
9
=
9
-
9
4
F
L
U
X
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
-
3
occurs
x
2
=
6
=
6
-
6
-
-
6
-
-
6
occurs
x
2
=
12
1+2
3
4
F
L
U
X
-
-
9
-
-
4
-
18
-
9
-
-
-
-
-
-
-
`-
-
-
-
-
1+8
-
`-
4
F
L
U
X
-
-
9
-
-
4
-
9
-
9

 

 

q-
6
C
O
L
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
6
-
-
+
=
12
1+2
=
3
=
3
=
3
-
-
-
15
-
15
-
-
+
=
30
3+0
=
3
=
3
=
3
q-
6
C
O
L
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
3
-
3
-
3
9
+
=
18
1+8
=
9
=
9
=
9
-
-
3
-
12
-
21
18
+
=
54
5+4
=
9
=
9
=
9
q-
6
C
O
L
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
3
15
12
15
21
18
+
=
84
8+4
=
12
1+2
3
=
3
-
-
3
6
3
6
3
9
+
=
30
3+0
=
3
=
3
=
3
-
6
C
O
L
O
U
R
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
3
--
3
--
3
-
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
6
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
=
9
27
6
C
O
L
O
U
R
-
-
18
-
-
6
-
30
-
21
2+7
-
-
-
-
-
-
9
-
-
1+8
-
-
-
-
3+0
-
2+1
9
6
C
O
L
O
U
R
-
-
9
-
-
6
9
3
9
3
-
3
6
3
6
3
9
9
-
-
-
-
-
-
-
-
-
-
9
6
C
O
L
O
U
R
-
-
9
-
-
6
9
3
9
3

 

 

6
C
O
L
O
U
R
-
-
-
-
-
--
-
-
-
-
-
-
6
-
6
-
-
+
=
12
1+2
=
3
=
3
=
3
-
-
15
-
15
-
-
+
=
30
3+0
=
3
=
3
=
3
6
C
O
L
O
U
R
-
-
-
-
-
--
-
-
-
-
-
3
-
3
-
3
9
+
=
18
1+8
=
9
=
9
=
9
-
3
-
12
-
21
18
+
=
54
5+4
=
9
=
9
=
9
6
C
O
L
O
U
R
-
-
-
-
-
--
-
-
-
-
-
3
15
12
15
21
18
+
=
84
8+4
=
12
1+2
3
=
3
-
3
6
3
6
3
9
+
=
30
3+0
=
3
=
3
=
3
6
C
O
L
O
U
R
-
-
-
-
-
-
-
-
-
-
-
3
--
3
--
3
-
-
-
3
occurs
x
3
=
9
=
9
-
-
6
-
6
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
9
-
-
9
occurs
x
1
=
9
=
9
6
C
O
L
O
U
R
-
-
18
-
-
6
-
30
-
21
-
-
-
-
-
-
9
-
-
1+8
-
-
-
-
3+0
-
2+1
6
C
O
L
O
U
R
-
-
9
-
-
6
9
3
9
3
3
6
3
6
3
9
9
-
-
-
-
-
-
-
-
-
-
6
C
O
L
O
U
R
-
-
9
-
-
6
9
3
9
3

 

 

9
PARTICLES
103
40
4
2
OF
21
12
3
5
LIGHT
56
29
2
16
Add to Reduce
90
81
9
1+6
Reduce to Deduce
9+0
8+1
-
7
Essence of Number
9
9
9

 

 

C
=
3
-
4
COAT
39
12
3
O
=
6
-
2
OF
21
12
3
M
=
4
--
4
MANY
53
17
8
C
=
3
-
7
COLOURS
103
31
4
-
-
16
-
17
-
216
90
18
-
-
1+6
-
1+7
-
2+1+6
8+1
1+8
--
--
7
--
8
--
9
9
9

 

 

q-
17
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
-
6
-
-
-
-
5
-
-
-
6
-
6
-
-
1
+
=
30
3+0
=
3
=
3
=
3
-
-
-
15
-
-
-
15
-
-
-
-
14
-
-
-
15
-
15
-
-
19
+
=
93
9+3
=
12
1+2
3
=
3
q-
17
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
--
-
-
-
-
-
-
3
-
1
2
-
-
6
-
4
1
-
7
-
3
-
3
-
3
9
-
+
=
42
4+8
=
42
4+2
6
=
3
-
-
3
-
1
20
-
-
6
-
13
1
-
25
-
3
-
12
-
21
18
-
+
=
123
1+2+3
=
6
=
6
=
6
q-
17
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
--
-
-
-
-
-
-
3
15
1
20
-
15
6
-
13
1
14
25
-
3
15
12
15
21
18
19
+
=
216
2+1+6
=
9
=
9
=
9
-
-
3
6
1
2
-
6
6
-
4
1
5
7
-
3
6
3
6
3
9
1
+
=
72
7+2
=
9
=
9
=
9
-
17
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
-
-
-
-
-
q-
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
3
=
3
=
3
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
--
-
-
-
--
-
-
-
-
-
-
-
3
--
3
--
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
q-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
6
6
-
-
-
-
-
-
-
6
-
6
-
-
-
-
-
6
occurs
x
5
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
9
occurs
x
1
=
9
=
9
8
17
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
37
-
-
6
-
72
-
36
-
1+7
-
6
-
-
-
6
6
-
-
-
-
-
-
-
6
-
6
-
-
-
-
-
3+7
-
-
-
-
7+2
-
3+1
8
8
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
10
-
-
6
-
72
-
9
-
3
6
1
2
-
6
6
-
4
1
5
7
-
3
6
3
6
3
9
1
-
-
1+0
-
-
-
-
-
-
-
8
6
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
1
-
-
6
9
9
9
9

 

 

q-
21
G
O
D
S
-
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
1
-
-
6
-
-
-
6
-
-
-
-
5
-
-
-
6
-
6
-
-
1
+
=
37
3+7
=
10
1+0
1
=
1
-
-
-
15
-
19
-
-
15
-
-
-
15
-
-
-
-
14
-
-
-
15
-
15
-
-
19
+
=
127
1+2+7
=
10
1+0
1
=
1
q-
21
G
O
D
S
-
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
--
-
-
-
-
-
-
7
-
4
-
-
3
-
1
2
-
-
6
-
4
1
-
7
-
3
-
3
-
3
9
-
+
=
53
5+3
=
8
=
8
=
8
-
-
7
-
4
-
-
3
-
1
20
-
-
6
-
13
1
-
25
-
3
-
12
-
21
18
-
+
=
134
1+3+4
=
8
=
8
=
8
q-
21
G
O
D
S
-
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
--
-
-
-
-
-
-
7
15
4
19
-
3
15
1
20
-
15
6
-
13
1
14
25
-
3
15
12
15
21
18
19
+
=
261
2+6+1
=
9
=
9
=
9
-
-
7
6
4
1
-
3
6
1
2
-
6
6
-
4
1
5
7
-
3
6
3
6
3
9
1
+
=
90
9+0
=
9
=
9
=
9
-
21
G
O
D
S
-
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
-
-
-
-
-
-
-
-
q-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
4
=
4
=
4
-
``-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
3
--
-
-
-
--
-
-
-
-
-
-
-
3
--
3
--
3
-
-
-
-
3
occurs
x
4
=
12
1+2
3
q-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
6
-
-
-
6
6
-
-
-
-
-
-
-
6
-
6
-
-
-
-
-
6
occurs
x
6
=
36
3+6
9
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
9
occurs
x
1
=
9
=
9
8
21
G
O
D
S
-
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
37
-
-
21
-
90
-
45
-
2+1
-
-``
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
3+7
-
-
2+1
-
9+0
-
4+5
8
3
G
O
D
S
-
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
10
-
-
3
-
9
-
9
-
-
7
6
4
1
-
3
6
1
2
-
6
6
-
4
1
5
7
-
3
6
3
6
3
9
1
-
-
1+0
-
-
-
-
-
-
-
8
3
G
O
D
S
-
C
O
A
T
-
O
F
-
M
A
N
Y
-
C
O
L
O
U
R
S
-
-
1
-
-
3
9
9
9
9

 

 

-
19
E
A
C
H
-
F
O
R
-
A
L
L
-
A
L
L
-
F
O
R
-
G
O
D
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
6
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
6
-
+
=
26
2+6
=
8
=
8
=
8
-
-
-
-
-
8
-
-
15
-
-
-
-
-
-
-
-
-
-
-
15
-
-
-
15
-
+
=
53
5+3
=
8
=
8
=
8
-
19
E
A
C
H
-
F
O
R
-
A
L
L
-
A
L
L
-
F
O
R
-
G
O
D
-
-
-
-
-
--
-
-
-
-
-
-
5
1
3
-
-
6
-
9
-
1
3
3
-
1
3
3
-
6
-
9
-
7
-
4
+
=
64
6+4
=
10
 1+0
1
=
1
-
-
5
1
3
-
-
6
-
18
-
1
12
12
-
1
12
12
-
6
-
18
-
7
-
4
+
=
118
1+1+8
=
10
1+0
1
=
1
-
19
E
A
C
H
-
F
O
R
-
A
L
L
-
A
L
L
-
F
O
R
-
G
O
D
-
-
-
-
-
--
-
-
-
-
-
-
5
1
3
8
-
6
15
18
-
1
12
12
-
1
12
12
-
6
15
18
-
7
15
4
+
=
171
1+7+1
=
90
9+0
9
=
9
-
-
5
1
3
8
-
6
6
9
-
1
3
3
-
1
3
3
-
6
6
9
-
7
6
4
+
=
90
9+0
=
9
=
9
=
9
-
19
E
A
C
H
-
F
O
R
-
A
L
L
-
A
L
L
-
F
O
R
-
G
O
D
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
3
-
-
3
3
-
-
-
-
-
-
-
-
-
-
3
occurs
x
5
=
15
1+5
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
4
occurs
x
1
=
4
=
4
-
-
5
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
-
5
-
-
-
-
-
-
-
6
6
-
-
-
-
-
-
-
-
-
-
6
6
-
-
-
6
-
-
-
6
occurs
x
5
=
30
3+0
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
7
occurs
x
1
=
7
-
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
2
19
E
A
C
H
-
F
O
R
-
A
L
L
-
A
L
L
-
F
O
R
-
G
O
D
-
-
43
-
-
19
-
90
-
45
-
1+9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
4+3
-
-
1+0
-
9+0
-
4+5
2
10
E
A
C
H
-
F
O
R
-
A
L
L
-
A
L
L
-
F
O
R
-
G
O
D
-
-
7
-
-
1
-
9
-
9
-
1+0
5
1
3
8
-
6
6
9
-
1
3
3
-
1
3
3
-
6
6
9
-
7
6
4
-
-
-
-
-
-
-
-
-
-
2
1
E
A
C
H
-
F
O
R
-
A
L
L
-
A
L
L
-
F
O
R
-
G
O
D
-
-
7
-
-
1
-
9
-
9

 

 

-
5
G
O
D
-
I
S
-
-
-
-
-
--
-
-
-````
-
-
6
-
-
9
1
+
=
16
1+6
=
7
=
7
-
-
-
15
-
-
9
19
+
=
43
4+3
=
7
=
7
-
5
G
O
D
-
I
S
-
-
-
-
-
-
-
-
-
-
7
-
4
-
-
-
+
=
11
1+1
=
2
=
2
-
5
G
O
D
-
I
S
-
-
-
-
-
--
-
-
-
-
7
15
4
-
9
19
+
=
54
5+4
=
9
=
9
-
-
7
6
4
-
9
1
+
=
27
2+7
=
9
=
9
-
5
G
O
D
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
5
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
--
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
-
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
18
5
G
O
D
-
I
S
-
-
17
-
-
5
-
27
1+8
-
-
-
-
-
9
-
-
-
1+7
-
-
-
-
2+7
9
5
G
O
D
-
I
S
-
-
8
-
-
5
-
9

 

 

5
G
O
D
-
I
S
-
-
-
-
-
--
-
-
-
-
6
-
-
9
1
+
=
16
1+6
=
7
=
7
-
-
15
-
-
9
19
+
=
43
4+3
=
7
=
7
5
G
O
D
-
I
S
-
-
-
-
-
-
-
-
-
7
-
4
-
-
-
+
=
11
1+1
=
2
=
2
5
G
O
D
-
I
S
-
-
-
-
-
--
-
-
-
7
15
4
-
9
19
+
=
54
5+4
=
9
=
9
-
7
6
4
-
9
1
+
=
27
2+7
=
9
=
9
5
G
O
D
-
I
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
-
-
-
4
-
-
-
-
-
4
occurs
x
1
=
4
-
-
6
-
-
-
-
-
-
6
occurs
x
1
=
6
-
7
-
-
-
-
-
-
-
7
occurs
x
1
=
7
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
5
G
O
D
-
I
S
-
-
17
-
-
5
-
27
-
-
-
-
-
9
-
-
-
1+7
-
-
-
-
2+7
5
G
O
D
-
I
S
-
-
8
-
-
5
-
9

 

 

-
9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
-
-
6
1
-
6
1
+
=
22
2+2
=
4
=
4
-
4
-
`-
-
8
-
-
-
15
19
-
15
19
+
=
76
7+6
=
13
1+3
4
-
4
-
9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
2
-
5
-
3
-
-
4
-
-
+
=
14
1+4
=
5
1+0
5
-
5
-
`-
20
-
5
-
3
-
-
13
-
-
+
=
41
4+1
=
5
=
5
-
5
-
9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
`-
20
8
5
-
3
15
19
13
15
19
+
=
117
1+1+7
=
9
-
9
-
9
-
-
2
8
5
-
3
6
1
4
6
1
+
=
36
3+6
=
9
1+0
9
-
9
-
9
T
H
E
-
C
O
S
M
O
S
T
-
-
-
-
-
-
-
-
-
--
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-2-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
--
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
--
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
--
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
7
-
7
7
-
-
-
9
-
-
-
-
-
-
-
16
9
T
H
E
-
C
O
S
M
O
S
-
-
29
-
-
9
-
36
-
27
1+6
-
-
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
-
-
3+6
-
2+7
7
9
T
H
E
-
C
O
S
M
O
S
-
-
11
-
-
9
-
9
-
9
-
-
2
8
5
-
3
6
1
4
6
1
-
 -
1+1
-
-
-
-
-
-
-
7
9
T
H
E
-
C
O
S
M
O
S
-
-
2
-
-
9
-
9
-
9

 

 

9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
8
-
-
-
6
1
-
6
1
+
=
22
2+2
=
4
=
4
-
4
`-
-
8
-
-
-
15
19
-
15
19
+
=
76
7+6
=
13
1+3
4
-
4
9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
2
-
5
-
3
-
-
4
-
-
+
=
14
1+4
=
5
1+0
5
-
5
`-
20
-
5
-
3
-
-
13
-
-
+
=
41
4+1
=
5
=
5
-
5
9
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
`-
20
8
5
-
3
15
19
13
15
19
+
=
117
1+1+7
=
9
-
9
-
9
-
2
8
5
-
3
6
1
4
6
1
+
=
36
3+6
=
9
1+0
9
-
9
9
T
H
E
-
C
O
S
M
O
S
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
T
H
E
-
C
O
S
M
O
S
-
-
29
-
-
9
-
36
-
27
-
-
-
-
-
-
-
-
-
-
-
-
-
2+9
-
-
-
-
3+6
-
2+7
9
T
H
E
-
C
O
S
M
O
S
-
-
11
-
-
9
-
9
-
9
-
2
8
5
-
3
6
1
4
6
1
-
 -
1+1
-
-
-
-
-
-
-
9
T
H
E
-
C
O
S
M
O
S
-
-
2
-
-
9
-
9
-
9

 

 

-
14
G
O
D
-
I
S
-
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
9
1
-
-
8
-
-
-
6
1
-
6
1
+
=
38
1+6
=
11
1+1
2
1+1
2
-
-
-
15
-
-
9
19
-
-
8
-
-
-
15
19
-
15
19
+
=
119
1+1+9
=
11
1+1
2
1+1
2
-
14
G
O
D
-
I
S
-
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
-
-
-
-
-
-
-
7
-
4
-
-
-
-
2
-
5
-
3
-
-
4
-
-
+
=
25
2+5
=
7
=
7
=
7
-
-
7
-
4
-
-
-
-
20
-
5
-
3
-
-
13
-
-
+
=
52
1+1
=
7
=
7
=
7
-
14
G
O
D
-
I
S
-
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
--
-
-
-
-
-
-
7
15
4
-
9
19
-
20
8
5
-
3
15
19
13
15
19
+
=
171
1+7+1
=
9
=
9
=
9
-
-
7
6
4
-
9
1
-
2
8
5
-
3
6
1
4
6
1
+
=
63
6+3
=
9
=
9
=
9
-
14
G
O
D
-
I
S
-
T
H
E
-
C
O
S
M
O
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
3
=
3
=
3
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
4
occurs
x
2
=
8
=
8
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
6
--
-
6
-
-
-
-
-
-
-
-
-
-
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
9
-
-
-
-
-
-
-
7
-
7
7
-
-
-
9
occurs
x
1
=
9
=
9
45
14
G
O
D
-
I
S
-
T
H
E
-
C
O
S
M
O
S
-
-
45
-
-
14
-
63
-
54
4+5
1+4
-
-
-
-
9
-
-
-
-
-
-
-
7
-
7
7
-
-
-
4+5
-
-
 1+4
-
6+3
-
5+4
9
5
G
O
D
-
I
S
-
T
H
E
-
C
O
S
M
O
S
-
-
9
-
-
5
-
9
-
9
-
-
7
6
4
-
9
1
-
2
8
5
-
3
6
1
4
6
1
-
-
-
-
-
-
-
-
-
-
9
5
G
O
D
-
I
S
-
T
H
E
-
C
O
S
M
O
S
-
-
9
-
-
5
-
9
-
9

 

 
 
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