unit 5: machine learning & ai · midterm 2 ‣ in class, monday ... 42 37 173 170 157 147 147...
TRANSCRIPT
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March 2nd, 2016
Dave Abel
Unit 5: Machine Learning & AI
Midterm
2
‣ In class, Monday, March 21st.
‣ 50 Minutes long.
‣ Mostly short answer similar to homeworks. Some multiple choice.
‣ Covers Unit 0 (Binary) through Unit 6 (Vision/NLP).
‣ Review Session, Saturday, March 19th, 4:30pm. Room TBD.
‣ Material from Lecture, Homeworks, Labs.
‣ I’ll release some practice questions and sheets that summarize each unit.
Machine Learning
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‣ Problem: Classification
- INPUT: Some labeled training data, set of labels.
- OUTPUT: A classifier.
‣ Algorithm: Memorize and Guess
- Make a classifier that remembers all of the training data’s labels.
- Given a new item, if it’s the same as one of the training data, then report that training data’s item. If not, guess randomly.
Machine Learning: Features
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Dog
Not a Dog
Machine Learning: Features
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0 0 1 0 2 12 7 0 0 0 0 0 0 0 0 0 0 0 4 0 4 20 9 0 0 0 0 0 0 0 2 4 0 0 8 0 5 17 8 0 0 0 0 0 0 0 11 20 11 2 15 1 4 8 3 0 0 0 0 0 0 1 18 37 25 7 24 2 3 6 9 6 0 0 0 0 0 1 18 38 26 6 30 3 1 22 41 30 1 0 0 0 0 0 9 19 19 6 29 3 0 12 37 34 1 0 0 0 0 0 2 3 13 4 45 6 0 2 21 24 0 0 0 0 0 0 0 2 11 2 57 5 0 0 7 9 0 0 0 0 0 2 0 2 8 2 53 3 0 0 0 0 0 0 0 0 2 6 1 5 13 3 40 1 0 0 0 0 0 0 0 1 1 2 0 6 9 1 34 0 0 1 11 15 2 0 0 0 0 0 0 4 4 0 31 1 1 2 26 48 15 2 5 16 8 0 0 0 0 0 14 1 19 8 16 41 21 5 23 47 22 0 0 0 0 0 6 6 35 15 4 20 9 2 41 57 25 1 0 0 0 0 5 10 34 18 2 11 1 9 46 35 12 1 0 0 0 0 3 9 45 28 2 13 4 18 28 5 2 0 0 0 0 0 3 9 43 30 1 10 25 27 10 1 0 0 0 0 0 0 8 5 34 22 0 7
36 24 2 0 0 0 0 0 0 0 5 8 28 13 0 3 25 19 1 4 16 1 0 0 0 0 0 11 36 11 0 0 14 15 2 5 19 1 0 0 0 0 0 10 44 8 0 0 3 3 0 1 3 0 0 0 0 0 0 6 34 6 0 0 0 0 0 0 0 0 0 0 0 0 0 1 29 14 1 0 0 0 0 0 0 0 1 0 0 0 1 1 21 38 11 0 0 0 0 0 0 5 23 9 0 0 2 3 7 32 19 0 0 0 0 0 0 7 46 29 0 0 3 5 2 8 9 0 1 4 2 0 0 8 55 39 0 0 1 0 0 13 20 9 6 35 21 1 0 11 75 54 2 1 2 0 3 24 31 34 13 66 67 11 0 8 44 36 21 4 16 9 18 10 16 27 6 57 75 17 0 1 3 21 40 8 16 23 29 5 1 3 1 13 9 1 0 0 0 18 42 11 Columns 385 through 400 47 47 49 49 52 53 54 54 56 56 56 56 57 56 55 55 47 47 49 49 51 54 54 54 56 56 56 56 57 56 55 55 46 48 48 49 51 54 54 55 56 56 56 56 57 56 55 55 46 47 48 49 51 53 54 54 56 56 56 56 57 56 55 55 45 46 48 48 51 52 53 54 56 56 56 56 57 56 55 54 45 46 47 48 50 53 53 54 56 56 55 56 57 56 55 55 45 46 47 48 50 52 53 53 55 55 55 56 57 56 55 55 44 45 46 48 49 50 52 53 53 53 55 55 55 54 54 54 43 44 46 47 48 49 51 52 53 53 55 55 54 53 53 54 43 45 46 46 47 48 51 52 53 53 55 55 54 53 53 54 43 44 45 46 47 48 50 52 52 52 54 54 53 53 52 52 43 43 45 47 48 48 49 51 52 52 52 52 52 53 52 52 42 44 44 46 47 47 49 51 51 52 52 52 52 52 52 51 42 44 44 46 47 48 48 51 51 52 52 52 51 52 51 50 43 44 45 46 46 47 49 50 51 51 51 51 51 50 49 49 43 44 45 46 46 47 48 49 51 51 51 52 51 50 49 49 43 44 45 45 46 47 48 49 51 50 51 51 51 50 49 49 44 44 45 45 46 47 48 48 49 50 51 51 51 50 49 48 44 44 45 45 46 47 48 48 48 47 49 49 50 49 49 48 44 45 45 46 46 46 47 48 49 48 48 47 48 47 47 47 43 45 45 46 46 46 46 47 48 47 48 48 46 46 46 45 43 45 46 47 46 46 46 46 46 46 46 47 46 46 45 45 43 44 44 45 45 46 46 46 46 46 46 46 46 46 45 44 41 43 44 44 45 46 46 46 46 46 45 45 45 45 45 43 41 40 41 42 43 43 44 44 44 44 44 44 45 44 43 43 40 42 42 43 43 42 42 42 43 42 42 42 43 42 42 40 39 40 41 41 41 41 40 40 40 40 40 40 41 40 39 38 39 39 39 39 40 41 40 39 39 39 39 39 40 40 39 37 39 40 40 39 40 39 38 38 39 39 38 38 39 39 38 36 38 40 40 39 39 40 39 38 38 37 37 37 37 36 35 35 37 39 39 38 38 38 38 38 37 37 37 36 36 35 35 34 35 37 36 36 36 37 37 35 36 36 36 35 35 34 33 32 35 35 34 36 36 35 35 34 35 34 34 34 33 32 31 33 35 34 35 35 35 34 34 34 34 33 33 33 32 31 31 30 33 32 33 35 35 34 32 32 34 33 32 32 31 30 29 28 32 30 31 31 32 33 31 31 32 31 31 30 29 29 28 26 29 28 29 30 30 29 28 28 30 29 29 28 27 27 26 26 28 28 28 28 28 27 26 27 26 26 26 25 25 23 23 23 24 26 26 27 27 25 25 24 25 25 25 24 23 22 22 21 22 21 21 23 24 25 24 24 24 23 23 22 21 20 20 17 21 19 20 20 21 22 21 21 21 20 20 19 18 17 17 15 16 15 16 17 18 18 17 17 17 17 16 16 15 14 13 12 14 14 13 15 15 16 16 15 13 13 12 12 12 12 11 9 12 13 13 12 12 13 13 12 12 11 10 10 11 10 10 8 8 8 8 7 8 9 9 8 10 9 8 7 7 6 6 8 4 6 5 6 5 6 6 6 7 7 6 5 4 4 4 6 2 3 3 4 4 4 5 6 5 5 5 4 3 3 3 2 2 1 1 3 3 2 3 3 4 4 4 3 2 1 1 1 1 0 0 2 2 1 2 2 2 1 2 2 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 1 1 1 1 1 0 0 1 2 2 2 2 2 2 2 3 3 3 3 2 2 2 1 3 3 3 3 3 4 4 4 5 5 5 4 3 3 2 2 5 5 5 5 5 6 6 6 6 6 6 6 5 5 4 4 6 7 6 7 7 6 6 7 7 6 7 7 7 6 5 6 6 10 9 9 9 9 8 9 9 9 9 9 8 7 7 7 7 8 7 7 8 10 10 10 10 10 10 9 8 8 8 8 8 8 7 7 10 12 11 11 10 10 11 10 10 10 9 9 10 11 11 12 10 9 9 9 8 8 9 8 7 6 7 9 10 9 9 9 9 9 8 8 8 8 7 8 7 6 7 9 7 9 9 9 10 9 9 9 9 9 9 8 7 7 7 9 6 7 7 9 10 11 10
9 9 9 9 8 7 8 9 10 6 6 9 11 11 10 11 11 9 9 9 9 9 11 12 11 4 5 7 9 11 11 10 11 10 10 9 9 9 11 12 12 2 2 5 8 10 13 12 11 11 11 10 9 8 11 12 12 3 4 2 5 7 10 10 8 8 8 7 9 9 9 9 11 3 4 4 4 5 8 7 7 6 6 8 9 9 8 9 11 2 3 3 3 4 5 4 5 7 6 9 9 8 7 8 9 2 3 2 3 3 2 2 3 6 5 7 8 8 7 7 7 1 2 1 2 2 1 4 5 6 6 4 6 9 7 7 6 2 2 0 2 1 1 3 4 5 5 3 5 7 6 5 6 3 2 1 2 1 1 3 4 4 4 3 5 7 5 5 5 3 2 1 0 0 1 1 2 2 2 3 3 4 3 3 3 2 2 1 0 0 1 1 0 0 1 3 3 2 2 1 0 0 2 1 1 0 1 0 0 0 0 2 2 2 2 1 0 1 2 1 1 0 1 0 0 0 0 2 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 2 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 2 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 3 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 2 0 2 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 2 1 1 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 10 11 6 2 1 0 0 0 0 0 0 0 0 0 0 0 13 13 11 7 5 2 1 0 0 0 0 0 0 0 0 0 14 13 11 10 7 4 2 0 0 0 0 0 0 0 0 0 15 14 13 11 7 5 3 1 0 0 0 0 0 0 0 0 15 13 12 9 7 5 3 1 0 0 0 0 0 0 0 0 18 13 11 8 8 9 5 2 1 0 0 0 0 0 0 0 19 16 15 13 10 7 4 3 1 0 0 0 0 0 0 0 19 17 17 15 11 8 6 4 1 0 0 0 0 0 0 0 21 18 16 16 12 8 5 2 0 0 0 0 0 0 0 0 17 15 14 12 10 8 5 1 0 0 0 0 0 0 0 0 15 14 11 10 7 5 1 0 0 0 0 0 0 0 0 0 13 11 8 6 4 2 0 0 0 0 0 0 0 0 0 0 13 13 8 3 1 0 0 0 0 0 0 0 0 0 0 0 11 9 7 2 1 0 0 0 0 0 0 0 0 0 0 0 9 6 4 1 0 0 0 0 0 0 0 0 0 0 0 0 8 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 7 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 9 7 3 0 0 0 0 0 0 0 0 0 0 0 0 0 15 12 7 4 1 1 0 0 0 0 0 0 0 0 0 0 19 17 13 8 5 3 1 0 0 0 0 0 0 0 0 0 23 23 19 15 11 9 6 3 1 0 0 0 0 0 0 0 27 26 24 20 18 14 12 10 6 4 2 2 1 1 1 3 30 31 28 26 23 21 18 16 15 12 9 9 8 8 7 8 34 33 33 31 29 25 22 20 19 18 16 15 14 14 13 11 34 34 35 35 32 27 26 23 23 22 20 18 19 18 18 16 35 35 35 36 34 32 31 29 26 27 26 24 22 20 20 20 36 36 36 37 37 35 34 32 29 30 29 27 24 23 21 20 38 36 36 37 36 35 34 32 30 31 31 30 28 25 23 22 37 36 36 37 36 35 34 32 31 31 33 30 29 25 23 22 35 36 36 37 36 35 34 32 31 31 31 31 29 25 24 22 34 35 35 36 36 34 33 31 31 31 29 29 28 25 23 22 31 33 33 33 34 33 32 29 29 29 27 27 27 25 22 21 28 30 30 30 30 30 29 27 27 27 26 26 25 22 20 19 27 28 29 29 28 28 26 25 26 26 25 25 24 21 19 18 24 26 26 28 29 28 27 26 24 24 23 23 22 19 19 17 24 23 24 26 26 25 24 22 23 23 22 21 20 18 17 16 22 23 23 24 24 24 23 23 22 22 20 20 19 17 16 15 20 23 23 24 24 24 23 22 21 21 20 18 18 16 15 13 17 20 21 24 24 24 23 22 21 19 18 16 18 16 14 10 12 17 19 22 23 24 23 21 21 19 18 16 17 15 13 10 9 15 18 21 22 23 23 21 21 17 17 16 16 14 12 11 7 9 13 19 21 22 22 22 21 18 17 17 17 13 12 12 2 4 9 14 18 19 19 19 20 17 16 14 14 11 9 15 0 0 5 12 15 17 17 17 15 12 11 10 10 6 8 17 0 0 2 8 10 11 13 14 13 15 11 9 6 4 5 19 0 0 0 4 7 6 7 6 9 18 11 5 2 3 7 17 0 0 0 0 2 4 3 3 6 9 4 2 1 2 7 16 0 0 0 0 0 0 0 1 2 0 0 0 0 2 6 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 18 2 0 0 0 0 2 0 0 0 0 0 0 0 0 9 66 12 0 0 0 1 6 6 0 0 0 0 0 0 0 2 22 5 0 0 0 2 10 18 1 0 0 0 0 0 0 0 0 0 0 0 0 4 13 3 0 0 0 0 0 0 0 0 0 0 0 0 0 5 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 12 1 0 0 0 0 1 0 0 0 0 0 0 0 0 5 12 12 1 0 1 5 6 0 0 0 0 0 0 0 1 5 12 14 1 1 14 19 9 7 1 1 0 0 0 0 2 5 9 2 0 2 25 25 10 14 2 1 0 0 0 0 1 3 4 0 0 4 23 17 12 21 4 6 0 0 0 0 0 1 4 0 0 5 7 2 14 29 6 5 0 0 0 0 0 1 5 0 0 0 0 1 16 28 5 0 0 0 0 0 2 5 9 0 0 0 0 0 12 20 3 0 0 0 0 0 7 20 20 0 0 0 1 5 8 10 2 0 0 0 0 0 7 14 12 0 0 0 2 9 6 1 1 0 0 0 0 0 2 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 11 40 5 0 0 0 0 0 0 0 0 0 0 0 0 0 18 40 2 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 5 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 8 1 0
0 0 0 0 0 0 0 0 0 0 1 11 18 8 1 0 0 0 0 0 0 0 0 0 0 0 2 14 14 2 0 0 0 0 0 0 0 0 7 0 0 0 0 3 4 6 2 1 4 0 0 0 0 1 41 0 0 0 0 0 1 9 3 4 14 0 0 0 0 6 56 0 0 0 0 0 1 13 4 5 25 7 2 0 0 6 30 0 0 0 0 0 1 5 1 1 8 5 1 1 1 1 2 0 0 0 1 2 0 0 0 0 0 0 0 0 0 1 0 1 6 5 0 1 0 0 0 0 0 0 0 0 0 0 0 0 27 20 0 2 0 0 0 0 0 0 0 0 0 0 0 0 38 27 0 5 0 0 0 0 0 0 0 0 0 0 0 0 27 14 0 2 0 0 0 0 0 0 0 0 0 0 0 0 8 4 6 10 6 2 0 0 5 4 0 0 0 0 0 0 0 1 11 18 12 3 0 1 18 12 0 0 0 0 1 1 12 1 11 14 11 2 0 0 29 21 0 0 0 0 0 Columns 401 through 416 54 53 52 52 51 49 49 48 46 45 45 43 40 39 37 37 54 53 52 52 51 49 49 47 47 45 43 42 40 39 37 36 54 53 52 52 51 49 49 47 46 44 43 42 40 38 36 36 54 53 52 52 51 49 48
47 46 44 43 42 39 38 36 35 54 53 52 51 50 48 48 46 45 44 42 40 38 37 35 34 54 53 52 51 50 48 47 46 44 43 41 40 38 36 34 34 54 53 52 51 50 48 47 45 44 43 40 39 38 36 34 33 54 53 52 51 49 47 46 45 43 42 41 39 36 35 33 32 53 52 51 50 49 47 46 45 43 42 40 39 37 35 32 31 52 52 51 50 49 47 44 42 41 39 38 36 34 33 32 31 50 50 49 49 48 45 43 41 40 38 37 35 34 32 31 30 51 49 49 47 46 44 42 41 40 38 36 35 33 31 29 28 50 49 48 47 46 44 42 41 39 37 35 34 33 31 28 27 49 49 48 46 45 44 42 40 39 37 35 34 32 30 28 26 48 47 46 45 45 43 41 40 38 37 36 33 31 28 26 27 48 47 45 44 44 43 41 40 38 37 34 33 31 28 25 25 47 47 45 44 45 43 41 39 38 37 35 33 31 29 26 24 48 47 44 43 43 41 40 39 38 36 34 33 31 29 27 23 47 46 45 43 42 40 40 39 38 36 34 32 30 28 25 23 46 45 44 42 41 39 39 38 36 35 33 31 29 26 24 23 44 43 42 42 41 40 37 36 35 33 32 30 28 26 24 24 44 44 42 43 41 39 38 36 35 33 31 29 27 26 24 23 43 43 42 41 40 39 38 36 35 33 31 30 28 26 23 22 42 42 41 40 39 37 35 34 33 31 29 28 26 24 22 21 42 41 41 40 39 37 35 33 32 31 29 27 25 24 22 22 40 42 41 40 39 37 35 33 32 31 29 27 25 23 22 20 39 40 39 37 37 36 35 32 31 30 29 26 25 23 21 20 38 38 37 34 35 34 33 32 30 29 27 24 23 23 22 20 36 36 35 34 33 32 31 30 29 28 26 24 22 21 19 18 34 33 33 33 32 30 29 29 27 26 25 23 21 20 17 16 33 33 32 32 31 29 28 27 26 25 24 22 20 19 17 15 32 31 31 32 31 30 29 28 27 25 23 22 20 19 17 16 33 32 32 29 28 27 27 26 24 23 21 20 18 16 15 14 30 29 29 28 27 25 25 24 23 21 19 19 17 14 14 13 28 27 26 28 26 24 23 22 21 20 17 17 15 15 13 13 25 26 25 25 24 23 21 20 19 19 16 15 14 13 12 10 25 24 23 23 22 20 18
18 16 16 14 13 11 10 8 8 22 22 21 20 20 19 18 16 15 15 12 11 10 9 8 8 21 20 19 19 18 17 15 14 14 13 11 10 9 8 7 7 17 17 16 16 15 14 13 12 12 10 10 9 7 6 5 5 15 14 15 15 14 13 11 10 9 9 8 7 6 5 5 4 12 11 10 10 9 8 8 7 6 6 6 6 5 4 4 4 8 8 7 7 6 5 5 4 4 4 4 4 3 3 3 3 7 7 7 7 6 5 5 4 3 3 3 2 2 1 1 1 8 7 7 5 4 2 3 2 2 2 3 2 1 1 1 1 6 6 5 3 2 1 1 1 1 1 2 2 0 0 0 1 2 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 4 2 2 1 0 0 0 0 0 0 0 0 0 0 0 5 5 4 3 3 1 1 0 0 0 0 0 0 0 0 0 6 6 6 5 5 3 3 2 2 1 1 1 0 0 0 0 7 6 6 6 6 6 4 3 3 3 2 2 1 0 0 0 8 8 8 6 6 6 6 6 6 5 4 3 2 1 1 0 9 9 9 9 8 6 6 6 6 5 4 4 3 2 2 1 10 10 9 9 8 8 7 6 6 6 5 5 4 3 2 1 10 10 10 10 9 9 9 8 7 7 6 5 5 4 3 2 10 10 11 10 10 9 8 9 8 7 6 6 4 5 3 3 10 10 10 10 10 10 9 8 8 7 6 5 2 4 4 4 11 11 11 11 11 10 9 9 8 8 7 6 3 2 1 1 12 12 12 11 10 11 10 8 8 8 7 6 3 1 0 0 12 12 11 11 10 10 10 9 8 7 4 3 2 1 1 0 11 11 11 10 10 10 10 10 8 6 3 2 2 1 1 0 9 10 9 10 10 9 8 5 4 4 2 2 1 1 1 0 7 7 6 9 9 8 6 4 4 4 2 3 1 1 0 0 6 6 5 4 4 4 5 4 3 3 2 2 1 1 0 0 4 4 4 4 4 3 3 2 2 1 1 1 1 0 0 0 4 4 4 3 3 2 2 2 1 1 1 0 0 0 0 0 2 2 2 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 4 4 2 3 4 4 2 1 1 0 0 0 0 0 2 3 8 8 7 7 6 8 6 5 4 4 0 0 0 1 4 6 10 10 11 10 8 10 8 7 6 4 0 0 1 3 6 9 10 10 10 10 10 11 9 8 7 6 0 0 2 5 9 12 12 12 13 11 9 11 11 10 8 6 0 2 3 6 8 11 15 16 17 15 14 13 12 10 10 8 0 2 3 6 8 10 15 15 16 14 14 13 13 11 11 9 0 0 1 4 6 7 13 14 13 15 15 15 15 12 11 11 0 0 1 4 6 8 12 13 14 14 14 13 14 13 12 11 0 0 1 3 6 8 10 11 13 13 12 13 13 14 12 10 0 0 0 0 3 5 8 9 11 12 11 13 15 14 12 11 0 0 0 0 0 2
5 6 8 8 10 13 15 15 14 13 0 0 0 0 0 0 1 4 6 6 6 8 11 10 10 13 0 0 0 0 0 0 0 1 2 3 4 6 9 8 9 11 0 0 0 0 0 0 0 0 1 1 1 3 7 6 7 10 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5 6 0 0 0 0 0 0 0 0 0 0 0 0 3 2 3 3 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 3 3 1 0 2 1 1 1 1 1 1 1 1 2 4 4 5 6 4 4 6 5 3 3 2 2 4 6 6 7 5 6 6 10 9 9 10 8 6 5 5 5 7 10 10 11 7 6 6 16 17 15 12 10 8 6 7 7 8 9 10 11 8 7 7 19 20 18 15 13 10 9 9 10 9 9 10 10 10 10 8 19 21 20 17 16 13 12 12 11 12 11 12 12 12 11 11 20 19 18 19 17 15 14 13 11 13 15 16 16 15 13 11 20 19 18 20 18 17 15 15 14 15 17 17 16 15 12 10 20 19 18 16 16 15 16 16 17 16 16 17 16 15 13 12 20 18 16 14 14 15 15 16 16 17 19 19 18 14 12 10 19 18 16 15 15 15 15 14 15 18 20 20 19 13 11 9 18 17 15 13 12 13 16 16 17 18 19 19 17 15 12 10 17 16 14 12 11 12 17 17 18 19 19 19 17 15 13 12 13 13 12 10 11 12 18 18 19 20 19 19 17 13 12 13 12 10 10 11 12 13 16 16 16 18 20 19 17 12 12 15 10 8 11 12 13 14 15 16 16 17 18 16 14 11 11 14 12 12 11 13 14 16 16 17 17 19 17 16 14 11 11 14 15 15 11 14 15 16 17 17 17 18 16 15 13 11 10 14 15 16 12 15 16 17 17 17 17 16 16 14 12 10 9 13 17 17 14 16 17 17 17 16 15 15 15 13 11 8 8 12
15 17 19 21 19 18 16 16 15 14 14 12 9 7 7 11 20 20 22 21 21 19 18 15 15 11 9 7 5 3 4 8 22 22 23 23 21 20 17 15 14 9 6 5 3 2 2 6 24 25 24 24 23 20 17 13 10 6 3 3 1 0 0 5 22 23 23 25 25 22 17 12 6 4 2 2 0 0 0 4 23 24 26 24 24 22 17 11 5 3 1 1 0 0 0 3 22 26 27 25 24 22 17 12 4 3 1 1 0 0 0 1 22 26 27 26 25 23 18 12 5 2 2 1 0 0 0 0 22 27 27 26 25 24 19 13 5 4 3 1 0 0 0 0 22 27 27 27 25 23 19 12 5 4 3 0 0 0 0 0 22 25 28 27 23 21 18 13 6 2 2 0 0 0 0 0 22 23 26 26 23 19 18 13 9 5 2 1 0 0 0 0 19 22 25 26 21 18 18 14 10 4 2 0 0 0 0 0 16 20 23 24 19 16 18 14 8 3 2 0 0 0 0 0 12 17 21 22 18 17 17 11 5 3 1 0 0 0 0 0 9 17 19 19 17 16 14 7 2 1 0 0 0 0 0 0 6 17 19 19 16 11 10 4 2 1 0 0 0 0 0 0 7 18 19 19 14 9 8 4 1 0 1
0 0 0 0 0 9 20 18 15 12 8 4 2 1 0 0 0 0 0 0 0 9 19 19 15 12 5 2 2 1 0 0 0 0 0 0 0 10 18 21 18 15 4 0 3 3 0 0 0 0 0 0 0 13 20 26 26 24 9 1 3 2 0 0 0 0 0 0 0 20 23 29 31 27 10 3 4 1 0 0 0 0 0 0 0 23 27 30 33 26 7 5 2 1 1 0 0 0 0 0 0 23 28 31 33 24 7 2 0 0 1 0 0 0 0 0 0 25 28 31 32 24 9 1 0 1 0 0 0 0 0 0 0 21 27 29 29 22 9 2 0 0 0 0 0 0 0 0 0 18 23 28 25 15 6 2 1 0 0 0 0 0 0 0 0 13 15 22 15 3 2 1 0 0 0 0 0 1 0 0 0 8 11 14 5 0 0 0 0 0 3 7 0 0 0 0 0 4 8 7 0 0 0 0 3 1 2 4 0 0 0 0 0 3 4 2 0 0 0 0 3 2 0 0 3 5 0 0 0 6 1 0 0 0 0 0 0 0 0 0 16 13 0 0 0 11 2 0 0 0 0 0 0 0 0 3 17 8 0 0 0 6 2 1 0 0 0 0 0 0 0 4 11 2 0 0 0 0 4 3 0 0 0 0 0 0 0 1 3 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 6 2 0 0 0 0 4 3 0 0 0 0 1 2 0 8 22 11 1 0 0 0 3 4 1 0 0 0 4 13 2 21 26 10 1 0 0 0 0 2 0 0 0 0 9 21 6 31 24 4 0 1 0 0 0 0 0 0 0 0 20 17 4 28 26 6 9 10 1 0 0 0 0 0 0 2 24 9 3 22 20 12 25 24 4 0 0 5 16 7 7 11 25 7 15 6 5 19 37 33 6 0 2 30 47 17 12 46 35 11 32 0 3 18 38 31 4 0 17 72 84 31 17 59
26 16 38 1 1 9 25 15 1 1 43 93 64 20 8 20 6 15 17 4 2 4 2 1 0 8 56 78 31 2 3 10 2 3 8 5 0 0 0 0 2 22 58 66 19 0 5 7 1 0 9 15 0 0 0 17 28 48 65 52 11 0 9 3 0 1 7 12 1 0 0 47 62 73 52 21 2 4 14 3 0 0 2 1 0 7 6 42 46 49 19 4 1 6 6 0 0 0 0 2 3 11 10 27 16 13 1 0 0 5 2 0 0 2 3 23 20 6 7 27 11 0 0 0 0 0 0 0 0 4 8 42 33 0 1 21 16 0 0 3 3 0 0 0 0 16 17 45 29 0 0 17 7 0 10 9 2 0 0 0 0 34 24 54 29 0 1 12 3 1 18 15 6 0 0 0 2 33 22 51 20 0 0 7 3 0 5 26 18 0 0 0 7 18 17 39 6 0 0 11 5 0 7 46 23 0 0 0 8 12 14 31 2 3 2 5 1 0 14 37 9 1 1 0 8 8 16 34 2 2 1 0 0 8 32 19 0 9 18 3 2 3 16 31 1 1 0 0 0 18 45 15 0 24 49 8 0 0 8 12 2 2 21 9 2 Columns 417 through 424 35 33 32 31 32 31 30 29 35 33 32 30 31 31 29 28
34 33 31 30 31 30 29 27 34 33 30 29 29 29 29 27 33 32 30 28 27 27 28 27 33 31 29 28 26 26 27 26 32 30 29 27 25 25 26 26 30 29 27 26 25 25 24 24 29 28 26 25 25 24 23 22 29 27 26 25 25 24 23 23 27 26 25 25 24 23 22 22 26 25 24 24 23 23 21 21 26 24 22 23 23 22 21 20 25 24 23 23 22 21 21 20 24 23 22 21 21 20 19 18 24 23 21 20 20 20 19 18 23 23 21 21 20 19 19 18 22 23 21 21 20 19 19 18 22 22 22 20 18 17 18 18 22 21 20 18 16 15 16 17 22 20 19 17 14 15 16 16 22 20 18 17 15 15 15 14 20 19 16 15 15 14 12 12 19 18 16 16 15 13 13 12 19 17 16 16 14 14 13 12 19 17 17 16 14 14 14 13 19 17 16 15 13 12 12 11 19 17 15 14 12 11 10 9 16 15 14 13 11 10 10 10 14 13 12 11 10 10 10 10 15 13 12 11 10 10 10 10 15 12 11 11 10 10 9 9 13 11 10 10 9 9 8 8 12 10 10 9 8 8 7 7 12 11 10 10 9 9 9 8 9 9
9 8 7 7 7 7 6 7 6 6 5 5 5 5 6 6 5 5 4 4 3 3 6 5 5 5 3 3 3 3 4 5 4 3 3 3 3 3 3 4 3 2 2 2 2 2 3 3 2 2 2 2 1 1 2 2 2 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 2 2 2 1 1 0 0 0 4 2 2 1 0 1 1 0 1 2 2 2 0 2 1 1 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 5 3 1 0 0 0 0 0 5 3 1 0 0 0 0 0 5 4 1 0 0 0 0 0 5 4 1 0 0 0 0 0 6 4 3 1 0 0 0 0 7 6 5 1 0 0 0 0 9 7 4 2 0 0 0 0 9 10 6 2 0 0 0 0 11 12 8 4 2 0 0 0 13 11 9 5 3 1 0 0 10 9 10 8 6 4 3 2 10 10 9 7 5 4 2 2 10 8 8 6 4 3 2 1 6 8 7 5 3 2 2 2 4 7 5 4 1 2 3 4 3 6 5 5 2 2 4 5 3 6 5 4 3 4 4 5 2 2 2 2 4 4 4 3 1 2 2 3 4 5 5 4 0 3 3 3 4 3 2 1 1 3 3 3 4 4 3 3 1 2 3 3 3 3 3 3 2 3 3 3 3 3 2 2 3 4 4 5 4 4 3 3 3 2 2 4 5 5 4 3 4 2 3 4 4 4 4 4 5 2 3 4 4 4 4 4 7 4 5 3 3 2 3 3 6 5 4 0 0 1 0 0 7 6 3 0 0 0 0 0 9 6 4 0 0 1 0 1 9 6 6 2 0 2 4 5 10 6 6 5 2 4 6 7 9 7 7 6 3 5 8 9 8 6 9 9 6 8 11 12 7 7 9 11 10 11 15 17 9 9 12 13 13 14 18 19 11 10 13 15 15 17 20 23 12 12 15 18 18 20 23 25 12 12 16 20 22 23 27 29 12 15 18 22 24 26 30 33 14 16 18 22 25 30 34 37 14 19 20 24 28 33 36 38 14 20 21 25 32 34 35 36 14 19 21 26 35 35 35 35 13 18 21 28 34 34 35 36 13 14 19 26 32 33 33 34 8 9 17 25 29 28 29 30 6 4 12 22 26 25 26 25 4 1 11 20 21 21 21 21 3 0 4 14 15 16 15 14 3 1 1 6 7 6 4 4 1 1 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0 3 11 15 0 0 0 0 0 9 21 25 0 0 0 0 0 9 21 28 0 0 0 0 0 7 19 25 0 0 0 0 0 4 16 21 0 0 0 0 0 1 6 19 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 3 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 2 23 29 2 0 0 1 3 4 36 41 7
0 1 10 5 5 29 39 11 3 17 15 3 3 23 38 28 22 29 3 0 7 32 46 44 38 15 1 1 16 39 43 54 45 7 0 1 9 12 15 48 47 10 0 0 0 0 8 39 44 13 0 0 0 0 7 31 40 11 0 0 0 0 1 20 33 7 0 0 0 0 0 33 79 25 0 0 0 0 23 143 182 66 2 0 0 6 93 203 151 55 4 0 0 46 157 160 56 17 5 0 15 122 181 88 8 1 0
0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 8 1 0 0 0 0 0 0 0 0 0 0 0 1 11 18 8 1 0 0 0 0 0 0 0 0 0 0 0 2 14 14 2 0 0 0 0 0 0 0 0 7 0 0 0 0 3 4 6 2 1 4 0 0 0 0 1 41 0 0 0 0 0 1 9 3 4 14 0 0 0 0 6 56 0 0 0 0 0 1 13 4 5 25 7 2 0 0 6 30 0 0 0 0 0 1 5 1 1 8 5 1 1 1 1 2 0 0 0 1 2 0 0 0 0 0 0 0 0 0 1 0 1 6 5 0 1 0 0 0 0 0 0 0 0 0 0 0 0 27 20 0 2 0 0 0 0 0 0 0 0 0 0 0 0 38 27 0 5 0 0 0 0 0 0 0 0 0 0 0 0 27 14 0 2 0 0 0 0 0 0 0 0 0 0 0 0 8 4 6 10 6 2 0 0 5 4 0 0 0 0 0 0 0 1 11 18 12 3 0 1 18 12 0 0 0 0 1 1 12 1 11 14 11 2 0 0 29 21 0 0 0 0 0 Columns 401 through 416 54
53 52 52 51 49 49 48 46 45 45 43 40 39 37 37 54 53 52 52 51 49 49 47 47 45 43 42 40 39 37 36 54 53 52 52 51 49 49 47 46 44 43 42 40 38 36 36 54 53 52 52 51 49 48 47 46 44 43 42 39 38 36 35 54 53 52 51 50 48 48 46 45 44 42 40 38 37 35 34 54 53 52 51 50 48 47 46 44 43 41 40 38 36 34 34 54 53 52 51 50 48 47 45 44 43 40 39 38 36 34 33 54 53 52 51 49 47 46 45 43 42 41 39 36 35 33 32 53 52 51 50 49 47 46 45 43 42 40 39 37 35 32 31 52 52 51 50 49 47 44 42 41 39 38 36 34 33 32 31 50 50 49 49 48 45 43 41 40 38 37 35 34 32 31 30 51 49 49 47 46 44 42 41 40 38 36 35 33 31 29 28 50 49 48 47 46 44 42 41 39 37 35 34 33 31 28 27 49 49 48 46 45 44 42 40 39 37 35 34 32 30 28 26 48 47 46 45 45 43 41 40 38 37 36 33 31 28 26 27 48 47 45 44 44 43 41 40 38 37 34 33 31 28 25 25 47 47 45 44 45 43 41 39 38 37 35 33 31 29 26 24 48 47 44 43 43 41 40 39 38 36 34 33 31 29 27 23 47 46 45 43 42 40 40 39 38 36 34 32 30 28 25 23 46 45 44 42 41 39 39 38 36 35 33 31 29 26 24 23 44 43 42 42 41 40 37 36 35 33 32 30 28 26 24 24 44 44 42 43 41 39 38 36 35 33 31 29 27 26 24 23 43 43 42 41 40 39 38 36 35 33 31 30 28 26 23 22 42 42 41 40 39 37 35 34 33 31 29 28 26 24 22 21 42 41 41 40 39 37 35 33 32 31 29 27 25 24 22 22 40 42 41 40 39 37 35 33 32 31 29 27 25 23 22 20 39 40 39 37 37 36 35 32 31 30 29 26 25 23 21 20 38 38 37 34 35 34 33 32 30 29 27 24 23 23 22 20 36 36 35 34 33 32 31 30 29 28 26 24 22 21 19 18 34 33 33 33 32 30 29 29 27 26 25 23 21 20 17 16 33 33 32 32 31 29 28 27 26 25 24 22 20 19 17 15 32 31 31 32 31 30 29 28 27 25 23 22 20 19 17 16 33 32 32 29 28 27 27 26 24 23 21 20 18 16 15 14 30
29 29 28 27 25 25 24 23 21 19 19 17 14 14 13 28 27 26 28 26 24 23 22 21 20 17 17 15 15 13 13 25 26 25 25 24 23 21 20 19 19 16 15 14 13 12 10 25 24 23 23 22 20 18 18 16 16 14 13 11 10 8 8 22 22 21 20 20 19 18 16 15 15 12 11 10 9 8 8 21 20 19 19 18 17 15 14 14 13 11 10 9 8 7 7 17 17 16 16 15 14 13 12 12 10 10 9 7 6 5 5 15 14 15 15 14 13 11 10 9 9 8 7 6 5 5 4 12 11 10 10 9 8 8 7 6 6 6 6 5 4 4 4 8 8 7 7 6 5 5 4 4 4 4 4 3 3 3 3 7 7 7 7 6 5 5 4 3 3 3 2 2 1 1 1 8 7 7 5 4 2 3 2 2 2 3 2 1 1 1 1 6 6 5 3 2 1 1 1 1 1 2 2 0 0 0 1 2 2 2 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 4 4 2 2 1 0 0 0 0 0 0 0 0 0 0 0 5 5 4 3 3 1 1 0 0 0 0 0 0 0 0 0 6 6 6 5 5 3 3 2 2 1 1 1 0 0 0 0 7 6 6 6 6 6 4 3 3 3 2 2 1 0 0 0 8 8 8 6 6 6 6 6 6 5 4 3 2 1 1 0 9 9 9 9 8 6 6 6 6 5 4 4 3 2 2 1 10 10 9 9 8 8 7 6 6 6 5 5 4 3 2 1 10 10 10 10 9 9 9 8 7 7 6 5 5 4 3 2 10 10 11 10 10 9 8 9 8 7 6 6 4 5 3 3 10 10 10 10 10 10 9 8 8 7 6 5 2 4 4 4 11 11 11 11 11 10 9 9 8 8 7 6 3 2 1 1 12 12 12 11 10 11 10 8 8 8 7 6 3 1 0 0 12 12 11 11 10 10 10 9 8 7 4 3 2 1 1 0 11 11 11 10
10 10 10 10 8 6 3 2 2 1 1 0 9 10 9 10 10 9 8 5 4 4 2 2 1 1 1 0 7 7 6 9 9 8 6 4 4 4 2 3 1 1 0 0 6 6 5 4 4 4 5 4 3 3 2 2 1 1 0 0 4 4 4 4 4 3 3 2 2 1 1 1 1 0 0 0 4 4 4 3 3 2 2 2 1 1 1 0 0 0 0 0 2 2 2 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 4 4 2 3 4 4 2 1 1 0 0 0 0 0 2 3 8 8 7 7 6 8 6 5 4 4 0 0 0 1 4 6 10 10 11 10 8 10 8 7 6 4 0 0 1 3 6 9 10 10 10 10 10 11 9 8 7 6 0 0 2 5 9 12 12 12 13 11 9 11 11 10 8 6 0 2 3 6 8 11 15 16 17 15 14 13 12 10 10 8 0 2 3 6 8 10 15 15 16 14 14 13 13 11 11 9 0 0 1 4 6 7 13 14 13 15 15 15 15
12 11 11 0 0 1 4 6 8 12 13 14 14 14 13 14 13 12 11 0 0 1 3 6 8 10 11 13 13 12 13 13 14 12 10 0 0 0 0 3 5 8 9 11 12 11 13 15 14 12 11 0 0 0 0 0 2 5 6 8 8 10 13 15 15 14 13 0 0 0 0 0 0 1 4 6 6 6 8 11 10 10 13 0 0 0 0 0 0 0 1 2 3 4 6 9 8 9 11 0 0 0 0 0 0 0 0 1 1 1 3 7 6 7 10 0 0 0 0 0 0 0 0 0 0 0 2 4 4 5 6 0 0 0 0 0 0 0 0 0 0 0 0 3 2 3 3 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 3 3 1 0 2 1 1 1 1 1 1 1 1 2 4 4 5 6 4 4 6 5 3 3 2 2 4 6 6 7 5 6 6 10 9 9 10 8 6 5 5 5 7 10 10 11 7 6 6 16 17 15 12 10 8 6 7 7 8 9 10 11 8 7 7 19 20 18 15 13 10 9 9 10 9 9 10 10 10 10 8 19 21 20 17 16 13 12 12 11 12 11 12 12 12 11 11 20 19 18 19 17 15 14 13 11 13 15 16 16 15 13 11 20 19 18 20 18 17 15 15 14 15 17 17 16 15 12 10 20 19 18 16 16 15 16 16 17 16 16 17 16 15 13 12 20 18 16 14 14 15 15 16 16 17 19 19 18 14 12 10 19 18 16 15 15 15 15 14 15 18 20 20 19 13 11 9 18 17 15 13 12 13 16 16 17 18 19 19 17 15 12 10 17 16 14 12 11 12 17 17 18 19 19 19 17 15 13 12 13 13 12 10 11 12 18 18 19 20 19 19 17 13 12 13 12 10 10 11 12 13 16 16 16 18 20 19 17 12 12 15 10 8 11 12 13 14 15 16 16 17 18 16 14 11 11 14 12 12 11 13 14 16 16 17 17 19 17
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42 46 49 19 4 1 6 6 0 0 0 0 2 3 11 10 27 16 13 1 0 0 5 2 0 0 2 3 23 20 6 7 27 11 0 0 0 0 0 0 0 0 4 8 42 33 0 1 21 16 0 0 3 3 0 0 0 0 16 17 45 29 0 0 17 7 0 10 9 2 0 0 0 0 34 24 54 29 0 1 12 3 1 18 15 6 0 0 0 2 33 22 51 20 0 0 7 3 0 5 26 18 0 0 0 7 18 17 39 6 0 0 11 5 0 7 46 23 0 0 0 8 12 14 31 2 3 2 5 1 0 14 37 9 1 1 0 8 8 16 34 2 2 1 0 0 8 32 19 0 9 18 3 2 3 16 31 1 1 0 0 0 18 45 15 0 24 49 8 0 0 8 12 2 2 21 9 2 Columns 417 through 424 35 33 32 31 32 31 30 29 35 33 32 30 31 31 29 28 34 33 31 30 31 30 29 27 34 33 30 29 29 29 29 27 33 32 30 28 27 27 28 27 33 31 29 28 26 26 27 26 32 30 29 27 25 25 26 26 30 29 27 26 25 25 24 24 29 28 26 25 25 24 23 22 29 27 26 25 25 24 23 23 27 26 25 25 24 23 22 22 26 25 24 24 23 23 21 21
26 24 22 23 23 22 21 20 25 24 23 23 22 21 21 20 24 23 22 21 21 20 19 18 24 23 21 20 20 20 19 18 23 23 21 21 20 19 19 18 22 23 21 21 20 19 19 18 22 22 22 20 18 17 18 18 22 21 20 18 16 15 16 17 22 20 19 17 14 15 16 16 22 20 18 17 15 15 15 14 20 19 16 15 15 14 12 12 19 18 16 16 15 13 13 12 19 17 16 16 14 14 13 12 19 17 17 16 14 14 14 13 19 17 16 15 13 12 12 11 19 17 15 14 12 11 10 9 16 15 14 13 11 10 10 10 14 13 12 11 10 10 10 10 15 13 12 11 10 10 10 10 15 12 11 11 10 10 9 9 13 11 10 10 9 9 8 8 12 10 10 9 8 8 7 7 12 11 10 10 9 9 9 8 9 9 9 8 7 7 7 7 6 7 6 6 5 5 5 5 6 6 5 5 4 4 3 3 6 5 5 5 3 3 3 3 4 5 4 3 3 3 3 3 3 4 3 2 2 2 2 2 3 3 2 2 2 2 1 1 2 2 2 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 2 2 2 1 1 0 0 0 4 2 2 1 0 1 1 0 1 2 2 2 0 2 1 1 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 5 3 1 0 0 0 0 0 5 3 1 0 0 0 0 0 5 4 1 0 0 0 0 0 5 4 1 0 0 0 0 0 6 4 3 1 0 0 0 0 7 6 5 1 0 0 0 0 9 7 4 2 0 0 0 0 9 10 6 2 0 0 0 0 11 12 8 4 2 0 0 0 13 11 9 5 3 1 0 0 10 9 10 8 6 4 3 2 10 10 9 7 5 4 2 2
10 8 8 6 4 3 2 1 6 8 7 5 3 2 2 2 4 7 5 4 1 2 3 4 3 6 5 5 2 2 4 5 3 6 5 4 3 4 4 5 2 2 2 2 4 4 4 3 1 2 2 3 4 5 5 4 0 3 3 3 4 3 2 1 1 3 3 3 4 4 3 3 1 2 3 3 3 3 3 3 2 3 3 3 3 3 2 2 3 4 4 5 4 4 3 3 3 2 2 4 5 5 4 3 4 2 3 4 4 4 4 4 5 2 3 4 4 4 4 4 7 4 5 3 3 2 3 3 6 5 4 0 0 1 0 0 7 6 3 0 0 0 0 0 9 6 4 0 0 1 0 1 9 6 6 2 0 2 4 5 10 6 6 5 2 4 6 7 9 7 7 6 3 5 8 9 8 6 9 9 6 8 11 12 7 7 9 11 10 11 15 17 9 9 12 13 13 14 18 19 11 10 13 15 15 17 20 23 12 12 15 18 18 20 23 25 12 12 16 20 22 23 27 29 12 15 18 22 24 26 30 33 14 16 18 22 25 30 34 37 14 19 20 24 28 33 36 38 14 20 21 25 32 34 35 36 14 19 21 26 35 35 35 35 13 18 21 28 34 34 35 36 13 14 19 26 32 33 33 34 8 9 17 25 29 28 29 30 6 4 12 22 26 25 26 25 4 1 11 20 21 21 21 21 3 0 4 14 15 16 15 14 3 1 1 6 7 6 4 4 1 1 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0 3 11 15 0 0 0 0 0 9 21 25 0 0 0 0 0 9 21 28 0 0 0 0 0 7 19 25 0 0 0 0 0 4 16 21 0 0 0 0 0 1 6 19 0 0 0 0 0 0 1 12 0 0 0 0 0 0 0 3 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 5 0 0 0 0 0 2 23 29 2 0 0 1 3 4 36 41 7 0 1 10 5 5 29 39 11 3 17 15 3 3 23 38 28 22 29 3 0 7 32 46 44 38 15 1 1 16 39 43 54 45 7 0 1 9 12 15 48 47 10 0 0 0 0 8 39 44 13 0 0 0 0 7 31 40 11 0 0 0 0 1 20 33 7 0 0 0 0 0 33 79 25 0 0 0 0 23 143 182 66 2 0 0 6 93 203 151 55 4 0 0 46 157 160 56 17 5 0 15 122 181 88 8 1 0 92 77 71 76 75 66 60 51 43 47 57 71 80 77 63 40 87 82 76 75 70 61 57 49 48 53 65 73 73 72 59 39 81 72 67 67 62 56 57 47 48 57 69 73 66 65 53 36 80 62 56 59 58 54 56 49 48 56 65 72 62 57 50 34 76 62 52 54 56 52 53 48 46 50 58 68 59 51 47 32 60 53 44 47 49 44 43 41 35 40 52 60 53 47 42 31 53 49 41 41 43 37 41 42 34 35 48 57 50 45 40 30 46 45 43 42 40 38 44 44 36 31 40 49 48 46 39 32 37 39 38 37 37 39 45 43 38 31 34 42 47 46 40 34 32 37 37 33 31 39 47 46 45 40 33 41 48 46 40 37 32 37 38 31 30 43 53 51 48 43 37 43 48 47 44 41 29 31 34 30 34 47 54 54 49 42 40 48 51 50 47 45 28 22 24 25 34 46 52 54 50 41 44 53 53 53 50 50 28 18 18 23 34 40 46 52 48 43 48 54 54 55 55 53 23 14 18 26 33 40 46 49 45 46 52 56 57 58 59 57 17 14 20 33 37 39 41 39 40 50 57 58 59 61 61 59 12 13 21 33 37 39 39 33 42 54 58 60 61 63 62 61 11 16 22 28 35 39 37 36 48 58 60 59 61 62 62 62 17 25 26 25 28 30 34 46 54 60 61 61 62 62 63 63 19 26 26 27 22 19 29 52 58 61 61 60 61 63 64 62 23 28 24 23 20 17 35 53 57 61 60 60 60 63 64 61 28 29 21 18 18 24 43 54 57 59 60 61 60 61 60 59 26 25 20 16 19 33 48 56 57 58 59 61 61 60 58 57 23 20 21 17 26 43 50 55 58 59 59 60 59 59 58 56 24 19 18 21 36 47 50 55 57 57 59 59 58 57 56 53 26 18 15 28 41 48 50 53 54 56 57 57 56 56 53 50 24 19 22 34 41 48 50 51 52 53 54 54 53 51 50 48 20 21 33 38 42 45 46 48 49 50 50 50 49 47 46 44 21 30 40 41 43 42 43 44 45 46 45 46 45 43 41 38 30 44 45 41 41 41 40 40 40 40 40 40 40 37 36 33 52 56 48 42 40 38 35 34 33 34 34 32 32 30 29 27 73 63 51 42 38 34 31 29 28 27 26 26 25 23 22 22 98 79 60 45 39 32 27 28 24 20 18 17 17 15 13 15 125 99 76 55 41 33 25 23 18 13 10 9 7 5 3 6 153 127 101 71 48 34 24 16 11 6 2 1 0 0 0 1 171 150 122 90 58 38 25 14 7 3 1 0 0 0 0 0 183 166 139 110 73 48 29 15 6 1 0 0 0 0 0 0 193 179 159 131 93 62 35 19 9 3 0 0 0 0 0 0 200 190 174 148 110 76 42 22 13 5 0 0 0 0 0 0 206 196 185 162 129 90 55 27 16 6 0 0 0 0 0 0 213 202 192 174 146 106 71 37 21 9 2 0 0 0 0 0 217 208 197 179 157 122 86 48 26 15 5 0 0 0 0 0 220 211 200 186 167 138 101 58 33 20 5 0 1 0 0 0 221 214 203 191 175 150 113 67 40 25 8 3 2 0 0 0 222 214 207 195 181 159 127 80 49 30 16 13 7 1 0 0 222 216 209 198 185 163 138 94 59 35 23 20 12 5 0 0 223 217 209 199 188 171 148 106 70 44 30 24 16 11 5 1 223 216 210 202 192 175 154 118 83 56 36 29 22 16 10 4 222 216 210
204 195 179 159 129 97 68 43 32 25 21 15 8 221 219 213 206 197 185 166 138 109 79 51 35 27 23 20 14 222 221 214 207 199 189 173 146 118 87 58 40 31 25 22 17 223 221 216 208 200 191 179 157 130 100 67 45 34 28 24 21 224 221 216 209 202 195 185 164 141 110 76 52 40 32 27 23 223 221 218 212 206 197 186 166 144 118 86 59 48 38 30 26 223 222 219 213 207 199 189 169 150 126 94 66 51 40 32 28 225 222 219 213 208 200 191 174 156 134 101 73 54 43 35 31 224 221 219 214 208 201 193 179 161 139 110 80 55 44 39 32 223 222 219 215 210 203 195 181 166 142 118 85 58 46 41 32 223 222 219 215 210 204 196 183 167 145 120 87 62 49 42 31 223 222 219 215 210 205 197 184 168 147 123 90 66 50 41 30 223 219 217 214 210 205 197 184 167 148 126 96 70 53 40 32 218 217 216 214 209 203 195 183 168 149 128 98 71 52 40 31 216 215 214 212 208 201 193 179 164 145 125 98 72 53 41 30 215 215 213 210
205 199 192 177 160 142 122 98 74 53 41 30 212 213 212 207 201 196 189 173 157 142 118 95 74 55 41 32 211 209 207 202 196 191 184 170 156 140 115 91 74 54 41 32 209 206 204 199 192 187 179 165 152 136 113 92 71 54 42 32 205 204 202 195 186 184 176 161 147 130 109 91 73 54 41 31 203 201 199 192 182 178 171 156 142 126 107 92 72 53 41 32 199 198 197 188 177 173 166 151 137 122 104 91 72 53 41 32 196 196 194 184 174 168 161 148 134 121 103 90 73 53 41 31 194 193 188 176 170 167 158 147 135 120 103 88 72 53 41 32 190 190 183 172 167 165 156 146 132 117 102 89 69 53 42 34 188 185 179 167 162 158 153 140 128 114 100 88 69 54 43 35 184 180 173 163 158 154 150 136 123 110 97 85 67 53 45 37 181 180 171 160 157 154 150 137 121 108 96 83 67 52 42 37 177 176 164 154 153 149 146 132 116 105 94 82 64 51 42 37 173 170 157 147 147 143 140 125 111 103 92 81 63 50 43 38 169 163 152 143 147
140 135 118 107 100 90 77 63 50 43 37 161 157 145 138 120 128 127 111 102 93 85 71 58 48 42 38 155 151 142 117 46 89 124 107 95 89 80 67 55 45 41 37 155 147 138 102 9 67 116 99 90 85 76 65 54 46 38 36 152 139 130 97 7 59 108 91 85 77 70 62 51 43 38 33 146 130 121 93 8 51 98 83 77 68 64 57 47 41 37 32 138 122 114 90 11 42 88 76 68 62 60 53 43 38 35 28 125 113 105 83 10 33 78 68 61 57 55 49 41 37 32 27 118 99 91 73 6 26 65 56 51 48 46 43 39 35 29 24 110 89 82 64 5 21 54 49 45 42 40 38 35 31 26 21 94 81 75 50 3 15 45 41 39 38 37 35 32 28 22 18 83 74 64 42 3 11 33 33 33 33 33 30 28 23 17 15 77 67 51 36 3 8 22 22 25 26 25 23 18 16 14 15 72 59 41 29 2 3 14 18 18 18 19 17 12 12 14 16 64 49 35 22 2 2 9 12 8 9 12 13 10 11 11 13 57 44 32 19 2 1 6 6 4 4 6 7 7 9 9 11 48 38 28 17 0 0 3 2 0 0 2 3 4 6 6 8 44 35 23 11 0 0 0 1 0 0 0 2 2 4 4 5 38 31 22 9 0 0 0 0 0 0 0 1 2 3 3 3 33 26 24 11 0 0 0 0 0 0 0 0 1 1 2 2 26 19 19 7 0 0 0 0 0 0 0 0 0 0 1 1 17 11 9 3 0 0 0 0 0 0 0 0 0 0 2 3 11 5 5 1 0 0 0 0 0 0 0 0 0 0 0 1 5 3 3 0 0 0 0 0 0 0 0 0 0 0 0 1 2 7 5 1 0 0 0 0 0 0 0 0 0 0 0 0 4 6 4 1 0 0 0 0 0 0 0 0 0 0 0 0 5 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 8 5 7 0 0 0 0 0 0 0 0 1 2 0 0 0 11 10 8 1 0 0 0 0 0 0 8 17 11 0 0 1 8 12 8 0 0 0 0 0 0 0 16 36 13 0 0 1 9 11 8 1 0 0 0 0 0 0 4 11 2 0 0 1 17 15 7 0 0 0 0 1 0 0 0 0 0 0 0 0 19 23 8 0 0 0 1 2 0 1 1 1 0 0 1 4 7 17 6 0 0 0 2 3 0 2 1 0 0 0 2 5 0 1 3 0 0 0 7 11 2 0 0 0 0 0 0 0 0 3 9 1 0 0 10 23 9 1 0 0 0 0 0 0 0 8 10 1 0 0 8 15 6 1 0 0 0 0 0 0 0 7 6 0 0 0 4 5 3 2 0 0 0 0 0 0 1 7 3 0 0 0 1 2 2 1 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 27 2 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 6 2 0 2 0 0 0 0 0 0 1 1 0 0 0 1 5 2 7 32 8 0 0 0 0 0 1 4 1 0 0 0 0 0 6 18 4 0 0 0 6 17 5 9 2 0 0 0 3 6 0 1 1 0 0 1 11 24 8 24 13 0 0 0 3 10 0 4 5 1 0 8 16 10 14 37 19 2 2 3 2 15 1 2 1 0 1 12 14 3 15 26 13 7 9 7 2 19 0 0 0 0 2 14 6 9 19 11 6 13 16 4 1 21 5 0 0 0 1 6 5 4 6 1 1 9 12 1 0 27 6 1 0 0 1 5 10 0 0 0 0 1 3 2 5 28 1 0 0 0 1 3 4 0 0 0 0 0 0 6 7 37 0 0 0 0 0 2 1 4 3 2 0 0 1 16 16 63 0 0 0 0 0 1 1 4 2 7 4 2 14 51 45 75 0 0 0 0 0 0 0 5 3 9 13 34 69 87 46 65 0 0 0 0 0 0 1 5 1 5 32 74 97 90 40 57 0 0 0 0 0 1 14 13 0 16 62 89 98 94 45 48 0 0 0 0 0 3 17 8 0 21 68 82 83 76 38 26 2 0 0 0 0 1 3 1 0 14 49 50 47 44 24 18 11 5 0 0 0 0 1 0 0 2 15 13 13 17 8 15 13 14 3 0 0 1 0 0 0 0 1 6 3 2 3 10 5 20 9 0 2 6 0 0 0 0 5 12 10 6 5 9 8 19 12 0 3 7 0 0 0 8 11 7 7 6 6 23 17 4 3 0 0 0 0 0 0 18 8 0 4 5 5 18 19 0 0 0 0 0 0 0 0 16 18 1 0 1 0 1 17 1 0 0 0 0 0 0 0 23 19 0 0 0 0 0 12 2 0 0 0 0 0 0 1 13 4 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 5 1 0 0 0 1 0 0 0 3 15 8 0 0 1 9 21 4 0 0 0 1 5 6 5 11 36 32 2 2 5 12 25 4 0 0 0 2 6 9 9 53 74 67 30 11 8 35 30 3 0 0 0 2 1 0 0 30 87 122 93 22 3 53 38 4 0 0 0 3 3 1 0 0 24 91 110 34 5 37 26 2 0 0 1 4 4 1 0 1 39 101 90 27 10 9 3 0 0 0 1 7 4 0 0 4 59 130 62 4 1 Columns 369 through 384 27 29 29 29 30 30 31 32 34 35 36 38 39 40 42 44 27 28 28 29 29 30 31 32 34 35 36 37 39 40 42 44 26 28 29 29
29 29 31 32 32 34 36 37 39 40 42 45 26 27 28 28 29 29 31 32 32 34 35 36 38 40 42 45 25 27 28 28 28 28 30 31 32 34 34 36 37 38 41 44 25 26 27 27 28 28 30 30 32 33 34 36 37 38 40 43 25 26 27 27 28 28 30 30 32 33 34 36 37 37 40 43 25 26 26 28 28 29 30 30 32 33 34 35 37 38 41 43 26 27 28 28 28 29 30 31 32 33 34 35 37 38 40 42 27 27 28 28 29 29 30 31 32 33 34 35 37 38 40 41 28 28 28 29 29 29 30 31 32 33 34 36 36 38 40 41 28 29 29 29 29 30 31 31 33 33 34 36 37 38 40 41 30 30 30 31 31 32 32 33 33 34 35 36 37 38 40 42 30 31 31 32 32 32 32 34 34 35 35 37 38 39 40 42 32 32 32 33 33 33 34 34 34 36 35 37 38 39 40 42 33 33 33 33 34 34 34 35 35 36 37 38 38 40 41 42 34 34 34 34 35 35 35 36 36 37 37 38 39 40 42 42 33 33 34 36 36 35 36 37 37 37 38 38 39 40 42 43 33 33 34 34 35 34 36 37 37 38 39 40 40 41 42 43 33 33 34 34 34 34 35 37 36 37 39 39 39 41 43 44 33 34 34 34 34 34 35 36 35 36 38 38 39 40 42 43 33 34 33 33 35 35 35 35 36 36 38 39 41 41 41 41 34 34 34 35 35 36 36 36 37 37 38 40 41 42 42 42 33 34 34 34 35 36 36 36 36 36 37 38 40 40 40 40 35 35 35 35 35 37 36 36 37 37 37 38 39 40 39 40 36 35 35 35 35 35 37 36 37 37 37 37 37 38 39 39 35 35 35 35 36 36 37 37 37 36 37 37 37 37 38 38 34 34 34 33 35 36 37 37 36 36 38 38 38 37 38 38 34 35 35 34 34 34 36 37 36 36 37 38 37 38 39 39 34 35 35 34 34 34 36 35 36 35 36 36 36 37 38 38 35 35 35 35 35 35 35 34 34 34 35 34 34 36 37 37 36 36 36 36 36 36 35 35 35 34 35 35 35 34 35 35 36 35 35 35 35 35 37 36 36 35 35 35 35 35 34 35 35 35 35 35 35 35 35 34 34 34 34 35 35 34 33 35 33 33 33 33 33 33 32 30 30 29 31 30 30 31 33 33 32 32 31 31 31 31 31 30 30 30 30 30 29 29 30 31 32 32 32 32 32 32 30 31 30 30 29 29 29 28 29 30 30 30 30 30 30 30 28 27 26 26 26 26 25 24 26 27 27 27 27 26 26 25 26 26 25 25 24 24 23 23 23 24 27 27 27 26 25 25 24 24 23 23 22 22 22 22 22 23 25 24 24 23 22 22 21 20 19 19 18 18 18 18 19 20 20 19 19 18 18 17 17 16 16 15 15 15 14 14 14 15 19 19 19 16 15 15 15 15 14 13 13 13 12 12 12 14 18 18 18 15 15 13 12 12 11 10 10 10 9 9 10 13 15 13 12 11 10 10 8 7 7 7 7 7 6 5 4 6 10 9 9 9 8 8 6 6 4 4 4 4 4 3 3 3 10 9 8 6 6 5 4 4 4 4 3 3 3 3 3 2 9 8 8 6 5 4 3 3 3 2 2 2 1 2 2 2 6 6 4 3 3 2 2 2 1 1 1 1 0 1 1 1 2 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 12 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 14 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0 18 11 6 0 0 0 0 0 0 0 0 0 0 0 0 0 21 12 6 4 1 0 0 0 0 0 0 0 0 0 0 0 24 15 7 4 1 0 0 0 0 0 0 0 0 0 0 0 28 17 8 5 1 0 0 0 0 0 0 0 0 0 0 0 30 19 12 5 1 0 0 0 0 0 0 0 0 0 0 0 29 21 14 6 2 1 0 0 0 0 0 0 0 0 0 0 28 20 13 6 3 1 0 0 0 0 0 0 0 0 0 0 27 20 11 6 2 1 1 0 0 0 0 0 0 0 0 0 28 20 12 7 3 2 1 0 0 0 1 1 1 1 1 1 28 20 13 8 4 2 1 1 1 1 2 2 2 2 2 3 29 21 14 9 6 4 3 3 3 3 3 4 3 5 5 5 30 22 15 11 8 5 3 3 3 4 3 4 4 5 5 5 29 21 16 13 8 3 3 2 2 2 2 4 4 4 4 4 28 20 16 12 7 2 3 4 4 4 4 4 5 5 5 6 27 21 16 11 6 3 5 5 5 5 5 5 7 7 8 8 28 22 17 10 6 5 4 3 3 3 3 3 3 5 8 8 28 22 15 10 7 6 4 4 3 3 3 3 3 7 8 9 27 20 13 8 4 3 2 1 1 2 5 5 5 5 5 6 25 19 13 10 7 5 4 3 2 3 5 4 4 5 6 6 24 19 14 11 8 6 5 5 4 3 3 3 3 5 7 6 25 20 16 13 11 9 7 5 5 3 3 3 3 3 5 4 26 21 17 13 11 7 8 7 5 4 2 2 2 2 3 3 29 25 21 15 12 10 11 10 9 6 3 2 2 3 3 3 32 28 25 20 17 14 11 11 10 9 6 4 2 4 6 3 36 33 30 24 21 18 13 10 12 10 8 6 4 3 2 2 40 37 35 30 26 23 16 13 12 12 12 8 6 4 2 2 44 42 38 36 32 29 22 18 14 11 13 10 7 5 3 2 49 46 43 41 37 34 28 24 21 15 12 7 5 5 5 3 51 50 47 44 40 37 32 29 26 20 13 9 5 6 6 4 55 54 49 47 44 41 36 32 28 23 17 13 9 8 7 4 58 56 53 50 46 43 38 34 31 25 19 15 11 9 6 4 60 58 54 52 48 45 40 36 33 27 21 17 12 9 5 2 62 59 56 54 50 46 41 38 34 29 22 18 15 11 6 3 63 60 57 54 50 46 42 38 35 30 23 19 16 11 7 5 60 58 56 53 49 46 40 37 32 27 24 19 15 12 8 6 58 57 54 51 47 44 39 35 30 26 23 19 15 12 9 6 57 55 52 50 45 43 38 34 29 25 23 19 16 11 8 6 55 52 50 49 44 41 37 32 28 24 22 18 15 12 8 6 54 50 48 47 43 39 35 31 27 22 19 16 14 10 7 4 51 48 45 43 41 37 32 27 23 20 18 15 12 8 6 4 48 46 42 39 37 35 30 23 20 19 14 12 9 6 5 3 46 43 40 36 34 32 27 21 18 16 12 10 8 5 4 3 42 37 34 31 29 27 22 18 15 11 13 11 9 6 6 4 36 33 32 27 25 22 20 17 14 11 9 7 7 6 5 3 31 29 27 23 21 18 16 15 12 8 6 5 4 3 1 0 27 26 23 18 18 17 13 10 6 3 3 2 2 1 1 1 21 20 19 15 14 10 7 4 2 1 1 0 0 0 0 0 14 11 9 10 6 5 2 1 1 0 0 0 0 0 0 0 5 3 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 4 1 2 1 0 0 0 0 1 1 2 2 4 5 4 6 8 7 5 5 4 3 3 4 4 5 7 8 8 9 7 10 13 12 11 10 9 9 9 9 7 8 10 13 14 13 13 13 15 15 14 11 10 11 11 11 11 12 13 16 16 16 16 17 17 16 18 15 13 14 14 15 15 16 18 20 19 20 20 20 19 16 20 18 16 16 16 17 17 18 20 21 22 22 22 21 20 18 22 18 16 16 16 17 18 19 20 22 21 21 20 19 20 20 25 21 19 16 16 16 18 19 21 22 21 22 20 20 22 21 28 24 20 18 17 16 18 19 20 21 21 22 22 22 21 20 28 24 20 18 17 16 17 18 19 20 20 21 21 21 21 20 27 23 20 19 16 15 16 16 17 18 18 19 19 19 19 18 27 23 19 19 16 15 15 16 15 16 16 16 17 17 17 17 26 22 18 17 13 12 14 14 14 15 16 16 17 17 16 15 28 24 20 13 10 9 10 12 13 13 13 13 13 15 17 15 26 21 17 12 8 7 9 12 11 11 12 11 11 14 15 13 24 19
14 10 9 7 9 10 11 11 11 12 10 12 13 11 23 18 13 9 7 7 8 9 10 10 10 10 9 11 12 10 22 16 13 8 6 7 7 8 10 10 10 9 9 10 10 9 21 15 11 7 7 6 7 8 10 10 10 10 8 9 8 6 21 15 12 7 7 7 8 9 10 10 10 10 10 9 7 5 23 15 10 11 8 7 8 8 9 9 10 10 11 9 6 5 24 17 12 12 8 8 9 10 11 12 13 12 12 10 8 6 24 18 13 13 10 11 12 13 15 16 14 14 14 12 10 7 24 19 15 16 14 14 15 16 17 17 16 16 15 14 11 9 26 22 19 18 18 18 18 17 18 18 18 18 17 16 14 12 28 24 22 19 20 20 21 21 22 23 21 21 21 21 19 16 31 27 24 21 22 22 23 23 23 24 23 23 23 23 22 20 32 29 26 25 25 25 26 27 27 27 27 26 26 25 25 24 33 29 26 26 26 26 26 27 29 29 29 28 29 28 27 27 33 29 26 26 26 26 27 28 29 29 29 29 29 30 31 31 33 30 28 27 26 26 27 28 29 29 29 30 31 33 34 34 33 31 30 29 27 27 27 28 29 29 29 32 34 35 35 34 34 30 28 29 27 27 27 29 29 30 30 32 34 34 35 34 33 29 27 29 27 27 27 29 29 30 30 32 34 34 35 35 32 30 27 26 26 27 28 28 29 30 30 30 31 32 35 36 30 28 25 24 26 26 26 26 26 27 30 30 30 31 33 35 28 25 24 22 23 24 25 26 26 27 27 28 28 30 32 33 24 23 21 22 22 24 23 23 23 24 26 26 27 29 29 32 23 22 21 20 21 22 22 23 23 24 24 24 25 26 28 30 22 20 19 19 21 22 23 23 23 24 24 24 24 24 26 27 20 19 20 20 22 23 22 23 22 23 24 24 24 24 24 25 17 18 19 18 20 21 20 21 21 21 20 22 24 23 22 23 16 18 16 17 20 21 19 17 18 18 17 18 22 22 21 22 17 16 16 13 15 16 15 14 14 13 13 14 16 17 19 20 15 15 12 12 14 16 13 10 11 10 10 10 12 14 15 19 14 12 9 10 13 14 10 8 8 6 7 8 8 9 12 14 12 9 9 10 11 10 6 5 6 2 2 2 5 6 8 10 8 7 7 9 6 4 1 0 1 0 0 0 0 1 3 6 5 5 5 3 3 1 0 0 0 0 0 0 0 0 0 3 3 3 4 3 1 0 0 0 0 0 0 0 0 0 0 0 1 2 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 2 1 0 2 4 1 0 0 0 0 0 0 0 0 0 0 2 0 1 7 8 6 2 0 0 0 0 0 0 0 0 0 1 0 2 14 13 12 8 2 0 0 0 0 0 0 0 0 0 0 3 15 19 18 13 4 0 0 0 0 0 0 0 0 0 0 5 14 22 22 15 6 1 0 0 0 0 0 0 0 1 0 7 15 24 26 22 13 3 0 0 0 0 0 0 0 1 1 7 19 29 29 26 15 3 0 0 0 0 0 0 0 0 0 8 23 29 30 30 16 3 1 4 1 0 0 0 0 0 0 4 18 27 26 25 14 2 1 14 13 0 0
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0 0 0 3 9 43 30 1 10 25 27 10 1 0 0 0 0 0 0 8 5 34 22 0 7 36 24 2 0 0 0 0 0 0 0 5 8 28 13 0 3 25 19 1 4 16 1 0 0 0 0 0 11 36 11 0 0 14 15 2 5 19 1 0 0 0 0 0 10 44 8 0 0 3 3 0 1 3 0 0 0 0 0 0 6 34 6 0 0 0 0 0 0 0 0 0 0 0 0 0 1 29 14 1 0 0 0 0 0 0 0 1 0 0 0 1 1 21 38 11 0 0 0 0 0 0 5 23 9 0 0 2 3 7 32 19 0 0 0 0 0 0 7 46 29 0 0 3 5 2 8 9 0 1 4 2 0 0 8 55 39 0 0 1 0 0 13 20 9 6 35 21 1 0 11 75 54 2 1 2 0 3 24 31 34 13 66 67 11 0 8 44 36 21 4 16 9 18 10 16 27 6 57 75 17 0 1 3 21 40 8 16 23 29 5 1 3 1 13 9 1 0 0 0 18 42 11 Columns 385 through 400 47 47 49 49 52 53 54 54 56 56 56 56 57 56 55 55 47 47 49 49 51 54 54 54 56 56 56 56 57 56 55 55 46 48 48 49 51 54 54 55 56 56 56 56 57 56 55 55 46 47 48 49 51 53 54 54 56 56 56 56 57 56 55 55 45 46 48 48 51 52 53 54 56 56 56 56 57 56 55 54 45 46 47 48 50 53 53 54 56 56 55 56 57 56 55 55 45 46 47 48 50 52 53 53 55 55 55 56 57 56 55 55 44 45 46 48 49 50 52 53 53 53 55 55 55 54 54 54 43 44 46 47 48 49 51 52 53 53 55 55 54 53 53 54 43 45 46 46 47 48 51 52 53 53 55 55 54 53 53 54 43 44 45 46 47 48 50 52 52 52 54 54 53 53 52 52 43 43 45 47 48 48 49 51 52 52 52 52 52 53 52 52 42 44 44 46 47 47 49 51 51 52 52 52 52 52 52 51 42 44 44 46 47 48 48 51 51 52 52 52 51 52 51 50 43 44 45 46 46 47 49 50 51 51 51 51 51 50 49 49 43 44 45 46 46 47 48 49 51 51 51 52 51 50 49 49 43 44 45 45 46 47 48 49 51 50 51 51 51 50 49 49 44 44 45 45 46 47 48 48 49 50 51 51 51 50 49 48 44 44 45 45 46 47 48 48 48 47 49 49 50 49 49 48 44 45 45 46 46 46 47 48 49 48 48 47 48 47 47 47 43 45 45 46 46 46 46 47 48 47 48 48 46 46 46 45 43 45 46 47 46 46 46 46 46 46 46 47 46 46 45 45 43 44 44 45 45 46 46 46 46 46 46 46 46 46 45 44 41 43 44 44 45 46 46 46 46 46 45 45 45 45 45 43 41 40 41 42 43 43 44 44 44 44 44 44 45 44 43 43 40 42 42 43 43 42 42 42 43 42 42 42 43 42 42 40 39 40 41 41 41 41 40 40 40 40 40 40 41 40 39 38 39 39 39 39 40 41 40 39 39 39 39 39 40 40 39 37 39 40 40 39 40 39 38 38 39 39 38 38 39 39 38 36 38 40 40 39 39 40 39 38 38 37 37 37 37 36 35 35 37 39 39 38 38 38 38 38 37 37 37 36 36 35 35 34 35 37 36 36 36 37 37 35 36 36 36 35 35 34 33 32 35 35 34 36 36 35 35 34 35 34 34 34 33 32 31 33 35 34 35 35 35 34 34 34 34 33 33 33 32 31 31 30 33 32 33 35 35 34 32 32 34 33 32 32 31 30 29 28 32 30 31 31 32 33 31 31 32 31 31 30 29 29 28 26 29 28 29 30 30 29 28 28 30 29 29 28 27 27 26 26 28 28 28 28 28 27 26 27 26 26 26 25 25 23 23 23 24 26 26 27 27 25 25 24 25 25 25 24 23 22 22 21 22 21 21 23 24 25 24 24 24 23 23 22 21 20 20 17 21 19 20 20 21 22 21 21 21 20 20 19 18 17 17 15 16 15 16 17 18 18 17 17 17 17 16 16 15 14 13 12 14 14 13 15 15 16 16 15 13 13 12 12 12 12 11 9 12 13 13 12 12 13 13 12 12 11 10 10 11 10 10 8 8 8 8 7 8 9 9 8 10 9
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0 0 0 0 0 0 0 0 11 40 5 0 0 0 0 0 0 0 0 0 0 0 0 0 18 40 2 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 5 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 2 0 0 0 0 0 0
???
???
Machine Learning: Features
6
Learning that “the top left pixel has 57/100 green”, basically says nothing about whether or not there’s a dog
in the image.
Conclusion: Pixel values are pretty meaningless on their own
Machine Learning: Features
7
Dog
Not a Dog
Machine Learning: Features
8
Dog
Not a Dog
Machine Learning: Features
9
Dog
Not a Dog
Location/Description of
edges
Location/Description of
edges
Machine Learning: Features
10
Dog
Not a Dog
Has Eyes
Does Not Have Eyes
Machine Learning: Features
11
Dog
Not a Dog
Has Fur
Does Not Have Fur
Machine Learning: Features
AND(Has Eyes, Has Fur) Dog
Billion 0’s, 1’s Thousand 0’s, 1’s Two 0’s and 1’s
Not Dog
NOT(AND(Has Eyes, Has
Fur))
13
Classifier
More RedMore Blue
Bigger
Smaller
= strawberry= apple
= testing data
= training data
14
Classifier
More RedMore Blue
Bigger
Smaller
= strawberry= apple
Note: There may be huge strawberries! And tiny apples.
15
ClassifierDefinition: A classifier that draws a line to separate the
data is called a linear classifier
16
ClassifierDefinition: A classifier that draws a line to separate the
data is called a linear classifier
y = mx+b
(Learning means finding m and b!)
17
Classifier: SPAM!
False True
False
True
Email Contains Link
Email Has “Credit Card”= SPAM
= HAM
18
Classifier: SPAM!
False True
False
True
Email Contains Link
Email Has “Credit Card”= SPAM
= HAM
19
Classifier: SPAM!
False True
False
True
Email Contains Link
Email Has “Credit Card”= SPAM
= HAM
20
Classifier: SPAM!
False True
False
True
Email Contains Link
Email Has “Credit Card”= SPAM
= HAM
21
Classifier Shapes
Takeaway: Not all data can be divided into groups by all shapes
Our First Classification Algorithm: Memorize And Guess
22
1. Memorize every training data-label pair we see.
2. Create a classifier that, when given any item seen in our training data, reports exactly that item’s label. If it gets an item it’s never seen before, guess the label randomly.
Our First Classification Algorithm: Memorize And Guess‣ So, is this Memorize and Guess thing a good idea?
‣ Sure! If you’re guaranteed to see just about every possible data point during training.
‣ Well that’s crazy…
‣ Conclusion: no. Memorize and Guess is a bad idea.
‣ Q: Can we do better?
‣ A: Of course!23
Our Second Classification Algorithm: Nearest Neighbor‣ Idea: instead of randomly guessing when we
haven’t seen an item before, guess the label of the thing that is most similar to it!
24
Our Second Classification Algorithm: Nearest Neighbor‣ Idea: instead of randomly guessing when we
haven’t seen an item before, guess the label of the thing that is most similar to it!
Strawberry (known from training)
25
Our Second Classification Algorithm: Nearest Neighbor‣ Idea: instead of randomly guessing when we
haven’t seen an item before, guess the label of the thing that is most similar to it!
Strawberry (known from training)
Given this item to classify
26
Our Second Classification Algorithm: Nearest Neighbor‣ Idea: instead of randomly guessing when we
haven’t seen an item before, guess the label of the thing that is most similar to it!
Strawberry (known from training)
Given this item to classify
They’re super similar!27
Our Second Classification Algorithm: Nearest Neighbor‣ Idea: instead of randomly guessing when we haven’t
seen an item before, guess the label of the thing that is most similar to it!
1. Memorize the label of every training data we get.
2. Create a classifier that, for a given item X, will do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.28
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
29
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
30
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Label guess: blue (apple)
31
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Q1: Halts?
32
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Q1: Halts?
A: Yes!
33
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Q2: Correct?
A: Again, correctness in learning is tricky. If we ask for the perfect classifier,
we’re setting ourselves up for a loss.
34
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Q3: Growth Rate?
A: Memorize each item.
35
Nearest Neighbor1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Q3: Growth Rate?
A: Memorize each item.
Note: do we care about the growth rate of the classifier,
too?36
Clicker Question!
= class one= class two
Q: Which dataset would Nearest Neighbors likely do better on?
[A] [B]
37
Clicker Question!
= class one= class two
Q: Which dataset would Nearest Neighbors likely do better on?
[A] [B](hint)
38
Clicker Answer!
= class one= class two
Q: Which dataset would Nearest Neighbors likely do better on?
[B]
39
Multiple Classes‣ So far we’ve always been talking about choosing
between class one and class two.
‣ We can extend all of this to many classes!
‣ Consider MNIST:
40
MNIST
Each object is a 20x20, black and white image. 0 = black, 1 = white.
41
MNIST‣ 70,000 images total.
‣ Even slightly sophisticated learning algorithms can achieve a nearly perfect score on this dataset (train on 60,000, test on 10,000).
‣ E.g. an extension of nearest neighbors called K Nearest Neighbors gets 99.5 percent correct.
‣ So how does it work with multiple classes?
42
MNIST
43
INPUT:
: “five”
: “four”
: “two”
MNIST
44
INPUT:
: “five”
: “four”
: “two”
= class one= class two= class three
MNIST
45
INPUT:
: “five”
: “four”
: “two”
= class one= class two= class three
Clicker Question!1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Nearest Neighbor
Q: Does Nearest Neighbor need to change at all to account for more classes (instead of just class one vs
class two)?
Clicker Question!1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Nearest Neighbor
Q: Does Nearest Neighbor need to change at all to account for more classes (instead of just class one vs
class two)?
[A] Yes!
[B] No!
Clicker Answer!1. Memorize the label of every training data we get.
2. Create a classifier that will report, for a given item X, do the following:
I. Find the item most similar to X.
II. Report this similar item’s training label.
Nearest Neighbor
Q: Does Nearest Neighbor need to change at all to account for more classes (instead of just class one vs
class two)?
[A] Yes!
[B] No!
Overfitting‣ Generalization is the goal of learning.
‣ If all we cared about was how well you did on the training data, then the Memorize and Guess algorithm would be amazing!
‣ We can test how well our learner does by how well its classifier does on the test data relative to the training data (hopefully just as well!).
‣ In the algorithms we saw, 100% on training. ??% on Test.
49
Clicker Question!
50
= class one= class two= class three
Q: Which classifier is overfitting more?
[A] [B]
Clicker Question!
51
= class one= class two= class three
Q: Which classifier is overfitting more?
[A] [B]
Hint: Which one would we expect to perform worse during testing?
Clicker Answer!
52
= class one= class two= class three
Q: Which classifier is overfitting more?
[A] [B]
Hint: Which one would we expect to perform worse during testing?
Clicker Answer!
53
= class one= class two= class three
Q: Which classifier is overfitting more?
[A] [B]
Hint: Which one would we expect to perform worse during testing?
Clicker Answer!
54
= class one= class two= class three
Q: Which classifier is overfitting more?
[A] [B]
Hint: Which one would we expect to perform worse during testing?
Occam’s Razor
55
We ought to prefer simpler explanations
Occam’s Razor
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We ought to prefer simpler explanations
Isaac Newton
Bertrand Russell
Ray Solomonoff
William of Ockham
AristotlePtolemy
Our Final Classification Algorithm: K-Nearest Neighbor‣ Idea: instead of randomly guessing when we haven’t seen
an item before, guess the label of some things that are most similar to it!
1. Memorize the label of every training data we get.
2. Create a classifier that, for a given item X, do the following:
I. Find the K items most similar to X.
II. Each of these K items vote on the label for the new item
57
K Nearest Neighbor
58
= class one= class two= class three
K = 3
K Nearest Neighbor
59
= class one= class two= class three
K = 3
K Nearest Neighbor
60
= class one= class two= class three
K = 3
K Nearest Neighbor
61
= class one= class two= class three
K = 3
K Nearest Neighbor
62
= class one= class two= class three
K = 3
K Nearest Neighbor
63
= class one= class two= class three
K = 3
K Nearest Neighbor
64
For both K-NN and Nearest Neighbor, we need a notion of distance
Reflection on Classification
65
‣ Problem: Come up with a classifier that can distinguish objects from different classes.
‣ Algorithms: Memorize and Guess, NN, K-NN
‣ Train: think really hard, based on what objects you’ve seen so far, about how to make the classifier.
‣ Test: evaluate how well your classifier does.
‣ Overfitting: your way better on training than on testing (don’t generalize well)
‣ Features: the relevant pieces of information an algorithm gets access to in order to learn (i.e. an image wouldn’t be pixel values, it would be location of edges, presence of eyes, nose, fur, etc.).
One Final Philosophical Note…
66
The classification problem can be about any concept…
One Final Philosophical Note…
67
The classification problem can be about any concept…
Q: What is art?Q: What is a sport?
Q: What is a chair?
Q: What is language?
One Final Philosophical Note…
68
The classification problem can be about any concept… Q: What is art?
Q: What is a sport?
Q: What is a chair?
Q: What is language?
In some sense, our ability to define algorithms to learn these concepts paints a picture of how effective we can
be at defining these concepts.
One Final Philosophical Note…
69
In some sense, our ability to define algorithms to learn these concepts paints a picture of how effective we can
be at defining these concepts.
Q: What is a sport?
What would a classifier for this look like?
One Final Philosophical Note…
70
In some sense, our ability to define algorithms to learn these concepts paints a picture of how effective we can
be at defining these concepts.
Q: What is a sport?
What would a classifier for this look like?Can it be learned by pointing to positive and negative
examples?
Clicker Question!
71
[A] That’s a 1
[B] That’s a 7
[C] That’s a crowbar
Clicker Answer!
72"Kaninchen und Ente" ("Rabbit and Duck") from the 23 October 1892 issue of Fliegende Blätter
One Final Philosophical Note…
Our concepts have meaning in so far as they can be learned (algorithmically?)
73
One Final Philosophical Note…
Our concepts have meaning in so far as they can be learned (algorithmically?)
74
Things a regular computer can compute before the sun
goes supernova
Things that can be computed, period.
Things a domino computer could compute before the
sun goes supernova“Computability”
One Final Philosophical Note…
Our concepts have meaning in so far as they can be learned (algorithmically?)
75
Things that can be LEARNED, period.
“Learnability”
“A Theory of the Learnable”
Les Valiant, 1984
Reinforcement Learning
76
Demo time!
Reinforcement Learning
77
observation, reward
action
world
agent
Reinforcement Learning
78
observation, reward
action
world
agent
Reinforcement Learning
79
observation, reward
action
world
agent
Goal: Maximize reward!
Reinforcement Learning
80
observation,
rewardaction
world
agent
Goal: Maximize reward!
Any problem with a goal…