Homework #7

Description

Please answer question 7.2

Unformatted Attachment Preview

PROJECT 7
Guidelines:
1. Submit a compressed (Zipped) folder that contains your solution named
“lastname_firstname_project7” on Canvas by the due date.
2. Please write your name and your ID in the header in the following format.
Name:
ID:
The deadline for the project is Monday, Oct 23 at 4:50 pm.
Problems
Page 167, Problem 7.2:
Universal Bank is a relatively young bank growing rapidly in terms of overall
customer acquisition. The majority of these customers are liability customers
(depositors) with varying sizes of relationship with the bank.
The customer base of asset customers (borrowers) is quite small, and the bank is
interested in expanding this base rapidly to bring in more loan business. In
particular, it wants to explore ways of converting its liability customers to
personal loan customers (while retaining them as depositors). A campaign that
the bank ran last year for liability customers showed a healthy conversion rate of
over 9% success. This has encouraged the retail marketing department to
devise smarter campaigns with better target marketing. The goal is to use k NN
to predict whether a new customer will accept a loan offer. This will serve as the
basis for the design of a new campaign. The file UniversalBank.xlsx contains data
on 5000 customers. The data include customer demographic information (age,
income, etc.), the customer’s relationship with the bank (mortgage, securities
account, etc.), and the customer response to the last personal loan campaign
(Personal Loan). Among these 5000 customers, only 480 (= 9.6%) accepted the
personal loan that was offered to them in the earlier campaign.
a. Transform the categorical predictors with more than two categories into
dummy variables.
b. Partition the data into training (60%) and validation (40%) sets.
c. Perform a k NN classification with all predictors except ID and ZIP code
using k = 1. Specify the success class as 1 (loan acceptance), and use the
default cutoff value of 0.5.
d. What is a choice of k that balances between overfitting and ignoring the
predictor information?
e. Show the confusion matrix for the validation data that results from using
the best k.
Courtesy – Statistics.com
Background:
A relatively young bank is growing rapidly in terms of overall customer acquisition.
Majority of these are Liability customers with varying sizes of relationship with the bank.
The customer base of Asset customers is quite small, and the bank WANTS to grow
this base rapidly to bring in more loan business.
Specifically, it wants to explore ways of converting its liability customers to
Personal Loan customers.
A campaign the bank ran for liability customers last year showed a healthy conversion
rate of over 9% successes. This has encouraged the Retail Marketing department
to devise smarter campaigns with better target marketing.
Analytics Objectives:
1 While designing a new campaign, can we model the previous campaign’s customer behavior to
analyze what combination of parameters make a customer more likely to
accept a personal loan?
2 There are several special products / facilities the bank offers like CD and security accounts,
online services, credit cards, etc. Can we spot any association among these
for finding cross-selling opportunities?
Data Description:
ID
Age
Experience
Income
ZIPCode
Family
CCAvg
Education
Mortgage
Personal Loan
Securities Account
CD Account
Online
CreditCard
Customer ID
Customer’s age in completed years
#years of professional experience
Annual income of the customer ($000)
Home Address ZIP code.
Family size of the customer
Avg. spending on credit cards per month ($000)
Education Level. 1: Undergrad; 2: Graduate; 3: Advanced/Professional
Value of house mortgage if any. ($000)
Did this customer accept the personal loan offered in the last campaign?
Does the customer have a securities account with the bank?
Does the customer have a certificate of deposit (CD) account with the bank?
Does the customer use internet banking facilities?
Does the customer use a credit card issued by UniversalBank?
Note: Data are hypothetical
© Cytel, Inc. 2005
ID Age
1 25
2 45
3 39
4 35
5 35
6 37
7 53
8 50
9 35
10 34
11 65
12 29
13 48
14 59
15 67
16 60
17 38
18 42
19 46
20 55
21 56
22 57
23 29
24 44
25 36
26 43
27 40
28 46
29 56
30 38
31 59
32 40
33 53
34 30
35 31
36 48
37 59
38 51
39 42
40 38
41 57
42 34
43 32
44 39
45 46
46 57
47 39
48 37
49 56
50 40
51 32
52 61
53 30
54 50
55 29
56 41
Experience Income
1
49
19
34
15
11
9
100
8
45
13
29
27
72
24
22
10
81
9
180
39
105
5
45
23
114
32
40
41
112
30
22
14
130
18
81
21
193
28
21
31
25
27
63
5
62
18
43
11
152
19
29
16
83
20
158
30
48
13
119
35
35
16
29
28
41
6
18
5
50
24
81
35
121
25
71
18
141
13
80
32
84
9
60
7
132
15
45
20
104
31
52
14
43
12
194
26
81
16
49
8
8
37
131
6
72
26
190
5
44
17
139
ZIP Code Family CCAvg
91107
4
1,60
90089
3
1,50
94720
1
1,00
94112
1
2,70
91330
4
1,00
92121
4
0,40
91711
2
1,50
93943
1
0,30
90089
3
0,60
93023
1
8,90
94710
4
2,40
90277
3
0,10
93106
2
3,80
94920
4
2,50
91741
1
2,00
95054
1
1,50
95010
4
4,70
94305
4
2,40
91604
2
8,10
94720
1
0,50
94015
4
0,90
90095
3
2,00
90277
1
1,20
91320
2
0,70
95521
2
3,90
94305
3
0,50
95064
4
0,20
90064
1
2,40
94539
1
2,20
94104
1
3,30
93106
1
1,20
94117
1
2,00
94801
2
0,60
91330
3
0,90
94035
4
1,80
92647
3
0,70
94720
1
2,90
95814
1
1,40
94114
3
5,00
94115
4
0,70
92672
3
1,60
94122
3
2,30
90019
4
1,10
95616
1
0,70
94065
1
5,70
94720
4
2,50
95014
3
0,70
91380
4
0,20
95747
2
4,50
92373
1
1,80
92093
4
0,70
94720
1
2,90
94005
1
0,10
90245
3
2,10
95819
1
0,20
94022
2
8,00
Education
1
1
1
2
2
2
2
3
2
3
3
2
3
2
1
3
3
1
3
2
2
3
1
1
1
1
3
1
3
2
3
2
3
3
3
1
1
3
3
3
3
1
2
1
1
1
2
3
3
1
2
1
1
3
3
1
Mortgage
0
0
0
0
0
155
0
0
104
0
0
0
0
0
0
0
134
0
0
0
111
0
260
163
159
97
0
0
0
0
122
0
193
0
0
0
0
198
0
285
0
0
412
0
0
0
153
211
0
0
0
0
207
240
0
0
Personal
Loan
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
55
56
28
31
49
47
42
42
47
59
62
53
47
53
42
53
44
41
28
31
58
46
54
50
60
47
41
33
46
27
40
48
65
25
55
35
43
60
65
38
41
54
49
66
48
61
53
43
56
24
43
42
33
43
41
62
40
58
39
30
31
2
5
24
21
18
17
23
35
36
23
21
29
18
29
20
16
3
7
32
20
30
26
36
22
16
9
22
2
16
22
41
-1
30
10
19
34
39
12
15
28
23
41
23
36
23
18
32
0
17
18
7
17
14
38
15
34
14
29
131
93
188
39
125
22
32
105
131
105
45
60
20
115
69
130
85
135
135
12
29
133
19
41
40
82
50
18
109
42
78
51
113
118
29
34
64
121
48
80
161
94
15
74
30
44
22
38
35
69
43
32
49
9
45
82
92
39
94005
95616
94065
91320
90404
93407
90089
94523
90024
91360
95670
95123
93407
90045
91335
93907
92007
94606
94611
94901
91320
92220
93305
94720
95134
94612
92507
94305
91730
94005
94501
94305
94117
94303
90277
94105
94305
94550
92612
95617
95014
92121
92374
91711
94080
94608
93555
95670
93311
94704
92717
92037
95136
94542
91330
94143
91775
92703
92354
3
2
2
2
3
1
1
4
2
1
2
4
3
4
1
4
1
1
2
4
3
3
2
2
4
3
1
1
1
4
4
3
2
4
4
4
3
2
1
4
1
1
1
3
1
3
3
2
4
3
4
1
1
1
3
4
3
2
3
0,10
1,20
0,20
4,50
1,70
5,70
1,00
0,00
3,30
3,80
2,80
2,00
2,10
0,20
3,50
1,00
5,00
4,00
3,30
3,80
0,30
0,50
2,60
0,40
1,30
2,70
4,00
2,40
0,90
1,80
2,20
1,10
1,10
2,30
5,60
1,10
0,60
1,70
2,00
0,20
5,20
2,90
0,30
0,10
1,20
1,30
1,00
0,30
1,30
0,10
2,90
0,70
0,60
2,80
1,00
1,30
1,00
2,80
0,50
2
3
1
1
2
1
1
2
1
1
1
3
1
1
1
2
1
3
1
2
3
2
3
1
1
2
3
2
3
3
2
1
1
3
2
3
2
3
1
3
1
1
1
3
1
2
3
2
1
2
1
1
3
1
2
2
1
1
3
0
0
0
455
0
112
0
0
0
0
336
132
0
0
0
0
0
0
0
0
0
0
0
118
174
0
0
0
0
0
126
0
0
0
0
0
0
236
0
0
0
0
0
0
0
0
198
0
166
0
0
136
166
0
0
0
309
103
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
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
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
65
54
58
41
32
54
52
58
37
39
60
31
34
38
41
28
58
31
30
53
58
59
49
59
59
51
35
33
25
49
59
46
50
52
48
46
26
57
60
54
24
26
41
32
61
29
61
38
28
53
27
25
33
50
27
27
52
38
58
40
29
33
16
7
29
26
32
13
15
35
5
8
14
16
4
34
1
4
29
33
32
25
34
35
25
11
9
1
23
35
19
25
28
22
22
0
32
36
29
0
0
17
6
35
0
35
12
4
27
1
1
9
26
1
1
28
13
34
81
35
61
73
112
12
38
73
84
78
80
115
82
74
70
81
149
51
39
98
45
49
128
42
18
31
58
48
54
70
124
84
83
163
42
118
132
24
22
58
60
15
83
79
41
134
80
52
70
92
43
21
23
13
112
138
11
171
42
92024
92831
92833
92647
94304
90057
91711
94523
92130
92121
91301
92096
92646
92182
92131
94801
93720
90840
90245
95035
93010
95035
95054
94928
93305
90245
95831
91770
94117
92093
90007
94102
94542
91423
93955
94107
92834
93117
94551
92612
94596
92131
94025
94720
94545
95819
95053
90036
91125
95120
94706
95827
94305
91320
90503
90250
95817
92717
90095
3
1
2
3
1
2
3
2
1
4
3
2
1
2
3
3
4
2
3
3
4
4
2
3
1
2
3
1
4
2
1
1
4
2
3
2
3
1
2
4
4
4
4
2
4
4
2
1
4
2
1
3
3
4
4
2
3
2
4
1,80
1,50
2,30
3,00
4,60
0,20
0,90
0,70
3,60
2,40
0,50
1,30
2,70
0,00
0,50
1,50
7,20
1,75
1,10
1,80
2,10
2,50
0,40
1,50
1,20
0,40
2,00
2,10
1,60
1,50
7,40
2,67
3,60
0,40
2,20
7,50
6,50
1,30
1,00
1,30
1,60
0,40
2,67
1,50
1,70
6,50
2,80
2,00
2,60
1,10
1,50
1,00
0,90
1,00
2,10
2,00
0,40
7,80
1,50
2
2
3
1
1
3
3
2
2
1
1
1
2
1
3
1
2
3
2
2
1
2
1
1
3
3
1
3
1
2
1
2
3
1
2
1
3
1
1
3
1
1
1
3
2
3
1
1
1
1
1
2
3
1
3
1
1
1
1
0
0
193
0
366
0
0
0
0
118
0
101
251
0
0
276
0
0
0
0
0
0
0
0
0
161
149
0
0
0
0
0
188
116
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
42
45
52
29
53
62
51
36
24
29
52
39
48
46
64
55
60
51
50
48
53
34
48
55
27
36
32
35
30
58
56
38
49
34
40
64
51
44
46
57
54
38
27
39
44
56
32
45
26
55
52
39
24
47
47
48
47
35
46
17
20
25
3
29
37
27
12
0
3
26
14
23
21
40
29
36
25
23
24
29
10
24
31
3
11
6
9
3
34
31
12
25
10
16
39
26
18
22
33
28
14
3
14
20
30
6
19
2
25
27
13
-1
23
22
24
22
10
19
168
85
44
65
24
11
38
10
135
148
63
115
45
159
169
112
93
29
85
21
144
13
165
9
59
158
29
20
68
65
61
91
31
71
73
172
20
55
69
155
94
92
125
74
72
61
25
83
104
41
58
93
39
148
53
71
92
61
38
95503
91711
93111
94132
95818
91942
90401
93524
95133
92173
92717
91320
95616
94305
91320
94043
92521
90404
92122
93118
92697
94577
93407
91345
94123
92152
91355
94609
94306
95747
96150
95616
91355
94115
94110
94707
92131
94720
91604
91326
90291
95818
95521
94305
92807
94707
92130
95051
94306
95014
94305
94720
94085
94551
92677
93117
94720
94304
94122
2
4
3
4
4
1
2
4
1
3
2
1
1
3
2
2
1
1
1
4
2
4
1
4
4
1
1
2
4
4
2
4
1
4
4
4
2
1
2
1
1
2
2
3
3
1
2
2
3
3
4
1
2
2
4
2
1
4
3
7,90
1,10
1,00
1,80
0,20
0,10
1,00
0,70
1,50
4,10
1,50
1,00
0,30
1,90
2,10
1,40
4,30
0,30
2,67
0,60
6,80
1,00
5,00
0,70
0,00
5,10
1,90
1,40
2,00
2,20
1,90
1,40
1,00
0,10
2,67
3,10
0,00
0,20
1,70
7,40
1,90
0,00
0,60
3,00
0,30
2,20
0,30
1,70
2,50
1,00
1,80
1,50
1,70
7,50
1,90
1,70
2,80
2,10
2,50
2
2
2
2
1
1
3
2
1
1
2
3
1
3
1
1
1
3
2
1
1
1
1
1
1
3
3
3
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
3
3
1
2
1
3
3
3
2
1
3
1
2
3
2
0
0
135
244
0
0
164
81
0
0
0
0
0
315
122
0
0
140
0
0
0
95
0
89
90
0
0
0
0
0
105
100
0
0
0
282
0
0
209
0
0
249
0
0
0
0
0
0
0
0
91
0
0
0
98
145
0
0
135
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
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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
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
62
26
38
43
62
57
28
51
48
41
65
41
35
38
53
55
26
30
54
65
47
65
66
26
66
35
56
51
42
49
27
45
49
63
47
64
43
60
40
29
41
30
49
30
29
50
39
33
57
34
61
44
40
51
37
44
42
51
43
37
1
8
18
38
32
3
26
22
16
39
17
11
14
29
29
1
6
28
40
21
41
40
0
41
9
30
27
16
23
1
19
23
38
22
39
13
36
14
3
16
5
24
5
2
26
14
8
31
9
36
19
13
25
12
19
15
25
16
58
80
71
89
83
28
52
70
71
75
170
78
25
60
120
99
55
29
170
53
138
134
42
99
18
24
55
58
111
33
74
38
23
61
81
129
33
63
70
45
65
74
50
22
30
21
155
64
65
71
40
69
69
45
62
172
24
80
8
91320
95616
94720
93407
92521
95831
94112
90089
91711
94005
90095
94025
92614
94025
92626
92121
90089
94305
92182
91711
94583
91942
92103
92697
92691
95747
94107
92407
93106
90245
92121
90840
94305
94720
90504
94002
95039
94063
94923
95023
90095
95616
94706
90058
92126
91125
94577
92121
94118
91711
90029
92806
94305
94806
92110
94306
92121
92373
90089
4
1
4
3
1
3
4
1
1
1
3
4
2
2
4
2
3
3
2
3
1
3
2
4
3
4
1
1
2
1
4
2
4
2
1
1
1
4
4
4
3
4
4
4
4
4
2
4
4
4
3
3
3
3
3
2
3
1
3
1,70
0,80
1,80
0,50
1,80
0,20
1,70
1,20
1,40
3,70
7,90
0,80
1,00
0,60
2,70
1,40
2,60
1,00
6,20
2,20
0,00
3,90
0,70
2,30
0,50
0,30
1,40
0,00
1,20
0,30
1,80
0,70
0,60
1,50
2,90
2,50
0,75
2,20
1,40
0,20
0,50
2,20
1,80
0,50
1,00
1,00
3,90
2,10
2,60
0,70
0,50
0,50
2,33
0,60
0,70
4,30
1,00
4,90
0,67
1
2
3
3
3
1
2
1
3
3
3
1
2
3
2
1
3
2
2
1
1
3
3
3
1
1
1
1
3
3
2
1
3
1
1
1
3
1
2
1
3
1
3
3
3
1
1
3
3
3
2
3
2
2
2
3
2
1
2
0
150
0
0
0
0
0
169
0
280
99
78
0
0
111
264
113
117
325
0
0
121
138
0
0
0
77
0
251
0
112
0
98
0
138
0
0
0
0
158
0
0
0
109
0
0
0
164
0
0
0
0
0
131
0
391
0
0
88
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
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
1
0
0
0
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
30
45
35
60
34
55
43
41
34
65
45
49
48
60
55
42
32
62
57
52
36
34
63
24
57
40
27
65
60
44
63
59
56
54
52
58
60
28
54
32
59
63
48
56
36
57
29
39
59
31
43
35
54
51
44
25
40
26
39
5
19
9
34
9
25
19
15
9
39
21
25
23
35
29
18
8
38
32
26
6
9
37
-2
31
16
2
39
34
20
39
34
30
28
27
32
35
4
30
6
33
38
23
32
12
27
3
13
34
6
19
5
24
27
19
0
15
2
14
38
93
55
64
122
70
81
159
70
150
152
195
22
22
79
33
128
91
39
121
21
41
45
51
165
119
110
20
64
101
101
99
158
89
80
114
49
191
78
28
42
140
45
122
65
68
153
89
91
55
118
22
63
12
50
43
173
60
113
94542
90095
94536
94304
90623
93720
92069
90057
92843
92120
94550
95605
90740
91207
92373
90401
94720
95929
90277
94550
91741
93720
93437
90630
95054
91335
95670
90034
90266
92717
92007
90034
90089
95039
95616
91330
94110
90064
92374
94115
95630
92407
95053
95827
95051
94117
93657
92110
93524
92038
91304
93407
92606
92192
90745
94305
95060
93407
94301
4
4
1
2
1
3
2
1
4
2
2
4
1
1
3
1
2
1
4
1
1
3
2
3
1
2
4
3
1
3
1
1
4
1
1
2
3
1
4
3
1
1
1
2
3
1
2
4
1
4
2
1
3
4
3
2
4
2
1
0,80
2,60
2,00
1,70
0,00
1,40
3,20
5,50
1,30
6,90
7,50
3,00
0,10
1,30
0,80
1,40
4,33
3,80
0,90
7,30
0,67
2,30
0,70
0,30
1,60
4,20
1,80
0,70
0,80
4,40
3,90
4,40
6,10
1,90
1,30
2,00
0,50
6,33
1,00
1,00
0,80
2,50
1,30
0,30
2,60
1,40
2,00
1,40
2,60
2,00
3,30
0,67
1,40
0,50
2,70
1,60
6,60
3,00
1,00
1
3
1
3
1
3
1
3
1
1
1
1
1
1
1
3
1
1
1
1
3
1
3
3
2
2
3
2
2
2
1
1
1
2
3
1
2
1
2
1
2
1
2
1
2
3
1
2
1
2
1
3
3
2
2
3
1
1
3
129
0
0
0
0
0
0
0
0
196
0
617
0
123
0
0
0
0
0
167
0
0
0
0
0
0
190
0
248
82
0
0
0
0
0
402
0
0
0
0
0
0
0
360
0
0
392
0
0
185
0
103
138
78
0
0
0
132
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
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
1
1
0
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
28
52
53
44
43
56
38
30
32
35
43
58
25
54
57
50
32
63
31
36
58
56
49
30
33
45
30
47
25
63
55
65
44
51
35
30
31
54
45
45
58
54
53
33
60
50
26
54
28
36
29
54
55
61
36
45
64
60
49
4
28
29
20
19
30
14
6
6
10
19
32
0
24
32
24
8
37
6
12
34
30
25
5
7
21
5
23
0
33
29
41
18
25
9
5
5
30
20
19
32
29
28
9
35
24
2
30
3
10
2
28
30
36
11
19
40
36
22
155
91
55
173
71
24
42
141
32
55
153
113
30
29
174
35
98
30
58
25
19
44
20
98
90
61
40
38
28
34
73
133
53
21
40
41
82
100
155
45
9
48
18
80
64
29
48
23
84
179
30
93
39
60
133
125
58
89
82
92182
92692
95818
90277
92101
94704
94610
94539
93106
94539
90254
94590
92691
92028
90089
92717
95054
92054
95051
92101
92029
93105
90291
91941
92346
94304
94402
94618
92093
94305
95616
94904
94608
9307
93943
95051
95482
95814
90024
92521
94080
91709
90095
91311
94509
93023
90503
94608
90024
94542
95747
91604
92647
92866
90245
92354
93437
91745
90019
4
4
4
2
3
2
1
2
1
4
2
2
2
3
1
1
2
2
2
4
4
4
4
2
3
3
4
2
2
1
2
4
1
4
3
4
4
4
1
1
3
4
4
4
2
4
3
2
4
3
4
1
2
3
1
1
1
2
1
5,30
1,00
1,10
1,40
0,30
0,40
2,00
4,33
1,90
1,30
7,50
1,40
1,70
1,00
6,80
0,30
2,00
1,00
2,50
1,00
0,70
0,70
1,00
3,10
1,60
0,70
2,00
2,10
1,70
1,50
2,30
2,00
0,20
0,60
0,90
1,70
1,80
3,40
7,00
0,20
0,30
1,80
0,10
3,40
2,80
0,10
0,70
0,40
0,20
6,60
1,50
4,90
1,90
0,50
3,80
2,40
1,80
2,80
2,67
2
2
2
1
3
3
2
1
3
1
1
1
2
3
2
3
2
3
1
1
1
2
1
1
1
1
2
3
2
3
3
1
1
3
1
2
2
3
1
1
3
3
3
1
1
1
2
1
1
1
2
1
2
2
1
1
3
1
2
0
0
0
419
0
88
81
0
0
0
0
270
0
148
466
0
175
159
0
147
0
174
111
220
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
109
0
0
0
0
0
0
0
112
133
0
182
290
0
0
0
125
1
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
47
60
45
32
52
35
40
53
27
58
47
28
46
43
56
28
42
32
62
37
51
39
43
52
30
52
61
36
58
47
64
52
58
48
64
58
47
49
31
61
51
28
39
54
50
30
64
29
48
35
60
55
29
48
43
66
25
45
34
23
36
20
7
28
8
15
29
0
33
22
3
20
19
30
3
18
7
38
13
26
13
17
28
6
26
35
9
32
23
39
27
28
24
40
32
23
23
4
37
25
-2
13
28
24
4
39
3
24
10
36
30
4
22
19
42
0
20
10
110
54
89
42
41
38
85
83
33
50
58
115
145
161
38
28
75
35
24
78
113
75
91
31
45
80
50
31
113
29
59
43
122
29
91
65
22
71
60
60
69
48
21
53
29
60
42
69
20
200
141
81
183
149
83
35
13
39
21
94111
92182
93311
92407
94309
93106
94304
90073
90089
94501
93105
92333
91380
95616
92029
90505
92182
92521
94720
94998
94086
94305
91311
91330
95819
94709
92122
95825
93943
94304
92626
93555
95136
90509
93106
94590
93108
95134
94588
91706
95747
94132
94022
92109
94110
91107
92068
94303
95841
91107
90277
92123
91423
94928
94305
94305
91342
90232
92634
2
4
4
3
3
4
2
4
4
4
4
4
2
2
1
4
3
3
2
4
1
3
1
4
1
3
3
4
2
4
2
1
1
1
2
3
1
1
4
3
1
2
3
4
3
4
3
3
1
2
2
2
3
2
4
1
2
1
1
3,30
2,30
1,90
2,30
1,90
1,00
0,40
1,00
1,00
2,10
3,60
3,10
6,30
7,50
0,20
0,80
2,33
1,30
1,00
0,10
1,30
2,10
5,70
0,20
1,80
0,80
1,40
1,00
3,80
0,60
1,50
1,30
3,00
1,00
0,00
2,20
1,00
1,40
2,00
2,00
0,30
1,75
0,20
2,80
0,90
2,20
0,50
0,30
1,00
3,00
2,10
3,70
8,30
5,50
3,60
1,90
0,90
2,40
0,50
1
3
3
1
2
2
1
2
3
1
3
2
1
1
1
1
1
1
1
2
3
1
1
1
2
1
3
2
2
1
1
2
3
1
3
3
1
3
2
3
1
3
2
2
3
2
2
3
1
1
1
1
3
2
3
2
3
1
3
0
0
0
0
0
124
0
0
0
0
0
0
0
0
0
0
0
116
116
0
161
224
0
141
0
0
112
0
119
0
139
0
115
0
0
0
0
0
0
0
0
89
0
0
0
0
116
0
0
458
0
0
0
0
0
172
0
0
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0
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1
1
1
0
0
0
0
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
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486
487
488
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511
512
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516
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528
48
32
50
43
64
60
43
60
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44
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54
33
56
29
25
60
55
39
37
53
34
42
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50
41
25
50
48
32
50
59
50
44
31
40
36
51
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47
52
51
31
39
30
27
41
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54
28
34
61
48
36
56
24
64
26
33
23
6
24
19
39
34
19
34
39
20
36
29
9
32
5
1
34
30
13
13
28
10
18
36
24
17
0
24
22
8
25
33
26
19
5
10
12
25
40
22
28
26
5
14
6
1
16
27
27
4
9
37
24
11
31
-1
38
2
8
10
84
30
31
182
114
152
53
24
150
132
68
53
173
30
113
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84
88
43
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38
173
160
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94
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44
32
15
118
62
82
54
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81
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34
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54
75
72
39
75
79
205
65
94609
91006
91768
90007
93955
90028
92008
92717
95112
95060
92154
94998
94063
94022
90095
95023
95014
92173
94117
94122
91380
94303
92115
94596
94720
92647
94545
94301
90623
95023
93108
92177
90640
92833
94022
94720
94305
94608
91380
95521
90503
95136
94143
95035
94607
91730
92780
90009
92834
92677
95616
90024
92518
91007
93023
93014
94024
93106
90027
2
4
4
4
1
2
3
1
4
2
2
3
1
1
3
2
1
2
4
3
2
2
4
4
1
2
4
2
4
1
3
2
3
1
4
3
3
3
3
2
2
1
4
3
1
3
1
3
3
1
1
4
4
1
4
4
2
1
2
0,70
1,80
0,10
0,30
1,20
6,90
6,10
0,80
0,40
3,30
6,00
1,60
1,20
4,60
1,00
0,20
0,80
3,70
1,40
2,80
2,10
2,70
0,30
1,30
1,00
8,00
0,60
0,40
2,60
2,10
1,70
0,30
1,90
0,10
1,80
2,00
3,10
0,90
0,10
0,70
6,80
1,30
2,20
3,00
2,10
0,30
1,00
1,70
1,00
1,80
2,50
1,20
1,40
2,80
0,90
0,20
2,80
6,33
0,10
3
2
1
1
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2
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2
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1
3
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1
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0
161
156
547
0
0
0
78
0
470
0
0
88
0
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304
0
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104
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221
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169
0
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129
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224
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271
89
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529
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534
535
536
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540
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542
543
544
545
546
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550
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560
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562
563
564
565
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567
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569
570
571
572
573
574
575
576
577
578
579
580
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582
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585
586
587
64
39
54
32
62
27
53
51
25
44
31
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25
30
40
63
35
43
27
44
49
61
60
59
28
52
28
34
60
39
30
49
43
63
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51
33
55
53
34
34
40
49
35
39
55
29
54
25
52
46
57
52
28
44
24
40
34
39
39
15
30
6
37
2
28
25
-1
20
5
32
-1
6
14
38
10
19
2
14
23
36
34
34
3
28
2
8
34
15
5
25
18
33
3
27
7
29
28
8
9
14
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9
15
28
5
30
-1
28
19
33
22
3
18
-1
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4
14
122
82
21
50
39
101
41
132
43
131
11
21
109
141
81
54
164
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68
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54
14
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101
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24
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41
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79
175
28
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70
161
53
128
50
80
93
48
149
49
88
22
55
72
38
114
83
101
90089
95207
91706
90401
94305
92807
93117
94143
92173
90717
94534
94720
94010
95014
94709
94704
91614
94303
94025
94132
94117
94110
94301
93118
90024
91330
94720
92037
93105
95039
95064
95818
93943
94234
94035
94608
94904
90210
95060
95112
92101
95136
94928
94143
92333
95020
94709
91107
92870
94043
92124
93524
90049
94521
95678
95045
91604
92653
94305
4
1
2
4
2
1
2
1
3
1
1
1
4
2
3
3
2
4
3
3
1
3
3
1
4
2
2
4
3
2
4
4
1
4
1
4
1
3
3
3
2
3
3
4
1
3
2
1
3
2
3
1
4
4
1
2
1
4
2
0,20
0,80
0,20
2,10
2,80
1,90
0,60
0,30
2,40
4,90
0,40
0,30
2,30
4,33
0,10
2,40
7,80
0,30
2,60
2,00
1,40
1,30
0,30
0,10
2,20
0,30
7,20
0,80
0,30
1,90
2,00
0,20
3,70
1,67
0,80
1,00
0,60
0,80
3,60
0,90
0,10
2,10
6,50
2,20
3,40
1,00
2,00
2,70
0,30
6,80
2,50
2,70
0,40
2,20
0,70
1,70
3,40
4,00
0,40
1
2
1
3
1
1
3
1
2
3
2
3
3
1
1
1
1
1
3
3
3
2
2
1
1
1
1
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3
1
2
1
3
3
2
1
3
1
3
1
1
1
2
2
1
2
2
2
3
1
2
2
3
1
3
2
1
3
1
378
0
0
0
113
0
0
0
176
0
76
117
314
0
0
90
0
87
203
180
0
0
0
0
230
0
0
137
129
0
0
138
0
0
0
0
152
0
0
0
161
185
485
0
0
0
0
0
0
0
0
0
0
0
155
0
300
0
0
1
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
50
41
31
29
30
44
33
50
42
48
24
56
28
56
58
29
63
28
57
34
28
27
37
52
49
65
60
37
63
40
46
63
57
33
41
41
44
33
52
30
45
49
45
32
45
57
61
57
60
40
53
42
62
43
35
50
45
52
35
24
17
7
3
5
20
7
26
18
22
-2
31
4
30
32
5
38
3
31
8
3
2
11
28
23
40
35
12
37
14
20
37
27
8
17
17
19
6
28
6
19
24
19
7
18
32
31
31
35
16
28
16
36
18
10
24
21
27
9
94
40
128
39
51
79
48
85
41
152
125
11
103
141
38
135
28
70
41
81
170
55
24
81
32
129
108
180
139
33
74
42
73
115
114
92
34
54
64
42
70
51
71
35
40
165
18
32
35
120
31
35
32
85
139
103
152
33
84
93305
93117
92821
94612
92037
95051
90025
94143
92121
94022
92835
92374
94720
94143
91320
95035
94720
90245
91330
91741
95014
91910
91770
94132
94701
90095
94904
90034
93943
94025
94024
91320
93106
91129
91125
93555
95616
92821
95605
94305
92677
90071
91711
96651
94960
94720
94583
90034
90509
92037
90245
92054
92646
94960
95060
94132
91902
92121
95120
1
2
1
4
1
4
4
1
1
1
2
2
2
2
1
2
2
4
1
3
1
4
4
3
4
1
1
1
2
2
4
2
1
4
2
2
1
2
2
1
3
1
4
3
3
4
1
3
3
2
4
3
2
1
2
1
2
2
4
4,90
2,50
6,00
2,10
1,00
2,00
2,20
0,00
1,80
3,50
7,20
0,20
2,50
0,50
1,40
0,60
0,50
2,20
0,20
0,90
0,10
1,70
1,50
1,80
1,80
1,30
0,90
8,60
6,90
1,40
2,60
0,70
3,00
2,90
1,80
1,90
0,30
1,67
1,00
0,20
2,10
1,30
2,90
1,30
1,00
2,70
1,50
1,40
0,20
6,10
0,10
1,50
0,20
3,70
7,80
0,30
1,40
2,00
2,20
1
1
1
3
1
3
2
1
1
3
1
3
1
1
1
1
2
1
1
2
3
2
3
2
1
1
1
1
1
3
3
3
3
2
2
1
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2
3
3
1
2
1
1
2
3
3
1
1
1
3
1
3
3
1
1
1
2
2
272
0
0
0
0
0
0
144
94
0
0
90
0
0
0
0
89
240
0
208
0
0
0
275
83
0
0
0
0
0
0
115
0
0
0
131
78
122
211
100
0
0
218
108
0
0
0
0
169
196
0
0
0
327
0
0
0
0
322
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
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
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
58
62
50
25
47
28
34
49
54
50
37
38
52
63
39
63
65
46
54
54
52
63
66
56
23
65
51
34
49
29
47
46
52
55
61
34
58
40
43
35
24
48
44
54
59
45
26
40
32
29
51
42
64
44
37
44
35
41
56
33
38
25
-1
22
4
9
23
29
25
11
8
26
39
14
38
41
20
30
24
26
39
41
29
-1
41
27
10
23
2
23
21
27
31
36
9
34
16
17
8
-1
22
20
30
34
18
2
15
7
4
27
17
38
20
11
19
9
17
32
61
64
34
82
122
58
92
78
129
13
81
23
35
79
165
52
185
49
64
61
112
72
18
41
61
105
23
22
59
33
11
204
61
103
51
164
12
82
164
48
38
65
71
18
52
48
30
40
112
115
63
85
59
68
84
62
109
141
129
90033
95064
95621
92677
90037
92121
90005
92691
93940
91109
94539
95207
91711
93009
92126
94720
93561
90503
95126
92866
92120
93106
94010
94109
92374
92612
96651
95670
95827
91711
94063
92780
92101
92093
94706
94720
90504
91311
90266
93107
92612
92120
94304
94591
94115
90025
94720
92096
90740
92717
92251
92648
92028
95060
90089
93106
92709
94022
94065
4
4
1
4
1
3
1
2
4
2
1
1
3
4
2
2
3
3
1
4
1
3
3
4
4
1
1
1
3
1
1
2
4
3
3
1
1
1
1
2
4
2
4
1
2
3
1
2
1
1
2
1
1
1
2
3
3
2
1
1,70
2,20
1,30
2,10
5,10
1,50
2,80
2,40
4,20
0,70
2,80
0,67
0,90
1,70
3,30
2,80
2,00
2,20
1,80
2,00
2,40
2,00
0,50
2,50
2,60
3,00
0,20
0,50
2,10
2,00
0,90
2,80
1,80
1,80
1,50
6,00
0,10
3,60
2,40
1,67
0,60
1,50
1,90
0,30
1,60
2,50
1,00
2,20
3,80
1,90
1,00
3,70
2,50
0,80
1,80
0,80
4,00
7,60
7,40
1
1
2
3
3
1
1
2
3
3
3
3
3
2
1
1
2
2
3
3
1
3
1
2
1
2
1
3
1
2
3
1
3
2
1
3
2
2
1
2
2
2
1
1
3
2
3
3
1
1
3
3
3
3
1
3
1
1
1
0
123
0
0
163
131
0
205
0
0
145
0
0
0
0
0
0
0
227
0
0
190
0
0
239
282
0
85
0
160
103
0
207
364
0
0
0
0
449
0
0
0
207
0
75
113
111
107
81
0
82
0
220
91
0
0
0
92
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
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1
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0
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0
0
0
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0
0
1
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
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