Office Applications and Entertainment, Latin Squares
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Attachment 7.7.2 |
About the Author
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Construction of a Composed Simple Magic Square (29 x 29)
Based on a Self Orthogonal Latin Diagonal Square
A
22 |
24 |
27 |
28 |
14 |
26 |
25 |
17 |
19 |
18 |
15 |
20 |
21 |
16 |
23 |
2 |
4 |
3 |
0 |
5 |
6 |
1 |
9 |
11 |
10 |
7 |
12 |
13 |
8 |
25 |
23 |
14 |
26 |
27 |
28 |
22 |
21 |
16 |
20 |
19 |
17 |
15 |
18 |
24 |
6 |
1 |
5 |
4 |
2 |
0 |
3 |
13 |
8 |
12 |
11 |
9 |
7 |
10 |
23 |
27 |
24 |
14 |
28 |
25 |
26 |
16 |
17 |
15 |
20 |
19 |
18 |
21 |
22 |
1 |
2 |
0 |
5 |
4 |
3 |
6 |
8 |
9 |
7 |
12 |
11 |
10 |
13 |
26 |
22 |
28 |
25 |
24 |
14 |
23 |
19 |
20 |
21 |
18 |
15 |
16 |
17 |
27 |
4 |
5 |
6 |
3 |
0 |
1 |
2 |
11 |
12 |
13 |
10 |
7 |
8 |
9 |
24 |
28 |
22 |
27 |
26 |
23 |
14 |
15 |
18 |
17 |
16 |
21 |
19 |
20 |
25 |
0 |
3 |
2 |
1 |
6 |
4 |
5 |
7 |
10 |
9 |
8 |
13 |
11 |
12 |
14 |
25 |
26 |
23 |
22 |
27 |
24 |
18 |
21 |
19 |
17 |
16 |
20 |
15 |
28 |
3 |
6 |
4 |
2 |
1 |
5 |
0 |
10 |
13 |
11 |
9 |
8 |
12 |
7 |
27 |
14 |
23 |
24 |
25 |
22 |
28 |
20 |
15 |
16 |
21 |
18 |
17 |
19 |
26 |
5 |
0 |
1 |
6 |
3 |
2 |
4 |
12 |
7 |
8 |
13 |
10 |
9 |
11 |
2 |
4 |
3 |
0 |
5 |
6 |
1 |
7 |
9 |
12 |
13 |
14 |
11 |
10 |
8 |
24 |
26 |
25 |
22 |
27 |
28 |
23 |
17 |
19 |
18 |
15 |
20 |
21 |
16 |
6 |
1 |
5 |
4 |
2 |
0 |
3 |
10 |
8 |
14 |
11 |
12 |
13 |
7 |
9 |
28 |
23 |
27 |
26 |
24 |
22 |
25 |
21 |
16 |
20 |
19 |
17 |
15 |
18 |
1 |
2 |
0 |
5 |
4 |
3 |
6 |
8 |
12 |
9 |
14 |
13 |
10 |
11 |
7 |
23 |
24 |
22 |
27 |
26 |
25 |
28 |
16 |
17 |
15 |
20 |
19 |
18 |
21 |
4 |
5 |
6 |
3 |
0 |
1 |
2 |
11 |
7 |
13 |
10 |
9 |
14 |
8 |
12 |
26 |
27 |
28 |
25 |
22 |
23 |
24 |
19 |
20 |
21 |
18 |
15 |
16 |
17 |
0 |
3 |
2 |
1 |
6 |
4 |
5 |
9 |
13 |
7 |
12 |
11 |
8 |
14 |
10 |
22 |
25 |
24 |
23 |
28 |
26 |
27 |
15 |
18 |
17 |
16 |
21 |
19 |
20 |
3 |
6 |
4 |
2 |
1 |
5 |
0 |
14 |
10 |
11 |
8 |
7 |
12 |
9 |
13 |
25 |
28 |
26 |
24 |
23 |
27 |
22 |
18 |
21 |
19 |
17 |
16 |
20 |
15 |
5 |
0 |
1 |
6 |
3 |
2 |
4 |
12 |
14 |
8 |
9 |
10 |
7 |
13 |
11 |
27 |
22 |
23 |
28 |
25 |
24 |
26 |
20 |
15 |
16 |
21 |
18 |
17 |
19 |
28 |
26 |
25 |
22 |
23 |
24 |
27 |
13 |
11 |
10 |
7 |
8 |
9 |
12 |
14 |
16 |
19 |
20 |
21 |
18 |
17 |
15 |
1 |
4 |
5 |
6 |
3 |
2 |
0 |
9 |
11 |
10 |
7 |
12 |
13 |
8 |
2 |
4 |
3 |
0 |
5 |
6 |
1 |
17 |
15 |
21 |
18 |
19 |
20 |
14 |
16 |
24 |
26 |
25 |
22 |
27 |
28 |
23 |
13 |
8 |
12 |
11 |
9 |
7 |
10 |
6 |
1 |
5 |
4 |
2 |
0 |
3 |
15 |
19 |
16 |
21 |
20 |
17 |
18 |
14 |
28 |
23 |
27 |
26 |
24 |
22 |
25 |
8 |
9 |
7 |
12 |
11 |
10 |
13 |
1 |
2 |
0 |
5 |
4 |
3 |
6 |
18 |
14 |
20 |
17 |
16 |
21 |
15 |
19 |
23 |
24 |
22 |
27 |
26 |
25 |
28 |
11 |
12 |
13 |
10 |
7 |
8 |
9 |
4 |
5 |
6 |
3 |
0 |
1 |
2 |
16 |
20 |
14 |
19 |
18 |
15 |
21 |
17 |
26 |
27 |
28 |
25 |
22 |
23 |
24 |
7 |
10 |
9 |
8 |
13 |
11 |
12 |
0 |
3 |
2 |
1 |
6 |
4 |
5 |
21 |
17 |
18 |
15 |
14 |
19 |
16 |
20 |
22 |
25 |
24 |
23 |
28 |
26 |
27 |
10 |
13 |
11 |
9 |
8 |
12 |
7 |
3 |
6 |
4 |
2 |
1 |
5 |
0 |
19 |
21 |
15 |
16 |
17 |
14 |
20 |
18 |
25 |
28 |
26 |
24 |
23 |
27 |
22 |
12 |
7 |
8 |
13 |
10 |
9 |
11 |
5 |
0 |
1 |
6 |
3 |
2 |
4 |
20 |
18 |
17 |
14 |
15 |
16 |
19 |
21 |
27 |
22 |
23 |
28 |
25 |
24 |
26 |
17 |
19 |
18 |
15 |
20 |
21 |
16 |
24 |
26 |
25 |
22 |
27 |
28 |
23 |
2 |
9 |
11 |
10 |
7 |
12 |
13 |
8 |
0 |
6 |
3 |
4 |
5 |
14 |
1 |
21 |
16 |
20 |
19 |
17 |
15 |
18 |
28 |
23 |
27 |
26 |
24 |
22 |
25 |
0 |
13 |
8 |
12 |
11 |
9 |
7 |
10 |
4 |
1 |
6 |
5 |
2 |
3 |
14 |
16 |
17 |
15 |
20 |
19 |
18 |
21 |
23 |
24 |
22 |
27 |
26 |
25 |
28 |
3 |
8 |
9 |
7 |
12 |
11 |
10 |
13 |
14 |
5 |
2 |
1 |
6 |
0 |
4 |
19 |
20 |
21 |
18 |
15 |
16 |
17 |
26 |
27 |
28 |
25 |
22 |
23 |
24 |
1 |
11 |
12 |
13 |
10 |
7 |
8 |
9 |
5 |
14 |
4 |
3 |
0 |
6 |
2 |
15 |
18 |
17 |
16 |
21 |
19 |
20 |
22 |
25 |
24 |
23 |
28 |
26 |
27 |
6 |
7 |
10 |
9 |
8 |
13 |
11 |
12 |
2 |
3 |
0 |
14 |
4 |
1 |
5 |
18 |
21 |
19 |
17 |
16 |
20 |
15 |
25 |
28 |
26 |
24 |
23 |
27 |
22 |
4 |
10 |
13 |
11 |
9 |
8 |
12 |
7 |
6 |
0 |
1 |
2 |
14 |
5 |
3 |
20 |
15 |
16 |
21 |
18 |
17 |
19 |
27 |
22 |
23 |
28 |
25 |
24 |
26 |
5 |
12 |
7 |
8 |
13 |
10 |
9 |
11 |
3 |
2 |
14 |
0 |
1 |
4 |
6 |
B = T(A)
22 |
25 |
23 |
26 |
24 |
14 |
27 |
2 |
6 |
1 |
4 |
0 |
3 |
5 |
28 |
9 |
13 |
8 |
11 |
7 |
10 |
12 |
17 |
21 |
16 |
19 |
15 |
18 |
20 |
24 |
23 |
27 |
22 |
28 |
25 |
14 |
4 |
1 |
2 |
5 |
3 |
6 |
0 |
26 |
11 |
8 |
9 |
12 |
10 |
13 |
7 |
19 |
16 |
17 |
20 |
18 |
21 |
15 |
27 |
14 |
24 |
28 |
22 |
26 |
23 |
3 |
5 |
0 |
6 |
2 |
4 |
1 |
25 |
10 |
12 |
7 |
13 |
9 |
11 |
8 |
18 |
20 |
15 |
21 |
17 |
19 |
16 |
28 |
26 |
14 |
25 |
27 |
23 |
24 |
0 |
4 |
5 |
3 |
1 |
2 |
6 |
22 |
7 |
11 |
12 |
10 |
8 |
9 |
13 |
15 |
19 |
20 |
18 |
16 |
17 |
21 |
14 |
27 |
28 |
24 |
26 |
22 |
25 |
5 |
2 |
4 |
0 |
6 |
1 |
3 |
23 |
12 |
9 |
11 |
7 |
13 |
8 |
10 |
20 |
17 |
19 |
15 |
21 |
16 |
18 |
26 |
28 |
25 |
14 |
23 |
27 |
22 |
6 |
0 |
3 |
1 |
4 |
5 |
2 |
24 |
13 |
7 |
10 |
8 |
11 |
12 |
9 |
21 |
15 |
18 |
16 |
19 |
20 |
17 |
25 |
22 |
26 |
23 |
14 |
24 |
28 |
1 |
3 |
6 |
2 |
5 |
0 |
4 |
27 |
8 |
10 |
13 |
9 |
12 |
7 |
11 |
16 |
18 |
21 |
17 |
20 |
15 |
19 |
17 |
21 |
16 |
19 |
15 |
18 |
20 |
7 |
10 |
8 |
11 |
9 |
14 |
12 |
13 |
2 |
6 |
1 |
4 |
0 |
3 |
5 |
24 |
28 |
23 |
26 |
22 |
25 |
27 |
19 |
16 |
17 |
20 |
18 |
21 |
15 |
9 |
8 |
12 |
7 |
13 |
10 |
14 |
11 |
4 |
1 |
2 |
5 |
3 |
6 |
0 |
26 |
23 |
24 |
27 |
25 |
28 |
22 |
18 |
20 |
15 |
21 |
17 |
19 |
16 |
12 |
14 |
9 |
13 |
7 |
11 |
8 |
10 |
3 |
5 |
0 |
6 |
2 |
4 |
1 |
25 |
27 |
22 |
28 |
24 |
26 |
23 |
15 |
19 |
20 |
18 |
16 |
17 |
21 |
13 |
11 |
14 |
10 |
12 |
8 |
9 |
7 |
0 |
4 |
5 |
3 |
1 |
2 |
6 |
22 |
26 |
27 |
25 |
23 |
24 |
28 |
20 |
17 |
19 |
15 |
21 |
16 |
18 |
14 |
12 |
13 |
9 |
11 |
7 |
10 |
8 |
5 |
2 |
4 |
0 |
6 |
1 |
3 |
27 |
24 |
26 |
22 |
28 |
23 |
25 |
21 |
15 |
18 |
16 |
19 |
20 |
17 |
11 |
13 |
10 |
14 |
8 |
12 |
7 |
9 |
6 |
0 |
3 |
1 |
4 |
5 |
2 |
28 |
22 |
25 |
23 |
26 |
27 |
24 |
16 |
18 |
21 |
17 |
20 |
15 |
19 |
10 |
7 |
11 |
8 |
14 |
9 |
13 |
12 |
1 |
3 |
6 |
2 |
5 |
0 |
4 |
23 |
25 |
28 |
24 |
27 |
22 |
26 |
23 |
24 |
22 |
27 |
25 |
28 |
26 |
8 |
9 |
7 |
12 |
10 |
13 |
11 |
14 |
17 |
15 |
18 |
16 |
21 |
19 |
20 |
2 |
0 |
3 |
1 |
6 |
4 |
5 |
2 |
6 |
1 |
4 |
0 |
3 |
5 |
24 |
28 |
23 |
26 |
22 |
25 |
27 |
16 |
15 |
19 |
14 |
20 |
17 |
21 |
18 |
9 |
13 |
8 |
11 |
7 |
10 |
12 |
4 |
1 |
2 |
5 |
3 |
6 |
0 |
26 |
23 |
24 |
27 |
25 |
28 |
22 |
19 |
21 |
16 |
20 |
14 |
18 |
15 |
17 |
11 |
8 |
9 |
12 |
10 |
13 |
7 |
3 |
5 |
0 |
6 |
2 |
4 |
1 |
25 |
27 |
22 |
28 |
24 |
26 |
23 |
20 |
18 |
21 |
17 |
19 |
15 |
16 |
14 |
10 |
12 |
7 |
13 |
9 |
11 |
8 |
0 |
4 |
5 |
3 |
1 |
2 |
6 |
22 |
26 |
27 |
25 |
23 |
24 |
28 |
21 |
19 |
20 |
16 |
18 |
14 |
17 |
15 |
7 |
11 |
12 |
10 |
8 |
9 |
13 |
5 |
2 |
4 |
0 |
6 |
1 |
3 |
27 |
24 |
26 |
22 |
28 |
23 |
25 |
18 |
20 |
17 |
21 |
15 |
19 |
14 |
16 |
12 |
9 |
11 |
7 |
13 |
8 |
10 |
6 |
0 |
3 |
1 |
4 |
5 |
2 |
28 |
22 |
25 |
23 |
26 |
27 |
24 |
17 |
14 |
18 |
15 |
21 |
16 |
20 |
19 |
13 |
7 |
10 |
8 |
11 |
12 |
9 |
1 |
3 |
6 |
2 |
5 |
0 |
4 |
23 |
25 |
28 |
24 |
27 |
22 |
26 |
15 |
16 |
14 |
19 |
17 |
20 |
18 |
21 |
8 |
10 |
13 |
9 |
12 |
7 |
11 |
9 |
13 |
8 |
11 |
7 |
10 |
12 |
17 |
21 |
16 |
19 |
15 |
18 |
20 |
1 |
24 |
28 |
23 |
26 |
22 |
25 |
27 |
0 |
4 |
14 |
5 |
2 |
6 |
3 |
11 |
8 |
9 |
12 |
10 |
13 |
7 |
19 |
16 |
17 |
20 |
18 |
21 |
15 |
4 |
26 |
23 |
24 |
27 |
25 |
28 |
22 |
6 |
1 |
5 |
14 |
3 |
0 |
2 |
10 |
12 |
7 |
13 |
9 |
11 |
8 |
18 |
20 |
15 |
21 |
17 |
19 |
16 |
5 |
25 |
27 |
22 |
28 |
24 |
26 |
23 |
3 |
6 |
2 |
4 |
0 |
1 |
14 |
7 |
11 |
12 |
10 |
8 |
9 |
13 |
15 |
19 |
20 |
18 |
16 |
17 |
21 |
6 |
22 |
26 |
27 |
25 |
23 |
24 |
28 |
4 |
5 |
1 |
3 |
14 |
2 |
0 |
12 |
9 |
11 |
7 |
13 |
8 |
10 |
20 |
17 |
19 |
15 |
21 |
16 |
18 |
3 |
27 |
24 |
26 |
22 |
28 |
23 |
25 |
5 |
2 |
6 |
0 |
4 |
14 |
1 |
13 |
7 |
10 |
8 |
11 |
12 |
9 |
21 |
15 |
18 |
16 |
19 |
20 |
17 |
2 |
28 |
22 |
25 |
23 |
26 |
27 |
24 |
14 |
3 |
0 |
6 |
1 |
5 |
4 |
8 |
10 |
13 |
9 |
12 |
7 |
11 |
16 |
18 |
21 |
17 |
20 |
15 |
19 |
0 |
23 |
25 |
28 |
24 |
27 |
22 |
26 |
1 |
14 |
4 |
2 |
5 |
3 |
6 |
M = A + 29 * B + 1
661 |
750 |
695 |
783 |
711 |
433 |
809 |
76 |
194 |
48 |
132 |
21 |
109 |
162 |
836 |
264 |
382 |
236 |
320 |
209 |
297 |
350 |
503 |
621 |
475 |
559 |
448 |
536 |
589 |
722 |
691 |
798 |
665 |
840 |
754 |
429 |
138 |
46 |
79 |
165 |
105 |
190 |
19 |
779 |
326 |
234 |
267 |
353 |
293 |
378 |
207 |
565 |
473 |
506 |
592 |
532 |
617 |
446 |
807 |
434 |
721 |
827 |
667 |
780 |
694 |
104 |
163 |
16 |
195 |
78 |
135 |
51 |
748 |
292 |
351 |
204 |
383 |
266 |
323 |
239 |
531 |
590 |
443 |
622 |
505 |
562 |
478 |
839 |
777 |
435 |
751 |
808 |
682 |
720 |
20 |
137 |
167 |
106 |
45 |
75 |
192 |
666 |
208 |
325 |
355 |
294 |
233 |
263 |
380 |
447 |
564 |
594 |
533 |
472 |
502 |
619 |
431 |
812 |
835 |
724 |
781 |
662 |
740 |
161 |
77 |
134 |
17 |
196 |
49 |
108 |
693 |
349 |
265 |
322 |
205 |
384 |
237 |
296 |
588 |
504 |
561 |
444 |
623 |
476 |
535 |
769 |
838 |
752 |
430 |
690 |
811 |
663 |
193 |
22 |
107 |
47 |
133 |
166 |
74 |
725 |
381 |
210 |
295 |
235 |
321 |
354 |
262 |
620 |
449 |
534 |
474 |
560 |
593 |
501 |
753 |
653 |
778 |
692 |
432 |
719 |
841 |
50 |
103 |
191 |
80 |
164 |
18 |
136 |
810 |
238 |
291 |
379 |
268 |
352 |
206 |
324 |
477 |
530 |
618 |
507 |
591 |
445 |
563 |
496 |
614 |
468 |
552 |
441 |
529 |
582 |
211 |
300 |
245 |
333 |
276 |
418 |
359 |
386 |
83 |
201 |
55 |
139 |
28 |
116 |
169 |
714 |
832 |
686 |
770 |
659 |
747 |
800 |
558 |
466 |
499 |
585 |
525 |
610 |
439 |
272 |
241 |
363 |
215 |
390 |
304 |
414 |
329 |
145 |
53 |
86 |
172 |
112 |
197 |
26 |
776 |
684 |
717 |
803 |
743 |
828 |
657 |
524 |
583 |
436 |
615 |
498 |
555 |
471 |
357 |
419 |
271 |
392 |
217 |
330 |
244 |
298 |
111 |
170 |
23 |
202 |
85 |
142 |
58 |
742 |
801 |
654 |
833 |
716 |
773 |
689 |
440 |
557 |
587 |
526 |
465 |
495 |
612 |
389 |
327 |
420 |
301 |
358 |
247 |
270 |
216 |
27 |
144 |
174 |
113 |
52 |
82 |
199 |
658 |
775 |
805 |
744 |
683 |
713 |
830 |
581 |
497 |
554 |
437 |
616 |
469 |
528 |
416 |
362 |
385 |
274 |
331 |
212 |
305 |
243 |
168 |
84 |
141 |
24 |
203 |
56 |
115 |
799 |
715 |
772 |
655 |
834 |
687 |
746 |
613 |
442 |
527 |
467 |
553 |
586 |
494 |
334 |
388 |
302 |
415 |
240 |
361 |
213 |
275 |
200 |
29 |
114 |
54 |
140 |
173 |
81 |
831 |
660 |
745 |
685 |
771 |
804 |
712 |
470 |
523 |
611 |
500 |
584 |
438 |
556 |
303 |
218 |
328 |
242 |
417 |
269 |
391 |
360 |
57 |
110 |
198 |
87 |
171 |
25 |
143 |
688 |
741 |
829 |
718 |
802 |
656 |
774 |
696 |
723 |
664 |
806 |
749 |
837 |
782 |
246 |
273 |
214 |
356 |
299 |
387 |
332 |
421 |
510 |
455 |
543 |
486 |
628 |
569 |
596 |
60 |
5 |
93 |
36 |
178 |
119 |
146 |
68 |
186 |
40 |
124 |
13 |
101 |
154 |
699 |
817 |
671 |
755 |
644 |
732 |
785 |
482 |
451 |
573 |
425 |
600 |
514 |
624 |
539 |
286 |
404 |
258 |
342 |
231 |
319 |
372 |
130 |
38 |
71 |
157 |
97 |
182 |
11 |
761 |
669 |
702 |
788 |
728 |
813 |
642 |
567 |
629 |
481 |
602 |
427 |
540 |
454 |
508 |
348 |
256 |
289 |
375 |
315 |
400 |
229 |
96 |
155 |
8 |
187 |
70 |
127 |
43 |
727 |
786 |
639 |
818 |
701 |
758 |
674 |
599 |
537 |
630 |
511 |
568 |
457 |
480 |
426 |
314 |
373 |
226 |
405 |
288 |
345 |
261 |
12 |
129 |
159 |
98 |
37 |
67 |
184 |
643 |
760 |
790 |
729 |
668 |
698 |
815 |
626 |
572 |
595 |
484 |
541 |
422 |
515 |
453 |
230 |
347 |
377 |
316 |
255 |
285 |
402 |
153 |
69 |
126 |
9 |
188 |
41 |
100 |
784 |
700 |
757 |
640 |
819 |
672 |
731 |
544 |
598 |
512 |
625 |
450 |
571 |
423 |
485 |
371 |
287 |
344 |
227 |
406 |
259 |
318 |
185 |
14 |
99 |
39 |
125 |
158 |
66 |
816 |
645 |
730 |
670 |
756 |
789 |
697 |
513 |
428 |
538 |
452 |
627 |
479 |
601 |
570 |
403 |
232 |
317 |
257 |
343 |
376 |
284 |
42 |
95 |
183 |
72 |
156 |
10 |
128 |
673 |
726 |
814 |
703 |
787 |
641 |
759 |
456 |
483 |
424 |
566 |
509 |
597 |
542 |
631 |
260 |
313 |
401 |
290 |
374 |
228 |
346 |
279 |
397 |
251 |
335 |
224 |
312 |
365 |
518 |
636 |
490 |
574 |
463 |
551 |
604 |
32 |
706 |
824 |
678 |
762 |
651 |
739 |
792 |
1 |
123 |
410 |
150 |
64 |
189 |
89 |
341 |
249 |
282 |
368 |
308 |
393 |
222 |
580 |
488 |
521 |
607 |
547 |
632 |
461 |
117 |
768 |
676 |
709 |
795 |
735 |
820 |
649 |
179 |
31 |
152 |
412 |
90 |
4 |
73 |
307 |
366 |
219 |
398 |
281 |
338 |
254 |
546 |
605 |
458 |
637 |
520 |
577 |
493 |
149 |
734 |
793 |
646 |
825 |
708 |
765 |
681 |
102 |
180 |
61 |
118 |
7 |
30 |
411 |
223 |
340 |
370 |
309 |
248 |
278 |
395 |
462 |
579 |
609 |
548 |
487 |
517 |
634 |
176 |
650 |
767 |
797 |
736 |
675 |
705 |
822 |
122 |
160 |
34 |
91 |
407 |
65 |
3 |
364 |
280 |
337 |
220 |
399 |
252 |
311 |
603 |
519 |
576 |
459 |
638 |
491 |
550 |
94 |
791 |
707 |
764 |
647 |
826 |
679 |
738 |
148 |
62 |
175 |
15 |
121 |
408 |
35 |
396 |
225 |
310 |
250 |
336 |
369 |
277 |
635 |
464 |
549 |
489 |
575 |
608 |
516 |
63 |
823 |
652 |
737 |
677 |
763 |
796 |
704 |
413 |
88 |
2 |
177 |
44 |
151 |
120 |
253 |
306 |
394 |
283 |
367 |
221 |
339 |
492 |
545 |
633 |
522 |
606 |
460 |
578 |
6 |
680 |
733 |
821 |
710 |
794 |
648 |
766 |
33 |
409 |
131 |
59 |
147 |
92 |
181 |