矩阵相乘的次数 | 相乘矩阵自乘的方法 | 幂乘的方法 | 快速Warshall转移法 |
1 |
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B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
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1 |
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B2 |
1 |
1 |
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B3 |
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1 |
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1 |
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B4 |
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1 |
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1 |
B5 |
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1 |
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1 |
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B6 |
1 |
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1 |
1 |
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B7 |
|
1 |
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1 |
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1 |
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B8 |
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|
1 |
|
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B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
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1 |
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B2 |
1 |
1 |
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B3 |
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1 |
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1 |
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B4 |
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1 |
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1 |
B5 |
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1 |
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1 |
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B6 |
1 |
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1 |
1 |
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B7 |
|
1 |
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1 |
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1 |
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B8 |
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|
1 |
|
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B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
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1 |
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B2 |
1 |
1 |
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B3 |
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1 |
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1 |
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B4 |
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1 |
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1 |
B5 |
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1 |
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1 |
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B6 |
1 |
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1 |
1 |
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B7 |
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1 |
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1 |
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1 |
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B8 |
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1 |
|
2 |
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
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1 |
|
B2 |
1 |
1 |
|
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|
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1 |
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B3 |
1 |
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1 |
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1 |
1 |
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B4 |
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1 |
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1 |
B5 |
1 |
1 |
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1 |
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B6 |
1 |
1 |
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1 |
1 |
1 |
|
B7 |
1 |
1 |
|
1 |
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1 |
1 |
B8 |
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|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
|
B2 |
1 |
1 |
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|
|
1 |
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B3 |
1 |
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1 |
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1 |
1 |
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B4 |
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|
1 |
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|
1 |
B5 |
1 |
1 |
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1 |
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B6 |
1 |
1 |
|
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1 |
1 |
1 |
|
B7 |
1 |
1 |
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1 |
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1 |
1 |
B8 |
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|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
|
B2 |
1 |
1 |
|
1 |
|
|
1 |
|
B3 |
1 |
|
1 |
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1 |
1 |
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B4 |
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|
1 |
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|
1 |
B5 |
1 |
1 |
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1 |
1 |
|
1 |
|
B6 |
1 |
1 |
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1 |
1 |
1 |
1 |
|
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
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|
|
|
|
1 |
|
3 |
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
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1 |
|
B3 |
1 |
1 |
1 |
|
1 |
1 |
1 |
|
B4 |
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1 |
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|
1 |
B5 |
1 |
1 |
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1 |
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1 |
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B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
|
B7 |
1 |
1 |
|
1 |
|
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1 |
1 |
B8 |
|
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|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
B4 |
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1 |
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1 |
B5 |
1 |
1 |
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1 |
1 |
|
1 |
|
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
1 |
1 |
|
1 |
1 |
|
1 |
1 |
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
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|
|
|
|
|
1 |
|
4 |
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
1 |
1 |
|
1 |
1 |
|
1 |
|
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
1 |
1 |
|
1 |
1 |
|
1 |
1 |
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
1 |
1 |
|
1 |
1 |
|
1 |
1 |
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
|
|
|
|
|
1 |
|
5 |
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
1 |
1 |
|
1 |
1 |
|
1 |
1 |
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
1 |
1 |
|
1 |
1 |
|
1 |
1 |
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
|
|
|
|
|
1 |
| |
6 |
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B2 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
1 |
1 |
|
1 |
1 |
|
1 |
1 |
B6 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
B7 |
1 |
1 |
|
1 |
|
|
1 |
1 |
B8 |
|
|
|
|
|
|
|
1 |
| | |
矩阵相乘的次数 | 相乘矩阵自乘的方法 | 幂乘的方法 | 快速Warshall转移法 |
1 |
B1 |
B1、B7、 |
B2 |
B1、B2、 |
B3 |
B3、B6、 |
B4 |
B4、B8、 |
B5 |
B2、B5、 |
B6 |
B1、B5、B6、 |
B7 |
B2、B4、B7、 |
B8 |
B8、 |
|
B1 |
B1、B7、 |
B2 |
B1、B2、 |
B3 |
B3、B6、 |
B4 |
B4、B8、 |
B5 |
B2、B5、 |
B6 |
B1、B5、B6、 |
B7 |
B2、B4、B7、 |
B8 |
B8、 |
|
B1 |
B1、B7、 |
B2 |
B1、B2、 |
B3 |
B3、B6、 |
B4 |
B4、B8、 |
B5 |
B2、B5、 |
B6 |
B1、B5、B6、 |
B7 |
B2、B4、B7、 |
B8 |
B8、 |
|
2 |
B1 |
B1、B2、B4、B7、 |
B2 |
B1、B2、B7、 |
B3 |
B1、B3、B5、B6、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B5、 |
B6 |
B1、B2、B5、B6、B7、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
B1 |
B1、B2、B4、B7、 |
B2 |
B1、B2、B7、 |
B3 |
B1、B3、B5、B6、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B5、 |
B6 |
B1、B2、B5、B6、B7、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
B1 |
B1、B2、B4、B7、 |
B2 |
B1、B2、B4、B7、 |
B3 |
B1、B3、B5、B6、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、 |
B6 |
B1、B2、B4、B5、B6、B7、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
3 |
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、 |
B3 |
B1、B2、B3、B5、B6、B7、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B5、B7、 |
B6 |
B1、B2、B4、B5、B6、B7、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、B8、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、B8、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
4 |
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、B8、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、B8、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、B8、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、B8、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
5 |
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、B8、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、B8、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
|
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、B8、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、B8、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
| |
6 |
B1 |
B1、B2、B4、B7、B8、 |
B2 |
B1、B2、B4、B7、B8、 |
B3 |
B1、B2、B3、B4、B5、B6、B7、B8、 |
B4 |
B4、B8、 |
B5 |
B1、B2、B4、B5、B7、B8、 |
B6 |
B1、B2、B4、B5、B6、B7、B8、 |
B7 |
B1、B2、B4、B7、B8、 |
B8 |
B8、 |
| | |
矩阵相乘的次数 | 相乘矩阵自乘的方法 | 逐次平方法 | 快速转移法,Warshall快速转移 |
1 |
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
|
|
|
|
|
1 |
|
B2 |
1 |
1 |
|
|
|
|
|
|
B3 |
|
|
1 |
|
|
1 |
|
|
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
|
1 |
|
|
1 |
|
|
|
B6 |
1 |
|
|
|
1 |
1 |
|
|
B7 |
|
1 |
|
1 |
|
|
1 |
|
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
|
|
|
|
|
1 |
|
B2 |
1 |
1 |
|
|
|
|
|
|
B3 |
|
|
1 |
|
|
1 |
|
|
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
|
1 |
|
|
1 |
|
|
|
B6 |
1 |
|
|
|
1 |
1 |
|
|
B7 |
|
1 |
|
1 |
|
|
1 |
|
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 |
B1 |
1 |
|
|
|
|
|
1 |
|
B2 |
1 |
1 |
|
|
|
|
|
|
B3 |
|
|
1 |
|
|
1 |
|
|
B4 |
|
|
|
1 |
|
|
|
1 |
B5 |
|
1 |
|
|
1 |
|
|
|
B6 |
1 |
|
|
|
1 |
1 |
|
|
B7 |
|
1 |
|
1 |
|
|
1 |
|
B8 |
|
|
|
|
|
|
|
1 |
|
2 |
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 |
|
1 |
|
|
1 | |
B2 |
1 | 1 | |
|
|
|
1 |
|
B3 |
1 |
|
1 | |
1 |
1 | |
|
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 |
1 | |
|
1 | |
|
|
B6 |
1 | 1 |
|
|
1 | 1 | 1 |
|
B7 |
1 |
1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
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1 |
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B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 |
|
1 |
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|
1 | |
B2 |
1 | 1 | |
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|
1 |
|
B3 |
1 |
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1 | |
1 |
1 | |
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B4 |
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|
1 | |
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1 |
B5 |
1 |
1 | |
|
1 | |
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|
B6 |
1 | 1 |
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|
1 | 1 | 1 |
|
B7 |
1 |
1 | |
1 | |
|
1 | 1 |
B8 |
|
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|
1 |
|
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 |
|
1 |
|
|
1 | |
B2 |
1 | 1 | |
1 |
|
|
1 |
|
B3 |
1 |
|
1 | |
1 |
1 | |
|
B4 |
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|
1 | |
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|
1 |
B5 |
1 |
1 | |
1 |
1 | |
1 |
|
B6 |
1 | 1 |
|
1 |
1 | 1 | 1 |
|
B7 |
1 |
1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
|
3 |
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 |
|
|
1 | |
B3 |
1 | 1 |
1 | |
1 | 1 | 1 |
|
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
|
1 | |
1 |
|
B6 |
1 | 1 | |
1 |
1 | 1 | 1 | |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
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|
|
|
1 |
|
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 |
|
|
1 | 1 |
B3 |
1 | 1 |
1 | 1 |
1 | 1 | 1 |
|
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 |
1 | |
1 |
|
B6 |
1 | 1 | |
1 |
1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 | |
|
1 | 1 |
B3 |
1 | 1 |
1 | 1 |
1 | 1 | 1 |
1 |
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 | 1 | |
1 | 1 |
B6 |
1 | 1 | |
1 | 1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
|
4 |
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 | |
|
1 | 1 |
B3 |
1 | 1 | 1 | 1 |
1 | 1 | 1 | |
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 |
1 | |
1 | |
B6 |
1 | 1 | |
1 | 1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 | |
|
1 | 1 |
B3 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 | 1 | |
1 | 1 |
B6 |
1 | 1 | |
1 | 1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 | |
|
1 | 1 |
B3 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 | 1 | |
1 | 1 |
B6 |
1 | 1 | |
1 | 1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
|
5 |
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 | |
|
1 | 1 |
B3 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 | 1 | |
1 | 1 |
B6 |
1 | 1 | |
1 | 1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
|
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 | |
|
1 | 1 |
B3 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 | 1 | |
1 | 1 |
B6 |
1 | 1 | |
1 | 1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
| |
6 |
|
B1 |
B2 |
B3 |
B4 |
B5 |
B6 |
B7 |
B8 |
B1 |
1 | 1 | |
1 | |
|
1 | 1 |
B2 |
1 | 1 | |
1 | |
|
1 | 1 |
B3 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B4 |
|
|
|
1 | |
|
|
1 |
B5 |
1 | 1 | |
1 | 1 | |
1 | 1 |
B6 |
1 | 1 | |
1 | 1 | 1 | 1 | 1 |
B7 |
1 | 1 | |
1 | |
|
1 | 1 |
B8 |
|
|
|
|
|
|
|
1 |
| | |