Permutation and combination

5 boys ( B 1 , B 2 , B 3 , B 4 , B 5 B_1,B_2,B_3,B_4,B_5 ) and 5 girls ( G 1 , G 2 , G 3 , G 4 , G 5 G_1, G_2,G_3, G_4,G_5 ) are to be seated around a round table such that the boys and girls sit alternately and B i B_i does not sit beside G i i { 1 , 2 , 3 , 4 , 5 } G_i \forall i \in \{1,2,3,4,5\} . If the number of such arrangements is N N , submit your answer as the sum of digits of N N .


The answer is 9.

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