Seven players who represented the university are to be felicitated in a function. They are A, B, C, D, E, F and G. They are to be seated on the dias along one side of a rectangular table. Some of the conditions are:
i. A Gare to be seated at the extreme right, which is closest to the exit because they have to leave early.
ii. B has won the most medals and so has to be seated at the centre.
iii. C and D do not get along well and so have to be seated as far as possible.
iv. E and F are good friends and sit together.
Five friends A, B, C, D, and E are sitting in a row facing north, but not necessarily in the same order:
B is to the immediate left of C
E is not at any of the ends
D is to the right of E but not next to C
A is at one of the ends
Who is sitting in the middle?
When $10^{100}$ is divided by 7, the remainder is ?