Puzzle Challenge

Each of the small squares in the grid below contains either A, B or C. Every row, column and each of the two long diagonals has exactly two of each letter. The information in the clues refers only the squares in that row or column. To help you solve this problem there are as many clues as you will need! Can you tell the letter in each square?

ACROSS

1. The Bs are further right than the As.
2. Each B is directly next to and right of a C.
3. The As are further right than the Bs.
4. The As are further right than the Bs.
5. The Cs are not in adjacent squares.
6. The Bs are further right than the As.

DOWN

1. The Cs are between the As.
2. The Bs are higher than the Cs.
3. The Bs are lower than the Cs.
4. The As are between the Bs.
5. The Bs are lower than the Cs.