The Sultan of Nubia has no children, so she has decided that the country will
be split into up to *k* separate parts on her death and each part will be
inherited by whoever performs best at some test. It is possible for any
individual to inherit more than one or indeed all of the portions. To ensure
that only highly intelligent people eventually become her successors, the Sultan
has devised an ingenious test. In a large hall filled with the splash of
fountains and the delicate scent of incense have been placed *k*
chessboards. Each chessboard has numbers in the range 1 to 99 written on each
square and is supplied with 8 jewelled chess queens. The task facing each
potential successor is to place the 8 queens on the chess board in such a way
that no queen threatens another one, and so that the numbers on the squares thus
selected sum to a number at least as high as one already chosen by the Sultan.
(For those unfamiliar with the rules of chess, this implies that each row and
column of the board contains exactly one queen, and each diagonal contains no
more than one.)

Write a program that will read in the number and details of the chessboards and determine the highest scores possible for each board under these conditions. (You know that the Sultan is both a good chess player and a good mathematician and you suspect that her score is the best attainable.)

Input will consist of *k* (the number of boards), on a line by itself,
followed by *k* sets of 64 numbers, each set consisting of eight lines of
eight numbers. Each number will be a positive integer less than 100. There will
never be more than 20 boards.

Output will consist of *k* numbers consisting of your *k* scores,
each score on a line by itself and right justified in a field 5 characters wide.

1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 48 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

260