There are items. Setsuna wants you to divide items into two sets, set
and set
, and neither set can be empty.
For some mysterious reasons, when item and item
are in the same set, they will produce
power.
Thus, the total power will be
You should find the possible maximum power.
The first line contains one integers
(
).
The
-th line of the following n lines contains n integers
.
It is guaranteed that
and
.
Output the possible maximum power.