Problem B: The Most Potent Corner |

Every corner of the *N*-dimensional (*1< N<15*) unit cube has weight (some positive integer less than 256). We will call two corners neighbouring, if they have common edge. Potency of the corner is the sum of weights of all neighbouring corners. Weights of all the corners are given. You are to determine two neighbouring corners that have the maximum sum of potencies and to output this sum.

The input will consist of several input blocks.
Each input block begins with
the integer *N*, the dimension of the
cube. Then there are weights of the corners, one per line in the natural
order:
the first line contains the weight of the corner (0,...0,0,0),
the second one - the weight of (0,...,0,0,1),
then there is the weight of (0,...,0,1,0),
then (0,...,0,1,1), then (0,...,1,0,0),
the penultimate line contains the weight of the corner (1,...,1,1,0),
the last one - (1,...,1,1,1).

The input is terminated by <EOF>.

For each input block the output line should contain one number, the maximum potencies sum.

3 82 73 8 49 120 44 242 58 2 1 1 1 1

```
619
4
```

#### Sergey Karpovich, 2002