This problem is a programming version of Problem 149 from projecteuler.net
Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, vertical, diagonal or anti-diagonal) is ().
Now, let us repeat the search, but on a much larger scale.
First, generate pseudo-random numbers using the following generator:
The terms of are then arranged in a table, using the first numbers to fill the first row (sequentially), the next numbers to fill the second row, and so on.
For every from to , find the greatest sum of (any number of) adjacent entries in any direction (horizontal, vertical, diagonal or anti-diagonal), considering only the cells that belong to the first rows and columns.
Input Format
The input consists of exactly seven lines.
- The st line of input contains , the dimension of the square grid.
- The nd line contains a single integer .
- The rd line contains integers separated by single spaces: .
- The th line contains five integers and .
- The th line contains a single integer .
- The th line contains integers separated by single spaces: .
- The th line contains five integers and .
Constraints
In input files #01-#10:
In input files #11-#20:
Output Format
Output lines. The th line must contain a single integer, denoting the greatest sum of (any number of) adjacent entries in any direction considering only the cells that belong to the first rows and columns.
Sample Input
8
4
81 -89 45 6
3 2 2 1 0
3
-78 -45 54
1 0 0 1 2
Sample Output
-39
0
270
270
270
330
334
430
Explanation
The following is the whole grid:
As an example, the fifth answer is because the largest sum in the first five rows and columns is :
On the other hand, the sixth answer is because the largest sum in the first six rows and columns is :