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# Grid Paths

Problem Description

You are given a 2D grid A of size N x N. Rows are numbered from top to bottom from 0 to N - 1 and the columns are numbered from left to right from 0 to N - 1.

From a cell, you can either move left, right, up, and down. You cannot move outside of the grid. Some cells are blocked. A cell is blocked if A[i][j] is 0, otherwise A[i][j] denotes the value at ith row and jth column.

Consider every path from (0, 0) to (N-1, N-1) which visits each unblocked cell exactly once. The cost of a path is the sum of absolute values of adjacent cells of the path. Formally, if the values of the path are B1, B2, ...,, Br, the cost of the path is ∑ | Bi - Bi-1 | for i from 2 to r.

Find the sum of the cost of all such paths.

Note : Interpreter languages like Python may not work. Please try it in languages like C/ C++/ Java.

Problem Constraints

2 <= N <= 7

0 <= A[i][j] <= 100

0 < A[0][0], A[N-1][N-1] <= 100

Input Format
The first and only argument contains an 2D array A of size N x N.

Output Format
Return the sum of cost of all paths from (0, 0) to (N-1, N-1) which visits each unblocked cell exactly once.

Example Input

Input 1:

```  A :
[
[5, 2]
[0, 7]
]
```

Input 2:

```  A :
[
[79, 19, 59]
[45, 89, 63]
[79, 81, 37]
]
```

Example Output

Output 1:

```  8
```

Output 2:

```  472
```

Example Explanation

Explanation 1:

```  Valid path is [5, 2, 7]. Cost is |5-2| + |7-2| = 8
```

Explanation 2:

```  There are two valid paths-
1. [79, 19, 59, 63, 89, 45, 79, 81, 37]
Cost = 254
2. [79, 45, 79, 81, 89, 19, 59, 63, 37]
Cost = 218
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
Hints
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## Discussion

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