Path in Matrix
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  Difficulty: Medium   Marks: 4
       

Given a N X N  matrix Matrix[N][N] of positive integers.  There are only three possible moves from a cell Matrix[r][c].

1. Matrix[r+1][c]

2. Matrix[r+1][c-1]

3. Matrix[r+1][c+1]

Starting from any column in row 0, return the largest sum of any of the paths up to row N-1.

Input:
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer N denoting the order of matrix. Next line contains N*N integers denoting the elements of the matrix in row-major form.

Output:

Output the largest sum of any of the paths starting from any cell of row 0 to any cell of row N-1. Print the output of each test case in a new line.

Constraints:

1<=T<=20
2<=N<=20
1<=Matrix[i][j]<=1000 (for all 1<=i<=N && 1<=j<=N)

Example:

Input:
1
2
348 391 618 193

Output:
1009

Explanation: In the sample test case, the path leading to maximum possible sum is 391->618.  (391 + 618 = 1009)

** For More Input/Output Examples Use 'Expected Output' option **

Author: dipjal1996


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