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Difficulty Level:

Hard

Total Submissions: 1034 Accuracy:

21.08%

Minimum Cost Path

Given a square grid of size n, each cell of which contains integer cost which represents a cost to traverse through that cell, we need to find a path from top left cell to bottom right cell by which total cost incurred is minimum.

Note : It is assumed that negative cost cycles do not exist in input matrix.

Input:

The first line of input will contain number of test cases T . Then T test cases follow . Each test case contains 2 lines. The first line of each test case contains an integer n denoting the size of the grid. Next line of each test contains a single line containing N*N space separated integers depecting cost of respective cell from (0,0) to (n,n).


Output:

For each test case output a single integer depecting the minimum cost to reach the destination.


Constraints:

1<=T<=50
1<= n<= 50


Example:

Input

2
5
31 100 65 12 18 10 13 47 157 6 100 113 174 11 33 88 124 41 20 140 99 32 111 41 20
2
42 93 7 14

 

Output
327
63

Explanation:

Test Case 1:

Grid is:
31, 100, 65, 12, 18,
10, 13, 47, 157, 6,
100. 113, 174, 11, 33,
88, 124, 41, 20, 140,
99, 32, 111, 41, 20

A cost grid is given in below diagram, minimum 
cost to reach bottom right from top left 
is 327 (= 31 + 10 + 13 + 47 + 65 + 12 + 18 + 
6 + 33 + 11 + 20 + 41 + 20)

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

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