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Given a n*n matrix, find the maximum length path (starting from any cell) such that all cells along the path are in increasing order with a difference of 1.

We can move in 4 directions from a given cell (i, j), i.e., we can move to (i+1, j) or (i, j+1) or (i-1, j) or (i, j-1) with the condition that the adjacent cells have a difference of 1.

**Input:**

The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case contains an integer n denoting the size of the nxn matrix. The following lines contain the nxn matrix.

**Output:**

Print the length of the longest path.

**Constraints:**

1<=T<=100

1<=n<=50

1<=arr[i][j]<=50

**Example:
Input:**

2

3

1 2 9 5 3 8 4 6 7

4

1 7 8 9 2 11 12 17 3 15 14 13 4 5 25 30

**Output:**

4

5

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Longest Path in a matrix

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