Problem

During her journey with Kosuke, Sakurako and Kosuke found a valley that can be represented as a matrix of size $n×n$, where at the intersection of the $i-th$ row and the $j-th$ column is a mountain with a height of $ai,j$. If $ai,j<0$, then there is a lake there.

Kosuke is very afraid of water, so Sakurako needs to help him:

• With her magic, she can select a square area of mountains and increase the height of each mountain on the main diagonal of that area by exactly one.

More formally, she can choose a submatrix with the upper left corner located at $(i,j)$ and the lower right corner at $(p,q)$, such that $p−i=q−j$. She can then add one to each element at the intersection of the $(i+k)-th$ row and the $(j+k)$ -th column, for all k such that $0≤k≤p−i$.

Determine the minimum number of times Sakurako must use her magic so that there are no lakes.

Input

The first line contains a single integer $t$ $(1≤t≤10)$ — the number of test cases.

Each test case is described as follows:

• The first line of each test case consists of a single number $n(1≤n≤200)$.
• Each of the following n lines consists of n integers separated by spaces, which correspond to the heights of the mountains in the valley $a (−10^5≤ai,j≤10^5)$.

Output

For each test case, output the minimum number of times Sakurako will have to use her magic so that all lakes disappear.

Example : in

4
1
1
2
-1 2
3 0
3
1 2 3
-2 1 -1
0 0 -1
5
1 1 -1 -1 3
-3 1 4 4 -4
-1 -1 3 0 -5
4 5 3 -3 -1
3 1 -3 -1 5

Example : out

0
1
4
19