| During her journey with Kosuke, Sakurako and Kosuke found a valley that can be represented as a matrix of size $n \times n$, where at the intersection of the $i$-th row and the $j$-th column is a mountain with a height of $a_{i,j}$. If $a_{i,j} < 0$, 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 $0 \le k \le p-i$. | |
| Determine the minimum number of times Sakurako must use her magic so that there are no lakes. | |
| The first line contains a single integer $t$ ($1 \le t \le 200$) — the number of test cases. | |
| Each test case is described as follows: | |
| * The first line of each test case consists of a single number $n$ ($1 \le n \le 500$). * Each of the following $n$ lines consists of $n$ integers separated by spaces, which correspond to the heights of the mountains in the valley $a$ ($-10^5 \le a_{i,j} \le 10^5$). | |
| It is guaranteed that the sum of $n$ across all test cases does not exceed $1000$. | |
| For each test case, output the minimum number of times Sakurako will have to use her magic so that all lakes disappear. | |