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code_segments/segment_387.txt

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+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.
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+Kosuke is very afraid of water, so Sakurako needs to help him:
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+  * 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. 
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+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 $0 \le k \le p-i$.
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+Determine the minimum number of times Sakurako must use her magic so that there are no lakes.
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+The first line contains a single integer $t$ ($1 \le t \le 200$) — the number of test cases.
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+Each test case is described as follows:
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+  * 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 $a$ ($-10^5 \le a_{i,j} \le 10^5$). 
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+It is guaranteed that the sum of $n$ across all test cases does not exceed $1000$.
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+For each test case, output the minimum number of times Sakurako will have to use her magic so that all lakes disappear.
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