P8546 Xiao Wa’s X Sacrifice.

Given an $n \times n$ $01$ square matrix, compute the number of X’s in it. An X is defined as a connected component filled with $1$’s and shaped like an X. Specifically, an X is made up of a left-leaning diagonal `\` and a right-leaning diagonal `/`. You must ensure that the left-leaning diagonal and the right-leaning diagonal have **the same length**, and the X is centrally symmetric. The diagonal length must be greater than $1$. For example: ```cpp 101 010 101 ``` There is one X with diagonal length $3$. ```cpp 1001 0110 0110 1001 ```` There are two X’s with diagonal lengths $2$ and $4$. ```cpp 10001 01010 00100 01010 00001 ``` There is only one X with diagonal length $3$.

Line $1$ contains one positive integer $n$. The next $n$ lines each contain a $01$ string of length $n$, describing a $01$ matrix.

Output one line containing a non-negative integer, representing the number of X’s.

For $20\%$ of the testdata, $1 \leq n \leq 3$. For $40\%$ of the testdata, $1 \leq n \leq 10$. For $70\%$ of the testdata, $1 \leq n \leq 50$. For $100\%$ of the testdata, $1 \leq n \leq 100$. Translated by ChatGPT 5