9039: Cheeeeen the Cute Cat

*本题于2023/8/1增强了数据，之前提交的代码不重测。
Chen loves bipartite graph matching problems. As a cat, Chen also loves playing with woolen balls. So she thinks the graph should be dense.
And here's The Cute Cat Matching Problem:
Given a bipartite graph with $2n$ nodes and n(n−1)2\frac{n(n-1)}{2}2n(n−1) edges, guaranteed that there are no edges between nodes $1,2,\dots ,n$. There are no edges between nodes $n+1,n+2,\dots ,2n$ too. Also, there's no edge between $i$ ($1\le i\le n$) and $i+n$. If there's an edge between $i$ (1≤i,j≤n1\le i,j\le n1≤i,j≤n) and j+nj+nj+n, then there will be no edge between $j$ and $i+n$. That means the given graph guarantees that there'll be exactly one edge between (i,j+n)(i,j+n)(i,j+n) and (i+n,j)(i+n,j)(i+n,j).
Help Chen find the maximum matching of the given graph.

The first line contains one integer $n$ ($2\le n\le 3000$), meanings the graph has $2n$ node.
For the next $n$ lines, each line while contain $n$ $01$s, forms a $01$ matrix $e$ (ei,j∈0,1e_{i,j}\in{0,1}ei,j∈0,1). If ei,j=1e_{i,j}=1ei,j=1, there will be an edge between node $i$ and $n+j$.

One integer, means the maximum matching of the given graph.