I have been having trouble with a problem called the lazy cow (link: USACO) for a while now. I still do not quite understand this code, can someone help guide me through the code?

#define MAX 801

using namespace std;

int n,k,mat[MAX][MAX],best;

int main()
ifstream fin(“”);
fin >> n >> k;
// rotate the matrix 45 degrees
for (int i=0; i<n; i++)
for (int j=0; j<n; j++)
fin >> mat[i+j][n-i+j-1];

// 45 degree rotation expands the size of the matrix
// it also includes the cells with half distance
int t=(n+1)%2;	// t is used to avoid non-lattice points
for (int i=0; i<n; i++,t=1-t)
	// calculate the sum of 2k x 2k region
	// Bessie can only be positioned in lattice points
	int sum=0;
	for (int a=max(i-k,0); a<n && a<=i+k; a++)
		for (int b=max(t-k,0); b<n && b<=t+k; b++)
	if (best<sum) best=sum;

	// slide the region
	for (int j=t+1; j+k<n; j++)
		for (int a=max(i-k,0); a<n && a<=i+k; a++)
			if (j-k-1>=0) sum-=mat[a][j-k-1];
		// update the sum only in lattice points
		if (j%2==t && best<sum) best=sum;

ofstream fout("lazy.out");
fout << best << endl;