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=====B=====
* 题意:将 $1,2,\cdots,n^2$ 填入 $n \times n$ 的矩阵中，问存在多少种方式使得任意单调递增的序列 $p_1,p_2,\cdots,p_i$ 有 $p_1 = 1, p_i = n^2$ 且 $\sum_{j = 1}^{i - 1}dis(p_j, p_{j + 1})$ 为偶数，其中 $dis(p_j, p_{j + 1})$ 为两个点的曼哈顿距离。$n\le 10^3$ ，答案模 $10^9 + 7$
* 题解:先只考虑序列的第一个点和最后一个点的排列方式。在第一个点确定之后，$n^2$ 只能在与第一个点平行的斜线上，在这两个点确定之后会发现剩余的点无论如何排列都是满足条件的，乘上 $n!$ 即可。注意特判 $n = 1$
=====C=====
* 题意:
* 题解:
=====D=====
* 题意:
* 题解:
=====E=====
* 题意:
* 题解: