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Time Limit: 5 s Memory Limit: 2048 MB Total points: 100

統計

给定一个 $N \times N$ 的矩阵 $A_{ij}$，计算其行列式 $\det A$，取模 $998\,244\,353$。

输入格式

输入的第一行包含一个整数 $N$。

接下来 $N$ 行，每行 $N$ 个整数。第 $i$ 行第 $j$ 个整数表示 $A_{ij}$。

输出格式

输出一行一个整数，表示答案。

样例数据

样例输入

样例输出

998241417

子任务

对于所有数据，$1 \leq N \leq 500$，$0 \leq A_{ij} < 998\,244\,353$

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