汉明距离较大的数组AI (CI翻译)
Problem Statement
题目描述
AI (CI翻译)You are given an integer $N$. For length-$N^2$ integer sequences $a$ and $b$ consisting of integers between $1$ and $N$ (inclusive), we define their distance $d(a,b)$ as follows:
给定一个整数 $N$。对于两个长度为 $N^2$、由 $1$ 到 $N$（含）之间的整数构成的序列 $a$ 和 $b$，定义它们的距离 $d(a,b)$ 如下：AI (CI翻译)
$d(a,b)=$"the number of indices$i$($1 \leq i \leq N^2$) such that$a_i \neq b_i$."
$d(a,b)=$“满足$a_i \neq b_i$的下标$i$（$1 \leq i \leq N^2$）的数量”。
Now, you will create $N$ length-$N^2$ integer sequences consisting of integers between $1$ and $N$, and denote them as $x_1,x_2,\cdots,x_N$ (their order also matters). Find the number, modulo $998244353$, of instances of $(x_1,x_2,\cdots,x_N)$ satisfying the following condition.
现在，请构造 $N$ 个长度为 $N^2$、由 $1$ 到 $N$ 之间的整数构成的序列，并将它们记为 $x_1,x_2,\cdots,x_N$（序列的顺序也有影响）。求满足以下条件的 $(x_1,x_2,\cdots,x_N)$ 的方案数，答案对 $998244353$ 取模。AI (CI翻译)
- For any length-
$N^2$integer sequence$y$consisting of integers between$1$and$N$, there exists some$1 \leq i \leq N$such that$d(x_i,y) \geq N^2-N$.
- 对于任意一个长度为
$N^2$、由$1$到$N$之间的整数构成的序列$y$，都存在某个$1 \leq i \leq N$，使得$d(x_i,y) \geq N^2-N$。
Constraints
约束条件
AI (CI翻译)$1 \leq N \leq 50$- All input values are integers.
$1 \leq N \leq 50$- 输入的所有数值均为整数。
Input
输入格式
AI (CI翻译)The input is given from Standard Input in the following format:
输入通过标准输入给出，格式如下：AI (CI翻译)
NNOutput
输出格式
AI (CI翻译)Output the answer.
输出答案。AI (CI翻译)
样例
2
80
3
597965565
10
241191911
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（gpt-6.1-sol），如有出入请以原文为准。