CF1268D.Invertation in Tournament

You are given a tournament — complete directed graph.

In one operation you can pick any vertex $v$ and change the direction of all edges with $v$ on one of the ends (i.e all edges $u \to v$ change their orientation to $v \to u$ and vice versa).

You want to make the tournament strongly connected with the smallest possible number of such operations if it is possible.

Also, if it is possible, you need to find the number of ways to make this number of operations to make graph strongly connected (two ways are different if for some $i$ vertex that we chose on $i$-th operation in one way is different from vertex that we chose on $i$-th operation in another way). You only need to find this value modulo $998\,244\,353$.

给你一个竞赛图——即一个完全有向图。

在一次操作中，你可以任选一个顶点 $v$，并将所有以 $v$ 为一个端点的边的方向翻转（即所有形如 $u \to v$ 的边变为 $v \to u$，反之亦然）。

若可能，你希望用最少的操作次数使该竞赛图成为强连通图。

此外，若可行，你还需计算：有多少种不同的操作序列能达到该最少操作次数，从而使得图变为强连通图（两个序列不同，当且仅当存在某个操作序号 $i$，使得在第 $i$ 次操作中所选的顶点在两个序列中不同）。你只需输出该数值对 $998\,244\,353$ 取模的结果。

The first line of input contains one integer $n$ ($3 \leq n \leq 2000$): the number of vertices in the tournament.

Following $n$ lines contain a description of the given tournament, each of them contains a binary string of length $n$. If $j$-th character of $i$-th string is equal to '1', then the graph has an edge $i \to j$.

It is guaranteed that there are no edges $i \to i$ and the graph has exactly one edge among $i \to j$ and $j \to i$ for different $i$ and $j$.

输入的第一行包含一个整数 $n$（$3 \leq n \leq 2000$）：该竞赛图的顶点数。

接下来的 $n$ 行描述了给定的竞赛图，每行包含一个长度为 $n$ 的二进制字符串。若第 $i$ 行的第 $j$ 个字符为 '1'，则图中存在一条有向边 $i \to j$。

保证图中不存在自环边（即不存在 $i \to i$），且对任意不同的 $i$ 和 $j$，$i \to j$ 与 $j \to i$ 中恰好有一条边存在。

If it is not possible to convert tournament to strongly connected with the given operations, output "-1".

Otherwise, output two integers: the smallest number of operations that you need to make the given graph strongly connected and the number of ways to do this number of operations to make graph strongly connected, modulo $998\,244\,353$.

如果无法通过给定的操作将竞赛图转化为强连通图，则输出 -1。

否则，输出两个整数：使给定图变为强连通图所需的最少操作次数，以及以该最少操作次数使图变为强连通图的方案数（对 $998\,244\,353$ 取模）。