Quadratic Form

题号：NC209432
时间限制：C/C++/Rust/Pascal 5秒，其他语言10秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Bobo has a positive-definite $n \times n$ matrix $A$ and an $n$ -dimension vector $b$ . He would like to find $x_1, x_2, \dots, x_n$ where

$x_1, x_2, \dots, x_n \in \mathbb{R}$ ,
$\sum_{i = 1}^n \sum_{j = 1}^n A_{i, j} x_i x_j \leq 1$
$\sum_{i = 1}^n b_i x_i$ is maximum.

It can be shown that $\left(\sum_{i = 1}^n b_i x_i\right)^2 = \frac{P}{Q}$ , which is rational.
Find the value of $P \cdot Q^{-1} \bmod 998244353$ .

输入描述:

The input consists of several test cases terminated by end-of-file.

The first line of each test case contains an integer n.
The i-th of the following n lines contains n integers .
The last line contains n integers .

* 
* 
* 
*  for any 
* 
* The sum of n does not exceed .

输出描述:

For each test case, print an integer which denotes the result.

示例1

输入

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输出

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0
2
623902721