Problem Statement

You are given an $N\times N$ matrix $A = (A_{i,j})$ ($1\le i,j\le N$) whose entries are $0$ or $1$.

Find, modulo $998244353$, the number of trees $G$ on $N$ vertices numbered $1$ to $N$ that satisfy the following condition.

• $A_{i,j}=1$ if and only if at least one of the following holds:
• When $G$ is rooted at vertex $1$, Vertex $j$ is an ancestor of vertex $i$. That is, vertex $j$ lies on the unique path in $G$ between vertices $1$ and $i$.
  • When $G$ is rooted at vertex $1$, Vertex $i$ is an ancestor of vertex $j$. That is, vertex $i$ lies on the unique path in $G$ between vertices $1$ and $j$.

Here, the endpoints of a path are considered to be on that path. Note that $G$ being a tree guarantees uniqueness of the path between any two vertices.

There are $T$ test cases; solve each one.

Constraints

• $1\leq T\leq 10^5$
• $2\leq N\leq 400$
• $A_{i,j}\in \lbrace 0,1\rbrace$ $(1\leq i,j\leq N)$
• $A_{i,i}=1$ $(1\leq i\leq N)$
• $A_{i,j}=A_{j,i}$ $(1\leq i,j\leq N)$
• The sum of $N^2$ over all test cases is at most $400^2$.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\vdots
\text{case}_T

Each case is given in the following format:

N
A_{1,1} \cdots A_{1,N}
\vdots
A_{N,1} \cdots A_{N,N}

Output

Print $T$ lines. The $i$-th line should contain the number, modulo $998244353$, of trees $G$ satisfying the conditions for the $i$-th test case.