Problem Statement

We have a grid of squares with $N$ rows arranged vertically and $N$ columns arranged horizontally. The square at the $i$-th row from the top and $j$-th column from the left has an integer label $a_{i,j}$. Consider paths obtained by starting on one of the squares and going right or down to an adjacent square zero or more times. Find the number, modulo $998244353$, of such paths that start and end on squares with the same label. Two paths are distinguished when they visit different sets of squares (including the starting and ending squares).

Constraints

• $1 \leq N \leq 400$
• $1 \leq a_{i,j} \leq N^2$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_{1,1} \ldots a_{1,N}
\vdots
a_{N,1} \ldots a_{N,N}

Output

Print the answer.