Problem Statement

Given are an $N \times N$ matrix and an integer $K$. The entry in the $i$-th row and $j$-th column of this matrix is denoted as $a_{i, j}$. This matrix contains each of $1, 2, \dots, N^2$ exactly once.

Sigma can repeat the following two kinds of operation arbitrarily many times in any order.

• Pick two integers $x, y (1 \leq x < y \leq N)$ that satisfy $a_{i, x} + a_{i, y} \leq K$ for all $i$ ($1 \leq i \leq N$) and swap the $x$-th and the $y$-th columns.
• Pick two integers $x, y (1 \leq x < y \leq N)$ that satisfy $a_{x, i} + a_{y, i} \leq K$ for all $i$ ($1 \leq i \leq N$) and swap the $x$-th and the $y$-th rows.

How many matrices can he obtain by these operations? Find it modulo $998244353$.

Constraints

• $1 \leq N \leq 50$
• $1 \leq K \leq 2 \times N^2$
• $a_{i, j}$'s are a rearrangement of $1, 2, \dots, N^2$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
a_{1, 1} a_{1, 2} ... a_{1, N}
a_{2, 1} a_{2, 2} ... a_{2, N}
:
a_{N, 1} a_{N, 2} ... a_{N, N}

Output

Print the number of matrices Sigma can obtain modulo $998244353$.