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.

-----Sample Input-----
3 13
3 2 7
4 8 9
1 6 5

-----Sample Output-----
12

For example, Sigma can swap two columns, by setting x = 1, y = 2. After that, the resulting matrix will be:
2 3 7
8 4 9
6 1 5

After that, he can swap two row vectors by setting x = 1, y = 3, resulting in the following matrix:
6 1 5
8 4 9
2 3 7

见题面

见题面