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.

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.

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.

Sample Input 1

3 13
3 2 7
4 8 9
1 6 5

Sample Output 1

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

Sample Input 2

10 165
82 94 21 65 28 22 61 80 81 79
93 35 59 85 96 1 78 72 43 5
12 15 97 49 69 53 18 73 6 58
60 14 23 19 44 99 64 17 29 67
24 39 56 92 88 7 48 75 36 91
74 16 26 10 40 63 45 76 86 3
9 66 42 84 38 51 25 2 33 41
87 54 57 62 47 31 68 11 83 8
46 27 55 70 52 98 20 77 89 34
32 71 30 50 90 4 37 95 13 100

Sample Output 2

348179577

见题面 Input 部分

见题面 Output 部分