Problem Statement

You are given a prime $P$, positive integers $N,M$, and an $N\times M$ matrix $A$. The entries of $A$ satisfy $0\leq A_{ij}\lt P\ (1\leq i\leq N,\ 1\leq j\leq M)$.

Rueru is trying to memorize the matrix $A$, and in order to reduce the number of entries to memorize, he has decided to decompose $A$ into a product of multiple matrices.

Consider a non-empty sequence of matrices $(B^{(1)},\ B^{(2)},\ \ldots,\ B^{(L)})$ of length $L\ (L\geq 1)$, where $B^{(k)}$ is an $N_k\times M_k$ matrix $(1\leq k\leq L)$. $L=1$ is allowed, $0\leq B_{ij}^{(k)}\lt P\ (1\leq k\leq L,\ 1\leq i\leq N_k,\ 1\leq j\leq M_k)$ must hold, and addition and multiplication of entries are performed modulo $P$.

Among the sequences satisfying $A=B^{(1)}B^{(2)}\ldots B^{(L)}$, find $1$ example of a sequence that minimizes $\sum_{k=1}^L N_kM_k$. For the output format, refer to the "Output" block.

Input

$P$
$N\ M$
$A_{11}\ A_{12}\ A_{13}\ \ldots\ A_{1M}$
$A_{21}\ A_{22}\ A_{23}\ \ldots\ A_{2M}$
$A_{31}\ A_{32}\ A_{33}\ \ldots\ A_{3M}$
$\vdots$
$A_{N1}\ A_{N2}\ A_{N3}\ \ldots\ A_{NM}$

• All inputs are integers
• $P$ is a prime
• $2\leq P\leq 10^9$
• $1\leq N\leq 400$
• $1\leq M\leq 400$
• $0\leq A_{ij}\lt P\ (1\leq i\leq N,\ 1\leq j\leq M)$

Output

$L$
$N_1\ M_1$
$B_{11}^{(1)}\ B_{12}^{(1)}\ B_{13}^{(1)}\ \ldots\ B_{1M_1}^{(1)}$
$B_{21}^{(1)}\ B_{22}^{(1)}\ B_{23}^{(1)}\ \ldots\ B_{2M_1}^{(1)}$
$B_{31}^{(1)}\ B_{32}^{(1)}\ B_{33}^{(1)}\ \ldots\ B_{3M_1}^{(1)}$
$\vdots$
$B_{N_11}^{(1)}\ B_{N_12}^{(1)}\ B_{N_13}^{(1)}\ \ldots\ B_{N_1M_1}^{(1)}$
$N_2\ M_2$
$B_{11}^{(2)}\ B_{12}^{(2)}\ B_{13}^{(2)}\ \ldots\ B_{1M_2}^{(2)}$
$B_{21}^{(2)}\ B_{22}^{(2)}\ B_{23}^{(2)}\ \ldots\ B_{2M_2}^{(2)}$
$B_{31}^{(2)}\ B_{32}^{(2)}\ B_{33}^{(2)}\ \ldots\ B_{3M_2}^{(2)}$
$\vdots$
$B_{N_21}^{(2)}\ B_{N_22}^{(2)}\ B_{N_23}^{(2)}\ \ldots\ B_{N_2M_2}^{(2)}$
$\vdots$
$N_L\ M_L$
$B_{11}^{(L)}\ B_{12}^{(L)}\ B_{13}^{(L)}\ \ldots\ B_{1M_L}^{(L)}$
$B_{21}^{(L)}\ B_{22}^{(L)}\ B_{23}^{(L)}\ \ldots\ B_{2M_L}^{(L)}$
$B_{31}^{(L)}\ B_{32}^{(L)}\ B_{33}^{(L)}\ \ldots\ B_{3M_L}^{(L)}$
$\vdots$
$B_{N_L1}^{(L)}\ B_{N_L2}^{(L)}\ B_{N_L3}^{(L)}\ \ldots\ B_{N_LM_L}^{(L)}$

First print $L$, then print $N_k,\ M_k$ and the entries of $B^{(k)}$ $(1\leq k\leq L)$ in order.

Your output must satisfy $0\leq B_{ij}^{(k)}\lt P\ (1\leq k\leq L,\ 1\leq i\leq N_k,\ 1\leq j\leq M_k)$, and print a newline at the end.

Sample

998244353
5 4
21 17 13 9
18 16 14 12
15 15 15 15
12 14 16 18
9 13 17 21

2
5 2
1 5
2 4
3 3
4 2
5 1
2 4
1 2 3 4
4 3 2 1

5
2 2
1 2
3 4

1
2 2
1 2
3 4

7
3 4
2 3 4 5
4 6 1 3
6 2 5 1

2
3 1
1
2
3
1 4
2 3 4 5

998244353
3 3
0 0 0
0 0 0
0 0 0

2
3 1
0
0
0
1 3
0 0 0