Problem Statement

Determine whether there is an N-by-N matrix X that satisfies the following conditions, and present one such matrix if it exists. (Let x_{i,j} denote the element of X at the i-th row from the top and j-th column from the left.)

• $x_{i,j} \in$ { 0,1,2 } for every i and $j (1 \leq i,j \leq N)$.
• The following holds for each $i=1,2,\ldots,Q$.
• Let $P = \prod_{a_i \leq j \leq b_i} \prod_{c_i \leq k \leq d_i} x_{j,k}. Then, P$ is congruent to e_i modulo 3.

Input

The input is given from Standard Input in the following format:
N Q
a_1 b_1 c_1 d_1 e_1
$\vdots$
a_Q b_Q c_Q d_Q e_Q

Output

If no matrix X satisfies the conditions, print No.
If there is a matrix X that satisfies them, print Yes in the first line and one such instance of X in the following format in the second and subsequent lines.
$x_{1,1} x_{1,2} \ldots x_{1,N}$
$x_{2,1} x_{2,2} \ldots x_{2,N}$
$\vdots$
$x_{N,1} x_{N,2} \ldots x_{N,N}$

If multiple matrices satisfy the conditions, any of them will be accepted.

Constraints

• $1 \leq N,Q \leq 2000$
• $1 \leq a_i \leq b_i \leq N$
• $1 \leq c_i \leq d_i \leq N$
• $e_i \in$ {0,1,2 }
• All values in the input are integers.

Sample Input 1

2 3
1 1 1 2 0
1 2 2 2 1
2 2 1 2 2

Sample Output 1

Yes
0 2
1 2

For example, for i=2, we have $P = \prod_{a_2 \leq j \leq b_2} \prod_{c_2 \leq k \leq d_2} x_{j,k}= \prod_{1 \leq j \leq 2} \prod_{2 \leq k \leq 2} x_{j,k}=x_{1,2} \times x_{2,2}$.
In this sample output, we have x_{1,2}=2 and x_{2,2}=2, so $P=2 \times 2 = 4,$ which is congruent to e_2=1 modulo 3.
It can be similarly verified that the condition is also satisfied for i=1 and i=3.

Sample Input 2

4 4
1 4 1 4 0
1 4 1 4 1
1 4 1 4 2
1 4 1 4 0

Sample Output 2

No

见题面 Input 部分

见题面 Output 部分