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 $3$.

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.

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.