Problem Statement

You are given a sequence of positive integers $A=(A_1,A_2,\dots ,A_N)$ of length $N$ and a positive integer $X$. Here, each of the values $A_1,A_2,\dots, A_N,X$ is one of $1,2,3,4$.

A table $f$ of positive integers with $4$ rows and $4$ columns is called a nice table if it satisfies the following conditions. Here, the element in the $i$-th row from the top and the $j$-th column from the left of the table is denoted by $f(i,j)$.

• All $16$ elements contained in the table are one of $1,2,3,4$.
• $f(f(\dots f(f(A_1,A_2),A_3),\dots),A_N)=X$ holds.

Determine whether a nice table exists, and if it does, output $1$ such table.

Constraints

• All inputs are integers.
• $2\le N\le 100$
• Each of $A_1,A_2,\dots, A_N,X$ is one of $1,2,3,4$.

Input

$N$
$A_1$ $A_2$ $\dots A_N$
$X$

Output

On the first line, output Yes if a nice table exists, and No otherwise. If a nice table exists, output $4$ more lines. On the line for each $i=1,2,3,4$ among them, output $f(i,1),f(i,2),f(i,3),f(i,4)$ separated by spaces.

Sample

4
1 2 3 4
3

Yes
1 2 3 4
2 3 4 1
3 4 1 2
4 1 2 3

2
4 3
1

Yes
3 3 1 3
3 1 1 3
3 3 1 3
3 1 1 1