You are given a grid with $(3N + 1)$ rows and $(3N + 1)$ columns. Determine whether it is possible to color each cell either black or white so that all of the following conditions are satisfied. If it is possible, output one such coloring.

• No two distinct black cells share a side.
• Starting from any black cell, by repeatedly moving zero or more times to an adjacent black cell sharing a corner (i.e., one that is diagonally adjacent), it is possible to reach some black cell that is adjacent to the outer boundary of the grid.
• All white cells form a single connected component; that is, for any two white cells, it is possible to move from one to the other by repeatedly moving zero or more times to an adjacent white cell sharing a side.
• There are exactly $N + 1$ black cells in each of two specific rows, and exactly $N$ black cells in each of the remaining rows.
• There are exactly $N + 1$ black cells in each of two specific columns, and exactly $N$ black cells in each of the remaining columns.

Input

The input is given in the following format:

N

• All inputs are integers.
• $1 \le N \le 500$

Output

If there is no coloring that satisfies the conditions, print No on a single line.

Otherwise, print a coloring that satisfies the conditions in the following format. Let $a_{i,j}$ denote the character representing the cell at the $i$-th row from the top and the $j$-th column from the left: each character $a_{i,j}$ should be . if the corresponding cell is white, and # if it is black.

Yes
a_{1,1}...a_{1,3N+1}
:
a_{3N+1,1}...a_{3N+1,3N+1}

If multiple valid colorings exist, any one of them will be accepted.

Example

Sample Input 1

1

Sample Output 1

No

Note

The following three output examples match the required output format for $N = 1$, but they do not satisfy the conditions and are therefore judged incorrect.

Yes
##..
#...
...#
..##

Yes
#.#.
...#
#.#.
.#..

Yes
...#
.#..
..#.
#...

In the first example, there exist black cells that share a side.

In the second example, the white cells do not form a single connected component.

In the third example, the condition on the number of black cells is not satisfied. Moreover, for example, starting from the black cell in the $2$-nd row from the top and the $2$-nd column from the left, even if you repeatedly move to black cells that share a corner, you cannot reach any black cell that is adjacent to the outer boundary of the grid.

It can be proven that when $N = 1$, no coloring satisfying the conditions exists.