A board consists of $n \cdot n$ squares arranged in $n$ rows and $n$ columns, numbered from $1$ to $n$. The square in the $i$-th row and $j$-th column has coordinates $(i, j)$. We want to move from the square in the top-left corner (with coordinates $(1, 1)$) to the square in the bottom-right corner (with coordinates $(n, n)$). Some squares are blocked. We can only move through unblocked squares to the right and down; that is, from square $(i, j)$ we can move to square $(i, j+1)$ or $(i+1, j)$, provided they are not blocked.

Some boards can be traversed in only one way, others in many. Given a number $K$, design a board with dimensions no larger than $100$ for which the number of different paths is exactly $K$.

Input

The first line of input contains a single integer $K$ ($0 \le K$).

Output

In the first line of output, print a single integer $n$ ($1 \le n \le 100$) representing the size of the board. In the next $n$ lines, print $n$-character strings consisting of the characters . (unblocked square) and # (blocked square); the $j$-th character in the $i$-th row should describe the square $(i, j)$.

For the limits given in the problem statement, an answer always exists. If there is more than one, your program may output any of them.

Examples

Input 1

6

Output 1

4
...#
....
##..
###.

Subtasks

The test set is divided into the following subtasks. Tests for each subtask consist of one or more separate test groups.