Problem Statement

There is an $N\times N$ grid with horizontal rows and vertical columns, where all squares are initially painted white. Let (i,j) denote the square at the i-th row and j-th column.
Takahashi has integers A and B, which are between 1 and N (inclusive). He will do the following operations.

• For every integer k such that $\max(1-A,1-B)\leq k\leq \min(N-A,N-B), paint (A+k,B+k)$ black.
• For every integer k such that $\max(1-A,B-N)\leq k\leq \min(N-A,B-1), paint (A+k,B-k)$ black.

In the grid after these operations, find the color of each square (i,j) such that $P\leq i\leq Q$ and $R\leq j\leq S$.

Input

Input is given from Standard Input in the following format:
N A B
P Q R S

Output

Print Q-P+1 lines.
Each line should contain a string of length S-R+1 consisting of # and ..
The j-th character of the string in the i-th line should be # to represent that (P+i-1, R+j-1) is painted black, and . to represent that (P+i-1, R+j-1) is white.

Constraints

• $1 \leq N \leq 10^{18}$
• $1 \leq A \leq N$
• $1 \leq B \leq N$
• $1 \leq P \leq Q \leq N$
• $1 \leq R \leq S \leq N$
• $(Q-P+1)\times(S-R+1)\leq 3\times 10^5$
• All values in input are integers.

Sample Input 1

5 3 2
1 5 1 5

Sample Output 1

...#.

.#..

.#...

.#..

...#.

The first operation paints the four squares (2,1), (3,2), (4,3), (5,4) black, and the second paints the four squares (4,1), (3,2), (2,3), (1,4) black.
Thus, the above output should be printed, since P=1, Q=5, R=1, S=5.

Sample Input 2

5 3 3
4 5 2 5

Sample Output 2

.#.

...#

The operations paint the nine squares (1,1), (1,5), (2,2), (2,4), (3,3), (4,2), (4,4), (5,1), (5,5).
Thus, the above output should be printed, since P=4, Q=5, R=2, S=5.

Sample Input 3

1000000000000000000 999999999999999999 999999999999999999
999999999999999998 1000000000000000000 999999999999999998 1000000000000000000

Sample Output 3

.

.#.

.

Note that the input may not fit into a 32-bit integer type.

见题面 Input 部分

见题面 Output 部分