Tiles are aligned in NN horizontal rows and NN vertical columns. Each tile has a grid with AA horizontal rows and BB vertical columns. On the whole, the tiles form a grid XX with (A\times N)(A×N) horizontal rows and (B\times N)(B×N) vertical columns. For 1\leq i,j \leq N1≤i,j≤N, Tile (i,j)(i,j) denotes the tile at the ii-th row from the top and the jj-th column from the left. Each square of XX is painted as follows.
Each tile is either a white tile or a black tile.
Every square in a white tile is painted white; every square in a black tile is painted black.
Tile (1,1)(1,1) is a white tile.
Two tiles sharing a side have different colors. Here, Tile (a,b)(a,b) and Tile (c,d)(c,d) are said to be sharing a side if and only if |a-c|+|b-d|=1∣a−c∣+∣b−d∣=1 (where |x|∣x∣ denotes the absolute value of xx).
Print the grid XX in the format specified in the Output section.
Constraints
1 \leq N,A,B \leq 101≤N,A,B≤10
All values in input are integers.
Input
Input is given from Standard Input in the following format:
NNAABB
Output
Print (A\times N)(A×N) strings S_1,\ldots,S_{A\times N}S1,…,SA×N that satisfy the following condition, with newlines in between.
Each of S_1,\ldots,S_{A\times N}S1,…,SA×N is a string of length (B\times N)(B×N) consisting of . and #.
For each ii and jj(1 \leq i \leq A\times N,1 \leq j \leq B\times N)(1≤i≤A×N,1≤j≤B×N), the jj-th character of S_iSi is . if the square at the ii-th row from the top and jj-th column from the left in grid XX is painted white; the character is # if the square is painted black.