Graphing calculators are devices capable of plotting graphs, given a user-defined function. Given a function ~f(x)~, the view window (domain and range), and an ~x~-increment (described later), replicate the functionality of a graphing calculator by plotting the graph in the output.

For every coordinate in the domain and range, graph layout will consist as follows:

• Empty space will be represented by a period (.)
• The origin (0, 0) will be represented as a +
• X and Y axis lines will be represented by - and |, respectively
• The actual points where the graph exists will be represented by a #

For example, the function ~f(x) = x + 3~ would look like:

.....|...#.
.....|..#..
.....|.#...
.....|#....
.....#.....
....#|.....
...#.|.....
--#--+-----
.#...|.....
#....|.....

To get full points, your program must also allow for ~x~-increment specification. An ~x~-increment defines the difference between every value of ~x~ in ~f(x)~, essentially signifying the precision of the output of the graphing program. For example, with an ~x~-increment of ~1~, your program should only find the value of ~f(x)~ for every integer ~x~, such as ~-1~, ~0~, ~1~, and so on. Plotting ~f(x) = x^2~ with an ~x~-increment of 1 would produce such result:

..........|..........
.......#..|..#.......
..........|..........
..........|..........
..........|..........
..........|..........
........#.|.#........
..........|..........
..........|..........
.........#|#.........
----------#----------
..........|..........
..........|..........

where only the rounded result of ~f(x)~ for every integer ~x~ is displayed.

However, with an ~x~-increment of ~0.01~, ~f(x) = x^2~ really begins to take shape:

.......#..|..#.......
.......#..|..#.......
.......#..|..#.......
.......#..|..#.......
.......##.|.##.......
........#.|.#........
........#.|.#........
........#.|.#........
........##|##........
.........#|#.........
---------###---------
..........|..........
..........|..........

Note that you must round your output.

Input Specification

The first line will contain a string representing ~f(x)~. The string is guaranteed to only have the following possibly space-separated characters: x, +, -, *, /, ^, (, ), ., and the digits from 0-9. Note that multiplication will be represented with the *, so 2x (instead of 2 * x) will not be valid input. However, placing a negative sign before a number is valid and should be accounted for (e.g. -x).

The next line of input will contain the integers ~L~, ~R~, ~B~, ~T~, and the number ~I~. The first four (~L~, ~R~, ~B~, ~T~) represent the domain and range of the graph, or the left, right, bottom, and top values of the viewing window, where ~L \le x \le R~ and ~B \le f(x) \le T~, and ~0 \le R-L, T-B \le 100~. ~I~ ~(0.01 \le I \le 1)~ specifies the ~x~-interval of ~f(x)~. For 75% of the points, ~I = 1~.

Keep in mind that you must obey proper operation order. For 25% of the points, the input will not contain any brackets.

Output Specification

Graph ~f(x)~ using the appropriate view port.

Sample Input 1

x - 5
-10 10 -10 10 1

Sample Output 1

..........|..........
..........|..........
..........|..........
..........|..........
..........|..........
..........|.........#
..........|........#.
..........|.......#..
..........|......#...
..........|.....#....
----------+----#-----
..........|...#......
..........|..#.......
..........|.#........
..........|#.........
..........#..........
.........#|..........
........#.|..........
.......#..|..........
......#...|..........
.....#....|..........

Sample Input 2

(x - 5) * (x + 1)
-20 20 -15 15 1

Sample Output 2

....................|....................
....................|....................
....................|....................
....................|....................
....................|....................
....................|....................
....................|....................
....................|....................
..................#.|.....#..............
....................|....................
....................|....................
....................|....................
....................|....................
....................|....................
....................|....................
-------------------#+----#---------------
....................|....................
....................|....................
....................|....................
....................|....................
....................#...#................
....................|....................
....................|....................
....................|#.#.................
....................|.#..................
....................|....................
....................|....................
....................|....................
....................|....................
....................|....................
....................|....................

Sample Input 3

(x-5)*(x-3)/(x-5)
-10 10 -10 10 0.01

Sample Output 3

..........|..........
..........|..........
..........|..........
..........|.........#
..........|........#.
..........|.......#..
..........|......#...
..........|.....#....
..........|....#.....
..........|...#......
----------+--#-------
..........|.#........
..........|#.........
..........#..........
.........#|..........
........#.|..........
.......#..|..........
......#...|..........
.....#....|..........
....#.....|..........
...#......|..........

Sample Input 4

x^3/100
-10 10 -10 10 0.01

Sample Output 4

..........|.........#
..........|........##
..........|........#.
..........|........#.
..........|.......##.
..........|.......#..
..........|......##..
..........|.....##...
..........|....##....
..........|...##.....
------#########------
.....##...|..........
....##....|..........
...##.....|..........
..##......|..........
..#.......|..........
.##.......|..........
.#........|..........
.#........|..........
##........|..........
#.........|..........