Mixed Numbers
A mixed fraction is defined recursively as follows:
- A real value is a simple mixed fraction. For simplicity, we only consider one digit positive integer numbers greater than zero (digits 1 ... 9).
- If a is a real value (which is again assumed as an integer between 1 and 9), and b and c are two mixed fractions,
b
a- is a mixed fraction which is equal to a + b/c
c - Sum of a number of mixed fractions is also a mixed fraction.
One can draw a view of a mixed fraction using ASCII characters as described below:
- A simple mixed fraction can be drawn using one digit character.
b
The mixed fraction a- will be drawn using a digit showing a , and a horizontal line that starts
c
immediately after the letter representing a (in the same row) using '-' characters. b and c are drawn recursively above and below the horizontal line respectively, such that their figures do not exceed the line from left nor right.- Sum of mixed fractions is represented by drawing the mixed fractions and inserting a '+' character between each consequence pair such that the '+' character and the first character of the next and the previous mixed fractions make a horizontal line.
We want you to write a program to calculate the value of a mixed fraction from its figure.
Some 90 degree clockwise rotated figures of a number of mixed fractions are given in the input file. In the first line of each rotated mixed fraction n < 300 and m < 15000 , the length and the width of the figure, are written. In the next m lines the figure i s described ('-' is replaced with '|'). Note that each line will consists of exactly n characters so any number of spaces may be used in the shape, but anyway, the shape of the figure satisfies description explained above.
The input ends with a line containing two zeroes.
For each test case write its value in a separate line. Your answer must be rounded to two digits after decimal point and the output must contain exactly two digits after the decimal point.
8 6 1 2 | 2 4|2| 4|3 | + 1 0 0
3.10
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