*Not an official ACM page*

[1995 Regional problem set
| My ACM problem archive
| my home page]

# Problem G -- Roman Digititis -- Filename `ROMAN`

Many persons are familiar with the Roman numerals for relatively
small numbers. The symbols "i", "v", "x", "l", and "c" represent the
decimal values 1, 5, 10, 50, and 100 respectively. To represent other
values, these symbols, and multiples where necessary, are concatenated,
with the smaller-valued symbols written further to the right. For
example, the number 3 is represented as "iii", and the value 73 is
represented as "lxxiii". The exceptions to this rule occur for numbers
having units values of 4 or 9, and for tens values of 40 or 90. For
these cases, the Roman numeral representations are "iv" (4), "ix" (9),
"xl" (40), and "xc" (90). So the Roman numeral representations for 24,
39, 44, 49, and 94 are "xxiv", "xxxix", "xliv", "xlix", and "xciv",
respectively.
The preface of many books has pages numbered with Roman
numerals, starting with "i" for the first page of the preface, and
continuing in sequence. Assume books with pages having 100 or fewer
pages of preface. How many "i", "v", "x", "l", and "c" characters are
required to number the pages in the preface? For example, in a five
page preface weÆll use the Roman numerals "i", "ii", "iii", "iv", and
"v", meaning we need 7 "i" characters and 2 "v" characters.
### Input

The input will consist of a sequence of integers in the
range 1 to 100, terminated by a zero. For each such integer, except
the final zero, determine the number of different types of characters
needed to number the prefix pages with Roman numerals.
### Output

For each integer in the input, write one line
containing the input integer and the number of characters of each type
required. The examples shown below illustrate an acceptable format.
Example Input

1
2
20
99
0

### Expected Output

1: 1 i, 0 v, 0 x, 0 l, 0 c
2: 3 i, 0 v, 0 x, 0 l, 0 c
20: 28 i, 10 v, 14 x, 0 l, 0 c
99: 140 i, 50 v, 150 x, 50 l, 10 c

This page maintained by
Ed Karrels.

Last updated September 20, 1999