Indigo Real-estate Company is now planning to develop a new housing complex. The entire complex is a square,
all of whose edges are equally *a* meters. The complex contains *n* subdivided blocks, each of which is a *b*-meter
square. Here both *a* and *b* are positive integers.

However the project is facing a big problem. In this country, a percentage limit applies to the subdivision of a
land, under the pretext of environmental protection. When developing a complex, the total area of the subdivided
blocks must not exceed 50% of the area of the complex; in other words, more than or equal to 50% of the newly
developed housing complex must be kept for green space. As a business, a green space exceeding 50% of the
total area is a *dead space*. The primary concern of the project is to minimize it.

Of course purchasing and developing a land costs in proportion to its area, so the company also wants to minimize
the land area to develop as the secondary concern. You, a member of the project, were assigned this task, but can
no longer stand struggling against the problem with your pencil and paper. So you decided to write a program to
find the pair of minimum *a* and *b* among those which produce the minimum dead space for given *n*.

The input consists of multiple test cases. Each test case comes in a line, which contains an integer *n*. You may
assume 1 ≤ *n* ≤ 10000.

The end of input is indicated by a line containing a single zero. This line is not a part of the input and should not be processed.

For each test case, output the case number starting from 1 and the pair of minimum *a* and *b* as in the sample
output.

You may assume both *a* and *b* fit into 64-bit signed integers.

1 2 0

Case 1: 3 2 Case 2: 2 1

Source: ACM-ICPC Japan Alumni Group Practice Contest
, for World Finals, Tokyo, Japan, 2008-02-23

http://acm-icpc.aitea.net/

http://acm-icpc.aitea.net/