Subdividing a Land

Indigo Real-estate Company is 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 faces 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, at least 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 $1 \le n \le 10000$.

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.