Picture Perfect

Roy has a stack of student yearbook photos. He wants to lay them on a flat surface edge to edge to form a completely filled rectangle whose perimeter is as small as possible. Every photo must be fully visible, and each photo is a square measuring $1 \times 1$ unit.

For example, $12$ photos can be arranged as follows, where each photo is drawn as an X:

XXXX
XXXX
XXXX

They could also be turned the other way:

XXX
XXX
XXX
XXX

Both arrangements are completely filled rectangles with the same perimeter, $14$ units.

For a given number of photos $C$, find the filled rectangle formed by placing all $C$ photos edge to edge that has the smallest possible perimeter, and report both that perimeter and the rectangle's dimensions.

The input contains several test cases. Each test case is a single positive integer $C$ ($1 \le C < 65,000$), the number of photos to lay out. The input ends with a line containing $0$, which must not be processed.

For each value of $C$, print one line in exactly this format:

Minimum perimeter is P with dimensions W x H

Here $P$ is the smallest possible perimeter, and $W$ and $H$ are the side lengths of the rectangle that achieves it, with $W \le H$.