## Example 6.3

## Bee Breeding

Professor B. Heif is conducting experiments with a species of South
American bees that he found during an expedition to the Brazilian rain
forest. The honey produced by these bees is of superior quality compared
to the honey from European and North American honey bees. Unfortunately,
the bees do not breed well in captivity. Professor Heif thinks the reason
is that the placement of the different maggots (for workers, queens, etc.)
within the honeycomb depends on environmental conditions, which are
different in his laboratory and the rain forest.

As a first step to validate his theory, Professor Heif wants to quantify
the difference in maggot placement. For this he measures the distance
between the cells of the comb into which the maggots are placed. To this
end, the professor has labeled the cells by marking an arbitrary cell as
number 1, and then labeling the remaining cells in a clockwise fashion, as
shown in the following figure.

__ __ __ __
__/ \__/ \__/ \__/ \__
__/ \__/ \__/53\__/ \__/ \__
/ \__/ \__/52\__/54\__/ \__/ \
\__/ \__/51\__/31\__/55\__/ \__/
/ \__/50\__/30\__/32\__/56\__/ \
\__/49\__/29\__/15\__/33\__/57\__/
/ \__/28\__/14\__/16\__/34\__/ \
\__/48\__/13\__/ 5\__/17\__/58\__/
/..\__/27\__/ 4\__/ 6\__/35\__/ \
\__/47\__/12\__/ 1\__/18\__/59\__/
/..\__/26\__/ 3\__/ 7\__/36\__/ \
\__/46\__/11\__/ 2\__/19\__/60\__/
/..\__/25\__/10\__/ 8\__/37\__/ \
\__/45\__/24\__/ 9\__/20\__/61\__/
/..\__/44\__/23\__/21\__/38\__/ \
\__/70\__/43\__/22\__/39\__/62\__/
/ \__/69\__/42\__/40\__/63\__/ \
\__/ \__/68\__/41\__/64\__/ \__/
/ \__/ \__/67\__/65\__/ \__/ \
\__/ \__/ \__/66\__/ \__/ \__/
\__/ \__/ \__/ \__/ \__/
\__/ \__/ \__/ \__/

For example, two maggots in cells 19 and 30 are 5 cells apart. One of the
shortest paths connecting the two cells is via the cells 19 - 7 - 6 - 5 -
15 - 30, so you must move five times to adjacent cells to get from 19 to
30.
Professor Heif needs your help to write a program that computes the
distance, defined as the number of cells in a shortest path, between any
pair of cells.

### Input

The input consists of several lines, each containing two integers *a*
and *b* (*a*,*b* <= 10000), denoting numbers of cells.
The integers are always positive, except in the last line where
*a*=*b*=0 holds. This last line terminates the input and should
not be processed.

### Output

For each pair of numbers (*a*,*b*) in the input file, output the
distance between the cells labeled *a* and *b*. The distance is
the minimum number of moves to get from *a* to *b*.

Sample Input |
Output for the Sample Input |

`19 30` `0 0` |
`The distance between cells 19 and 30 is 5.` |