Playing with a Divider

Dima found a special drafting tool on his father's desk, one that looks like a compass: a divider. A divider differs from an ordinary compass in that both of its legs end in needles, while an ordinary compass has a needle on one leg and a pencil lead on the other.

Dima took a sheet of graph paper, set some distance between the needles of the divider and fixed it firmly, and started poking the divider into the sheet of paper. Each time, Dima poked both needles of the divider into the sheet, and he always did so in such a way that the holes landed on the intersection points of the lines that divide the sheet into cells. Dima could insert the divider into the same hole several times.

In the evening, Dima's father found the sheet his son had been playing with and decided to find out what distance between the needles of the divider Dima could have set. All the father knows is the coordinates of the holes made by the needles of the divider. Help the father solve this problem.

The first line of the input file contains the number $n$, the number of holes ($2 \le n \le 1000$). The following $n$ lines contain two integers each, the coordinates of the holes. The coordinates do not exceed $10^4$ in absolute value.

On the first line of the output file, print $k$, the number of distinct distances Dima could have set between the needles of the divider. The following $k$ lines must contain one real number each: the distances in question. The distances must be printed in increasing order. Each number must be printed with an accuracy of at least $10^{-9}$.

It is guaranteed that there is at least one distance Dima could have set between the needles of the divider.