Beehives

Bill’s hives all exist on a plane, and he knows some distance d such that two hives within $d$ of each other will fight, and both will produce sour honey. If a hive does not fight with any other hives, it produces sweet honey. Given $d$ and the positions of $N$ beehives, output how many hives will produce sweet honey and how many hives will produce sour honey.

Input

Input will be provided on multiple lines. There may be up to $10$ test cases in the input. Each case will begin with a floating point number $d$ ($0 < d < 1000$), the distance within which hives will fight, followed by an integer $N$ ($1 \le N \le 100$), the number of hives in that case. The next $N$ lines will contain two floating point numbers separated by a single space, $x$ and $y$ ($-1000 \le x,y \le 1000$), which give the position of each hive. No two hives will be at the exact same location. Input will be terminated by a line containing the string 0.0 0.

Output

For each case output a line of the following form: a sour, b sweet where $a$ and $b$ are the number of hives producing sour and sweet honey, respectively.

10.0 3
3.0 3.0
3.5 4.5
20.0 20.0
5.0 4
2.0 1.0
2.0 4.0
2.0 8.0
2.0 12.0
0.0 0

2 sour, 1 sweet
4 sour, 0 sweet