Spy Satellites

Martian spy satellites have taken a photo of an area on the dark side of the Moon. In this photo, only a lot of light points are seen in the dark. The Martian general suggests that the points are secret objects at lunar military bases. He wants to know how many bases there are on the Moon. The Martians suppose that the bases are seen at the photo as clusters of light points and satisfy the following property: the distance between any two objects at the same base is strictly less than the distance from any object at this base to any object at any other base. The area on the photo can be assumed flat, and the distance between objects having in the photo coordinates (A, B) and (С, D) is assumed to be

.

Input

The input contains several tests separated by an empty line. The first line of each test contains the number of objects on the photo N. The next N lines contain coordinates of the objects, two integers separated by a space per line. Absolute values of all coordinates do not exceed 10^4. After the last test there is an empty line and the number 0. The sum of all N in the input does not exceed 5000, the sum of all N^2 does not exceed 400000, and the sum of all N^3 does not exceed 250000000.

Output

For each test, you should output all possible numbers of bases on the photo in the form of a line of length N consisting of zeros and ones. For example, the line 110 means that there may be one or two bases on the photo, and the line 011 means that there may be two or three bases.