time limit per test: 0.25 sec.
memory limit per test: 4096 KB

input: standard
output: standard

Little known abstract artist Madzinsky-Kalevich painted one more masterpiece. He painted N arcs of circles on the rectangular sheet of paper. Radiuses of all arcs do not exceed 10^3. To increase popularity of the masterpiece he decided to include the quantity of arc crosses in the title of the picture. Your task is to help the artist.

The first line of the input contains integer N (1 <= N <= 50). The following N lines contain the descriptions of arcs. Each description is the sequence of three points. The first two are the end points of arc and the third is a intermediate point. All coordinates are integer numbers with the absolute values not greater than 1000.

Write the amount of different cross points of arcs M to the first line of the output. The following M lines should contain coordinates of crosses in ascending order of x-coordinates. If tie, output coordinates in order of increasing y-coordinates. The computed coordinates should be exact to three digits after the decimal point. If there is infinity number of crosses, print 'Infinity' (quotes added for clarity) on the single line. It is guaranteed that in the case of finite number of crosses the distance between any two different crosses will be not less than 0.005.

Input

3
7 4 7 -4 3 0
2 2 6 2 4 0
0 4 0 -4 4 0