Bridge Across Islands#1048
Thousands of years ago, there was a small kingdom located in the middle of the Pacific Ocean. The kingdom consisted of two islands. Due to the effects of ocean currents, both islands became convex polygons. The king wanted to build a bridge to connect the two islands. To minimize the construction costs, the king asks you to find the minimal distance between the two islands.
Consists of several test cases. Each test case begins with two integers and (3 \leq n, m \leq 10000). Each of the next lines contains a pair of coordinates describing a vertex of the first convex polygon in order. The following lines contain pairs of coordinates describing the vertices of the second convex polygon in order. A line with n = m = 0 indicates the end of input. All coordinates are within the range .
For each test case, output the minimal distance between the islands with an error not exceeding .
Example 1