Problem: For given two segments s1 and s2, print the distance between them.

s1 is formed by end points p0 and p1, and s2 is formed by end points p2 and p3.

Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xpi, ypi ≤ 10000
* p0 ≠ p1 and p2 ≠ p3.

Input

The entire input looks like:


q (the number of queries)
1st query
2nd query
...
qth query


Each query consists of integer coordinates of end points of s1 and s2 in the following format:


xp0 yp0 xp1 yp1 xp2 yp2 xp3 yp3


Output

For each query, print the distance. The output values should be in a decimal fraction with an error less than 0.00000001.

Example

Input

3
0 0 1 0 0 1 1 1
0 0 1 0 2 1 1 2
-1 0 1 0 0 1 0 -1


Output

1.0000000000
1.4142135624
0.0000000000

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;

public class Main {
	private static FastScanner sc = new FastScanner();

	public static void main(String[] args) {
		int q = sc.nextInt();
		StringBuilder ans = new StringBuilder();
		for(int i=0; i<q; i++) {
			double mind = Double.MAX_VALUE;
			Point p1 = new Point(sc.nextDouble(), sc.nextDouble());
			Point p2 = new Point(sc.nextDouble(), sc.nextDouble());
			Point p3 = new Point(sc.nextDouble(), sc.nextDouble());
			Point p4 = new Point(sc.nextDouble(), sc.nextDouble());
			
			if(checkCross(p1, p2, p3, p4)) {
				ans.append(0);
				ans.append("\n");
				continue;
			}
			
			Point per1 = perpLine(p1, p2, p3);
			if(per1.x >= Math.min(p1.x, p2.x) && per1.x <= Math.max(p1.x, p2.x)
					&& per1.y >= Math.min(p1.y, p2.y) && per1.y <= Math.max(p1.y, p2.y)) {
				if(distance(per1, p3) < mind) {
					mind = distance(per1, p3);
				}
			} else {
				if(distance(p1, p3) < mind) {
					mind = distance(p1, p3);
				}
				if(distance(p2, p3) < mind) {
					mind = distance(p2, p3);
				}
			}
			
			Point per2 = perpLine(p1, p2, p4);
			if(per2.x >= Math.min(p1.x, p2.x) && per2.x <= Math.max(p1.x, p2.x)
					&& per2.y >= Math.min(p1.y, p2.y) && per2.y <= Math.max(p1.y, p2.y)) {
				if(distance(per2, p4) < mind) {
					mind = distance(per2, p4);
				}
			} else {
				if(distance(p1, p4) < mind) {
					mind = distance(p1, p4);
				}
				if(distance(p2, p4) < mind) {
					mind = distance(p2, p4);
				}
			}
			
			Point per3 = perpLine(p3, p4, p1);
			if(per3.x >= Math.min(p3.x, p4.x) && per3.x <= Math.max(p3.x, p4.x)
					&& per3.y >= Math.min(p3.y, p4.y) && per3.y <= Math.max(p3.y, p4.y)) {
				if(distance(per3, p1) < mind) {
					mind = distance(per3, p1);
				}
			} else {
				if(distance(p1, p3) < mind) {
					mind = distance(p1, p3);
				}
				if(distance(p1, p4) < mind) {
					mind = distance(p1, p4);
				}
			}
			
			Point per4 = perpLine(p3, p4, p2);
			if(per4.x >= Math.min(p3.x, p4.x) && per4.x <= Math.max(p3.x, p4.x)
					&& per4.y >= Math.min(p3.y, p4.y) && per4.y <= Math.max(p3.y, p4.y)) {
				if(distance(per4, p2) < mind) {
					mind = distance(per4, p2);
				}
			} else {
				if(distance(p2, p3) < mind) {
					mind = distance(p2, p3);
				}
				if(distance(p2, p4) < mind) {
					mind = distance(p2, p4);
				}
			}
			
			ans.append(mind);
			ans.append("\n");
		}
		System.out.print(ans);
	}
	
	static Point perpLine(Point p1, Point p2, Point p) {
		double a = (p2.y - p1.y) / (p2.x - p1.x);
		double b = p1.y - a * p1.x;
		double x = 0;
		double y = 0;
		if(p1.y == p2.y) {
			x = p.x;
			y = p1.y;
		} else if(p1.x == p2.x) {
			x = p1.x;
			y = p.y;
		} else {
			x = (p.y + p.x / a - b) / (a + 1 / a);
			y = p.y + p.x / a - x / a;
		}
		
		return new Point(x, y);
	}
	
	static double distance(Point p1, Point p2) {
		return Math.sqrt((p2.x-p1.x)*(p2.x-p1.x) + (p2.y-p1.y)*(p2.y-p1.y));
	}
	
	static boolean checkCross(Point p1, Point p2, Point p3, Point p4) {
		if(p1.x >= p2.x) {
			if((p1.x<p3.x && p1.x<p4.x) || (p2.x>p3.x && p2.x>p4.x)) {
				return false;
			}
		} else {
			if((p2.x<p3.x && p2.x<p4.x) || (p1.x>p3.x && p1.x>p4.x)) {
				return false;
			}
		}
		
		if(p1.y >= p2.y) {
			if((p1.y<p3.y && p1.y<p4.y) || (p2.y>p3.y && p2.y>p4.y)) {
				return false;
			}
		} else {
			if((p2.y<p3.y && p2.y<p4.y) || (p1.y>p3.y && p1.y>p4.y)) {
				return false;
			}
		}
		
		if(((p1.x-p2.x)*(p3.y-p1.y)+(p1.y-p2.y)*(p1.x-p3.x))*((p1.x-p2.x)*(p4.y-p1.y)+(p1.y-p2.y)*(p1.x-p4.x))>0) {
			return false;
		}
		if(((p3.x-p4.x)*(p1.y-p3.y)+(p3.y-p4.y)*(p3.x-p1.x))*((p3.x-p4.x)*(p2.y-p3.y)+(p3.y-p4.y)*(p3.x-p2.x))>0) {
			return false;
		}
		
		return true;
	}

	static class Point {
		double x;
		double y;
		Point(double x, double y) {
			this.x = x;
			this.y = y;
		}
	}
	
	static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if(ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch(IOException e) {
                    e.printStackTrace();
                }
                if(buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
        public boolean hasNext() { skipUnprintable(); return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}