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.util.Scanner;

public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int q = sc.nextInt();
		for (int i = 0; i < q; i++) {
			int xp0 = sc.nextInt();
			int yp0 = sc.nextInt();
			int xp1 = sc.nextInt();
			int yp1 = sc.nextInt();
			int xp2 = sc.nextInt();
			int yp2 = sc.nextInt();
			int xp3 = sc.nextInt();
			int yp3 = sc.nextInt();

			if (Geom.lineSegsIntersect(xp0, yp0, xp1, yp1, xp2, yp2, xp3, yp3)) {
				System.out.println("0");
			} else {
				double min = Double.MAX_VALUE;
				min = Math.min(min, Math.sqrt(Geom.ptLineSegDistSq(xp0, yp0, xp1, yp1, xp2, yp2)));
				min = Math.min(min, Math.sqrt(Geom.ptLineSegDistSq(xp0, yp0, xp1, yp1, xp3, yp3)));
				min = Math.min(min, Math.sqrt(Geom.ptLineSegDistSq(xp2, yp2, xp3, yp3, xp0, yp0)));
				min = Math.min(min, Math.sqrt(Geom.ptLineSegDistSq(xp2, yp2, xp3, yp3, xp1, yp1)));

				System.out.printf("%.9f\n", min);
			}
		}

		sc.close();
	}
	
	@SuppressWarnings("unused")
	private static class Geom {
		static int dot(int xa, int ya, int xb, int yb) {
			return xa * xb + ya * yb;
		}

		static int cross(int xa, int ya, int xb, int yb) {
			return xa * yb - xb * ya;
		}
		
		static int sumofsquare(int xa, int ya) {
			return xa * xa + ya * ya;
		}

		static boolean lineIntersect(int xa, int ya, int xb, int yb, int xc, int yc, int xd, int yd) {
			/*
			 * ??´???AB??¨??????CD??¨??????????????????????????????
			 * 
			 * |AB|==0 && |CD|==0
			 *     ???A==???C
			 * |AB|==0 && |CD|!=0
			 *     ACxAD==0 && AC.AD<0
			 * |AB|!=0
			 *     ABxAC*ABxAD<=0
			 */
			int xab = xb - xa;
			int yab = yb - ya;
			if (xab != 0 || yab != 0) {
				int xac = xc - xa;
				int yac = yc - ya;
				int xad = xd - xa;
				int yad = yd - ya;
				return (long)cross(xab, yab, xac, yac) * cross(xab, yab, xad, yad) <= 0;
			} else {
				int xcd = xd - xc;
				int ycd = yd - yc;
				if (xcd != 0 || ycd != 0) {
					int xac = xc - xa;
					int yac = yc - ya;
					int xad = xd - xa;
					int yad = yd - ya;
					return cross(xac, yac, xad, yad) == 0 && dot(xac, yac, xad, yad) < 0;
				} else {
					return xa == xc && ya == yc;
				}
			}
		}

		static boolean lineSegsIntersect(int xa, int ya, int xb, int yb, int xc, int yc, int xd, int yd) {
			/*
			 * ??????AB??¨??????CD??¨??????????????????????????????
			 * 
			 * |AB|==0 && |CD|==0
			 *     ???A==???C
			 * |AB|==0 && |CD|!=0
			 *     ACxAD==0 && AC.AD<0
			 * |AB|!=0 && |CD|==0
			 *     CAxCB==0 && CA.CB<0
			 * |AB|!=0 && |CD|!=0
			 *     ABxCD==0
			 *         ACxAD==0 && (AB.AC>=0 || AB.AD>=0) && (BA.BC>=0 || BA.BD>=0)
			 *     ABxCD!=0
			 *         ABxAC*ABxAD<=0 && CDxCA*CDxCB<=0
			 */
			int xab = xb - xa;
			int yab = yb - ya;
			int xcd = xd - xc;
			int ycd = yd - yc;
			if ((xab != 0 || yab != 0) && (xcd != 0 || ycd != 0)) {
				int xac = xc - xa;
				int yac = yc - ya;
				int xad = xd - xa;
				int yad = yd - ya;
				if (cross(xab, yab, xcd, ycd) != 0) {
					int xca = -xac;
					int yca = -yac;
					int xcb = xb - xc;
					int ycb = yb - yc;
					return ((long)cross(xab, yab, xac, yac) * cross(xab, yab, xad, yad) <= 0)
							&& ((long)cross(xcd, ycd, xca, yca) * cross(xcd, ycd, xcb, ycb) <= 0);
				} else {
					int xba = -xab;
					int yba = -yab;
					int xbc = xc - xb;
					int ybc = yc - yb;
					int xbd = xd - xb;
					int ybd = yd - yb;
					return cross(xac, yac, xad, yad) == 0
							&& (dot(xab, yab, xac, yac) >= 0 || dot(xab, yab, xad, yad) >= 0)
							&& (dot(xba, yba, xbc, ybc) >= 0 || dot(xba, yba, xbd, ybd) >= 0);
				}
			} else if (xab != 0 || yab != 0) {
				int xca = xa - xc;
				int yca = ya - yc;
				int xcb = xb - xc;
				int ycb = yb - yc;
				return cross(xca, yca, xcb, ycb) == 0 && dot(xca, yca, xcb, ycb) < 0;
			} else {
				if (xcd != 0 || ycd != 0) {
					int xac = xc - xa;
					int yac = yc - ya;
					int xad = xd - xa;
					int yad = yd - ya;
					return cross(xac, yac, xad, yad) == 0 && dot(xac, yac, xad, yad) < 0;
				} else {
					return xa == xc && ya == yc;
				}
			}
		}

		static double ptLineSegDistSq(int xa, int ya, int xb, int yb, int xc, int yc) {
			/*
			 * ??????AB??¨???C??¨????????¢
			 * 
			 * |AB|==0
			 *     |AC|^2
			 * |AB|!=0 && AB.AC<=0
			 *     |AC|^2
			 * |AB|!=0 && BA.BC<=0
			 *     |BC|^2
			 * |AB|!=0 && AB.AC>0 && BA.BC>0
			 *     |ABxAC|/|AB|
			 */
			int xab = xb - xa;
			int yab = yb - ya;
			int xac = xc - xa;
			int yac = yc - ya;
			int xbc = xc - xb;
			int ybc = yc - yb;
			if (dot(xab, yab, xac, yac) <= 0) {
				return sumofsquare(xac, yac);
			} else if (dot(-xab, -yab, xbc, ybc) <= 0) {
				return sumofsquare(xbc, ybc);
			} else {
				long tmp = cross(xab, yab, xac, yac);
				return (double)(tmp * tmp) / sumofsquare(xab, yab);
			}
		}
	}
}