using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
static string InputPattern = "InputX";
static List<string> GetInputList()
{
var WillReturn = new List<string>();
if (InputPattern == "Input1") {
WillReturn.Add("3 2 1");
WillReturn.Add("1 3 2 1");
WillReturn.Add("0 2 0 0");
WillReturn.Add("3 0 2 0");
//6.44317475868633722080
}
else if (InputPattern == "Input2") {
WillReturn.Add("2 1 1");
WillReturn.Add("0 0 10 10");
WillReturn.Add("0 2 2 0");
//20.97056274847714058517
}
else if (InputPattern == "Input3") {
WillReturn.Add("6 3 2");
WillReturn.Add("-1000 -1000 1000 1000");
WillReturn.Add("1000 -1000 -1000 1000");
WillReturn.Add("-1000 -1000 1000 1000");
WillReturn.Add("1000 -1000 -1000 1000");
WillReturn.Add("1000 1000 -1000 -1000");
WillReturn.Add("-1000 1000 1000 -1000");
//9623.35256169626864153344
}
else if (InputPattern == "Input4") {
WillReturn.Add("6 10 8");
WillReturn.Add("1000 1000 -1000 -1000");
WillReturn.Add("1000 -1000 -1000 -1000");
WillReturn.Add("-1000 1000 1000 1000");
WillReturn.Add("-1000 1000 -1000 -1000");
WillReturn.Add("1000 1000 1000 -1000");
WillReturn.Add("1000 -1000 -1000 1000");
//2048.52813742385702910909
}
else {
string wkStr;
while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
}
return WillReturn;
}
struct SenbunDef
{
internal double StaX;
internal double StaY;
internal double EndX;
internal double EndY;
}
static List<SenbunDef> mSenbunList = new List<SenbunDef>();
struct PointDef
{
internal double X;
internal double Y;
}
static double mS;
static double mT;
static void Main()
{
List<string> InputList = GetInputList();
double[] wkArr = { };
Action<string> SplitAct = pStr =>
wkArr = pStr.Split(' ').Select(pX => double.Parse(pX)).ToArray();
SplitAct(InputList[0]);
mS = wkArr[1];
mT = wkArr[2];
foreach (string EachStr in InputList.Skip(1)) {
SplitAct(EachStr);
SenbunDef WillAdd;
WillAdd.StaX = wkArr[0];
WillAdd.StaY = wkArr[1];
WillAdd.EndX = wkArr[2];
WillAdd.EndY = wkArr[3];
mSenbunList.Add(WillAdd);
}
var SenbunIndList = new List<int>();
for (int I = 0; I <= mSenbunList.Count - 1; I++) {
SenbunIndList.Add(I);
}
var tmp1 = RubyPatternClass<int>.Permutation(SenbunIndList, SenbunIndList.Count).ToList();
var BaseList = new List<int>();
BaseList.Add(0);
BaseList.Add(1);
var tmp2 = RubyPatternClass<int>.RepeatedPermutation(BaseList, SenbunIndList.Count).ToList();
double Answer = double.MaxValue;
foreach (int[] EachArr1 in tmp1) {
foreach (int[] EachArr2 in tmp2) {
double CurrAnswer = DeriveAnswer(EachArr1, EachArr2);
Answer = Math.Min(Answer, CurrAnswer);
}
}
Console.WriteLine(Answer);
}
// 配列2つを引数として解候補を返す
static double DeriveAnswer(int[] pArr1, int[] pArr2)
{
int UB = pArr1.GetUpperBound(0);
var PointList = new List<PointDef>();
PointDef WillAdd;
WillAdd.X = 0;
WillAdd.Y = 0;
PointList.Add(WillAdd);
for (int I = 0; I <= UB; I++) {
PointDef WillAdd1;
WillAdd1.X = mSenbunList[pArr1[I]].StaX;
WillAdd1.Y = mSenbunList[pArr1[I]].StaY;
PointDef WillAdd2;
WillAdd2.X = mSenbunList[pArr1[I]].EndX;
WillAdd2.Y = mSenbunList[pArr1[I]].EndY;
if (pArr2[I] == 0) {
PointList.Add(WillAdd1);
PointList.Add(WillAdd2);
}
else {
PointList.Add(WillAdd2);
PointList.Add(WillAdd1);
}
}
double Answer = 0;
for (int I = 1; I <= PointList.Count - 1; I++) {
double StaX = PointList[I - 1].X;
double StaY = PointList[I - 1].Y;
double EndX = PointList[I].X;
double EndY = PointList[I].Y;
double Distance = DeriveDistance(StaX, StaY, EndX, EndY);
if (I % 2 == 1) {
Answer += Distance / mS;
}
else {
Answer += Distance / mT;
}
}
return Answer;
}
// ベクトル2つの距離を返す
static double DeriveDistance(double pStaX, double pStaY, double pEndX, double pEndY)
{
double wkDiff1 = pStaX - pEndX;
double wkDiff2 = pStaY - pEndY;
return Math.Sqrt(wkDiff1 * wkDiff1 + wkDiff2 * wkDiff2);
}
}
#region RubyPatternClass
// Rubyの場合の数
internal static class RubyPatternClass<Type>
{
// 順列を返す
private struct JyoutaiDef_Permutation
{
internal List<int> SelectedIndList;
}
internal static IEnumerable<Type[]> Permutation(IEnumerable<Type> pEnum, int pR)
{
if (pR == 0) yield break;
Type[] pArr = pEnum.ToArray();
if (pArr.Length < pR) yield break;
var Stk = new Stack<JyoutaiDef_Permutation>();
JyoutaiDef_Permutation WillPush;
for (int I = pArr.GetUpperBound(0); 0 <= I; I--) {
WillPush.SelectedIndList = new List<int>() { I };
Stk.Push(WillPush);
}
while (Stk.Count > 0) {
JyoutaiDef_Permutation Popped = Stk.Pop();
// クリア判定
if (Popped.SelectedIndList.Count == pR) {
var WillReturn = new List<Type>();
Popped.SelectedIndList.ForEach(X => WillReturn.Add(pArr[X]));
yield return WillReturn.ToArray();
continue;
}
for (int I = pArr.GetUpperBound(0); 0 <= I; I--) {
if (Popped.SelectedIndList.Contains(I)) continue;
WillPush.SelectedIndList = new List<int>(Popped.SelectedIndList) { I };
Stk.Push(WillPush);
}
}
}
// 重複順列を返す
private struct JyoutaiDef_RepeatedPermutation
{
internal List<int> SelectedIndList;
}
internal static IEnumerable<Type[]> RepeatedPermutation(IEnumerable<Type> pEnum, int pR)
{
if (pR == 0) yield break;
Type[] pArr = pEnum.ToArray();
var Stk = new Stack<JyoutaiDef_RepeatedPermutation>();
JyoutaiDef_RepeatedPermutation WillPush;
for (int I = pArr.GetUpperBound(0); 0 <= I; I--) {
WillPush.SelectedIndList = new List<int>() { I };
Stk.Push(WillPush);
}
while (Stk.Count > 0) {
JyoutaiDef_RepeatedPermutation Popped = Stk.Pop();
// クリア判定
if (Popped.SelectedIndList.Count == pR) {
var WillReturn = new List<Type>();
Popped.SelectedIndList.ForEach(X => WillReturn.Add(pArr[X]));
yield return WillReturn.ToArray();
continue;
}
for (int I = pArr.GetUpperBound(0); 0 <= I; I--) {
WillPush.SelectedIndList = new List<int>(Popped.SelectedIndList) { I };
Stk.Push(WillPush);
}
}
}
}
#endregion