Problem: Igor the analyst fell asleep on the work and had a strange dream. In the dream his desk was crowded with computer mice, so he bought a mousetrap to catch them.

The desk can be considered as an infinite plane, then the mousetrap is a rectangle which sides are parallel to the axes, and which opposite sides are located in points (x1, y1) and (x2, y2).

Igor wants to catch all mice. Igor has analysed their behavior and discovered that each mouse is moving along a straight line with constant speed, the speed of the i-th mouse is equal to (vix, viy), that means that the x coordinate of the mouse increases by vix units per second, while the y coordinates increases by viy units. The mousetrap is open initially so that the mice are able to move freely on the desk. Igor can close the mousetrap at any moment catching all the mice that are strictly inside the mousetrap.

Igor works a lot, so he is busy in the dream as well, and he asks you to write a program that by given mousetrap's coordinates, the initial coordinates of the mice and their speeds determines the earliest time moment in which he is able to catch all the mice. Please note that Igor can close the mousetrap only once.

Input

The first line contains single integer n (1 ≤ n ≤ 100 000) — the number of computer mice on the desk.

The second line contains four integers x1, y1, x2 and y2 (0 ≤ x1 ≤ x2 ≤ 100 000), (0 ≤ y1 ≤ y2 ≤ 100 000) — the coordinates of the opposite corners of the mousetrap.

The next n lines contain the information about mice.

The i-th of these lines contains four integers rix, riy, vix and viy, (0 ≤ rix, riy ≤ 100 000,  - 100 000 ≤ vix, viy ≤ 100 000), where (rix, riy) is the initial position of the mouse, and (vix, viy) is its speed.

Output

In the only line print minimum possible non-negative number t such that if Igor closes the mousetrap at t seconds from the beginning, then all the mice are strictly inside the mousetrap. If there is no such t, print -1.

Your answer is considered correct if its absolute or relative error doesn't exceed 10 - 6. 

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

4
7 7 9 8
3 5 7 5
7 5 2 4
3 3 7 8
6 6 3 2


Output

0.57142857142857139685


Input

4
7 7 9 8
0 3 -5 4
5 0 5 4
9 9 -1 -6
10 5 -7 -10


Output

-1

Note

Here is a picture of the first sample

Points A, B, C, D - start mice positions, segments are their paths.

<image>

Then, at first time when all mice will be in rectangle it will be looks like this:

<image>

Here is a picture of the second sample

<image>

Points A, D, B will never enter rectangle.

Solution (in JAVA):

Solution:
  import java.util.*; 
                                    import java.math.*;
                                    import java.io.*;
                                    import java.text.DecimalFormat;
                                    import java.math.BigInteger;
                                    public class Main{
                                        //static int d=20;
                                        static long mod=1000000007 ;
                                        
                                        static ArrayList<ArrayList<Edge>> arr;
                                       // static long[] dp1,dp2;
                                        static int[] a;
                                        static int[] vis,num;
                                        static long max;
                                        static HashSet<String> hs;
                                        //static int flag,ans;
                                        static long max1,max2,ans1;
                                        static long ct=0;
                                        static int flag=0;
                                        static int[] tin,tout,parent,level;
                                        static HashMap<Long,Integer> hm;
                                        static long[] dp1,dp2,dp3,dp4;
                                       
                                        public static void main(String[] args)  throws IOException {
                                            ///long start=System.currentTimeMillis();
                                            boolean online =false;
                                            String fileName = "B-small-attempt0 (3)";
                                            PrintWriter out; 
                                            if (online) {
                                                s.init(new FileInputStream(new File(fileName + ".in")));
                                                 out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                            }
                                             else {
                                                s.init(System.in);   
                                            
                                                out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
                                                //out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                            }//r,b,y,g

                                            int n=s.ni();
                                            double x1,y1,x2,y2;
                                            x1=s.nd();
                                            y1=s.nd();
                                            x2=s.nd();
                                            y2=s.nd();
                                            double[][] a=new double[n][4];
                                            double[][] b=new double[n][2];
                                            int flag=0;
                                            for(int i=0;i<n;i++){
                                                for(int j=0;j<4;j++)
                                                    a[i][j]=s.nd();
                                                double u1=(x1-a[i][0])/a[i][2];
                                                double u2=(x2-a[i][0])/a[i][2];
                                                if(a[i][2]==0){
                                                        if(a[i][0]>Math.min(x1,x2) && a[i][0]<Math.max(x1,x2)){
                                                            u1=Double.MIN_VALUE/2;
                                                            u2=Double.MAX_VALUE/2;
                                                        }
                                                        else
                                                            u2=u1=Double.MAX_VALUE/2;
                                                }
                                                if(u1>u2){
                                                    double w=u1;
                                                    u1=u2;
                                                    u2=w;
                                                }

                                                u1+=1e-15;
                                                u2-=1e-15;
                                                double v1=(y1-a[i][1])/a[i][3];
                                                double v2=(y2-a[i][1])/a[i][3];
                                                if(a[i][3]==0){
                                                    {
                                                        if(a[i][1]>Math.min(y1,y2) && a[i][1]<Math.max(y1,y2)){
                                                            v1=Double.MIN_VALUE/2;
                                                            v2=Double.MAX_VALUE/2;
                                                        }
                                                        else
                                                            v2=v1=Double.MAX_VALUE/2;
                                                    }
                                                }

                                                if(v1>v2){
                                                    double w=v1;
                                                    v1=v2;
                                                    v2=w;
                                                }
                                                v1+=1e-15;
                                                v2-=1e-15;

                                                double z1=Math.max(u1,v1);
                                                double z2=Math.min(u2,v2);
                                                //out.println(u1+" "+u2+" "+v1+" "+v2);
                                                if(z1>z2){
                                                    flag=1;
                                                    continue;
                                                }
                                                b[i][0]=z1;
                                                b[i][1]=z2;

                                            }
                                            double z1=b[0][0];
                                            double z2=b[0][1];
                                            for(int i=1;i<n;i++){

                                                z1=Math.max(z1,b[i][0]);
                                                z2=Math.min(z2,b[i][1]);
                                                if(z1>z2){
                                                    flag=1;
                                                    break;
                                                }
                                               

                                            }

                                            if(z1<0){
                                                if(z2>=Double.MAX_VALUE/2-1e-15)
                                                    flag=1;
                                                else if(z2>=0)
                                                    z1=0;
                                                else 
                                                    flag=1;
                                            }
                                            if(z1>=Double.MAX_VALUE/2-1e-15)
                                                flag=1;
                                            if(flag==1)
                                                out.println(-1);
                                            else
                                                out.println(z1);
                                            out.close();    
                             
                                        }
                                        
                                        public static int gcd(int a, int b){
                                                if (a == 0) return b;
                                                return gcd(b % a, a);
                                        }
                                            
                                        public static void cfs(ArrayList<HashSet<Integer>> arr,int c,int p,int g,int[] vis){
                                            vis[c]=1;
                                            if(g!=-1){
                                                if(!arr.get(c).contains(g)){
                                                    flag=1;
                                                    return;
                                                }
                                            }
                                            for(int x:arr.get(c)){
                                                if(x!=p && x!=g && vis[x]==0 ){
                                                    cfs(arr,x,c,p,vis);
                                                }
                                            }

                                        }
                                                              //   public static void dfs(int u,int p){
         //                            //       if(p>=0)
         //                            //           tin[u]=tout[u]=tt++;
         //                            //       if(p>=0)
         //                            //           level[u]=level[p]+1;
         //                            //       parent[u]=p;
         //                            //       for(int x:arr.get(u)){
         //                            //           if(x!=p){
         //                            //               dfs(x,u);
         //                            //               tout[u]=Math.max(tout[u],tout[x]);
         //                            //           }
         //                            //       }
         //                            //       
         //
         //
                                     //   }
                                        public static int lca(int[][] p,int a,int b){
                                            if(level[a]<level[b]){
                                                int x=a;
                                                a=b;
                                                b=x;
                                            }
                                            int log=p[0].length;
                                            for(int i=log-1;i>=0;i--){
                                                if(1<<i<=level[a]-level[b]){
                                                    a=p[a][i];
                                                }
                                            }
                                            if(a==b)
                                                return a;
                                            for(int i=log-1;i>=0;i--){
                                                if(p[a][i]!=p[b][i]){
                                                    a=p[a][i];
                                                    b=p[b][i];
                                                }
                                            }
                                            return p[a][0];
         
                                        }
                                        public static int[][] par(int[] parent){
                                            int n=arr.size();
                                            int[][] p=new int[n][17];
                                            for(int i=0;i<n;i++)
                                                p[i][0]=parent[i];
                                            for(int k=1;k<17;k++){
                                                for(int i=0;i<n;i++){
                                                    if(p[i][k-1]>-1)
                                                        p[i][k]=p[p[i][k-1]][k-1];
                                                    else
                                                        p[i][k]=-1;
                                                }
                                            }
                                            return p;
                                        }
                                        static class Edge {
                                               int from;
                                                int to;
                                                int cost;
                                        
                                               public Edge(int from, int to, int weight) {
                                                   this.from = from;
                                                   this.to = to;
                                                   this.cost= weight;
                                               }
                                        }                               
                                        static class Node {
                                            int start;
                                            int end;
                        
                                            int cost;
                                            int updated;
                        
                                            Node[] nodes;
                        
                                            public Node(int start, int end) {
                                                this.start = start;
                                                this.end = end;
                        
                                                if (start < end) {
                                                    int[] pos = {start, (start + end) / 2, end};
                                                    nodes = new Node[2];
                                                    for (int i = 0; i < 2; i++) {
                                                        nodes[i] = new Node(pos[i] + i, pos[i + 1]);
                                                    }
                                                }
                                            }
                        
                                            public void update(int queryStart, int queryEnd, int value) {
                                                if (queryEnd < start || end < queryStart) {
                                                    return;
                                                }
                        
                                                if (queryStart <= start && end <= queryEnd) {
                                                    cost += value;
                                                    updated += value;
                                                    return;
                                                }
                        
                                                propagate();
                                                for (Node node: nodes) {
                                                    node.update(queryStart, queryEnd, value);
                                                }
                                            }
                        
                                            public int query(int pos) {
                                                if (pos < start || end < pos) {
                                                    return 0;
                                                }
                        
                                                if (start == end) {
                                                    return cost;
                                                }
                        
                                                propagate();
                                                int ans = 0;
                                                for (Node node: nodes) {
                                                    ans = Math.max(ans, node.query(pos));
                                                }
                                                return ans;
                                            }
                        
                                            public void propagate() {
                                                if (updated != 0 && start < end) {
                                                    for (Node node: nodes) {
                                                        node.cost += updated;
                                                        node.updated += updated;
                                                    }
                                                    updated = 0;
                                                }
                                            }
                                        }
                                        public static double nthroot(int n, double A) {
                                            return nthroot(n, A, 0.00000000000001);
                                        }
                                        public static double nthroot(int n, double A, double p) {
                                            if(A < 0) {
                                                System.err.println("A < 0");// we handle only real positive numbers
                                                return -1;
                                            } else if(A == 0) {
                                                return 0;
                                            }
                                            double x_prev = A;
                                            double x = A / n;  // starting "guessed" value...
                                            while(Math.abs(x - x_prev) > p) {
                                                x_prev = x;
                                                x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
                                            }
                                            return x;
                                        }
                                        
                                        static class item implements Comparable<item> {
                                            int x,y,turn,dir;
                                            public item(int a,int b,int c,int d){
                                                
                                                x=a;
                                                y=b;
                                                turn =c;
                                                dir=d;
                                            }
                                            public int compareTo(item o){
                                                return turn-o.turn;
                                            }
                                            
                                        }
                                       
                                        public static void dfs2(int c,int p,int[] a){
                                            //System.out.println(c+" "+p);
                                           
                                            
                                            
                 
                                        }
        //public static void dfs(int x,int[] vis,Stack<Integer> st){
                                        //    vis[x]=1;
                                        //    ArrayList<Integer> arr2=arr.get(x);
                                        //    Collections.sort(arr2);
                                        //    for(int i=arr2.size()-1;i>=0;i--){
                                        //        int z=arr2.get(i);
                                        //        if(vis[z]==0)
                                        //            dfs(z,vis,st);
                                        //    }
                                        //    st.push(x);
                 //
                                        //}
                                        public static long gcd(long a, long b){
                                                if (a == 0) return b;
                                                return gcd(b % a, a);
                                        }
                                            
                                        public static boolean check(long x){
                                            if(x%4==0 || x%7==0 || x%11==0)
                                                return true;
                                            if(x<4 || x<7 || x<11)
                                                return false;
                                            if(x%2==0){
                                                return check(x/2);
                                            }
                                            else
                                                return check(x/2) && check((x+1)/2);
                                        }
                                        public static int angle(int x1,int x2,int x3,int y1,int y2,int y3){
                                            long val=(y2-y1)*1L*(x3-x2)-(y3-y2)*1L*(x2-x1);
                                            if(val<0)
                                                return 1;
                                            else if(val>0)
                                                return -1;
                                            else
                                                return 0;
                                        }
                                        
                                        static class BIT{
                                        
                                            int N;
                                            long tree[];
                                            
                                            BIT(int N){
                                                this.N = N;
                                                tree = new long[N + 1];
                                            }
                                            
                                            void update(int idx,long val){
                                                while(idx <= N){
                                                    tree[idx]+=val;
                                                    idx += (idx & -idx);
                                                }
                                            }
                                            
                                            long query(int l,int r){
                                                if(l == 1)
                                                    return read(r);
                                                else
                                                    return read(r) - read(l-1);
                                            }
                                            
                                            long read(int idx){
                                                long sum = 0;
                                                while(idx > 0){
                                                    sum += tree[idx];
                                                    idx -= (idx & -idx);
                                                }
                                                return sum;
                                            }
                                        }
                                        public static boolean pal(String a){
                                            int i=0;
                                            int j=a.length()-1;
                                            while(i<j){
                                                if(a.charAt(i)!=a.charAt(j)){
                                                    return false;
                                                }
                                                i++;
                                                j--;
                                            }
                                            return true;
                                                
                                        }
                                        public static long find(long n,long k){
                                            if(n==2){
                                                if(k==1 || k==3)
                                                    return 1;
                                                else
                                                    return 2;
                                            }
                                            long t=pow2(2,n,mod)-1;
                                            long z=(t+1)/2;
                                            if(k==z)
                                                return n;
                                            if(k<z)
                                                return find(n-1,k);
                                            else
                                                return find(n-1,k-z);
                                        }
                                        public static long pow2(long a,long b,long mod){
                                                
                                                long ans=1;
                                               // long z=b;
                                                while(b>0){
                                                   
                                                    if(b%2==1)
                                                        ans=(a*ans)%mod;
                                                    a=(a*a)%mod;
                                                    b/=2;
                                                }
                                              
                                                return  ans;
                                        }
                                         public static long pow3(long a,long b){
                                                
                                                long ans=1;
                                               // long z=b;
                                                while(b>0){
                                                   
                                                    if(b%2==1)
                                                        ans=(a*ans);
                                                    a=(a*a);
                                                    b/=2;
                                                }
                                              
                                                return  ans;
                                        }
                                        public static long fib(long n){
                                            long[][]    f=new long[][]{{1L,1L},{1L,0}};
                                            if(n==0)
                                                return 0;
                                            f=arrpow(f,n-1);
                                            return f[0][0];
                                        }
                                        public static long[][] arrpow(long[][] a,long b){
                                           
                                                int n=a.length;
                                              //  long z=b;
                                                long[][] ans=new long[n][n];
                                                for(int i=0;i<n;i++)
                                                    ans[i][i]=1L;
                                                while(b>0){
                                                    
                                                    if(b%2==1)
                                                        ans=mul(a,ans);
                                                    a=mul(a,a);
                                                    b/=2;
                                                }
                                                
                                                return  ans;
                                        }
                                        public static long[][] mul(long[][] a,long[][] b){
                                            int n=a.length;
                                            int m=b[0].length;
                                            long[][] ans=new long[n][m];
                                            if(n==2 && m==2 && b.length==2){
                                                ans[0][0]=((a[0][0]*b[0][0])%mod+(a[0][1]*b[1][0]))%mod;
                                                ans[0][1]=((a[0][0]*b[0][1])%mod+(a[0][1]*b[1][1]))%mod;
                                                ans[1][0]=((a[1][0]*b[0][0])%mod+(a[1][1]*b[1][0]))%mod;
                                                ans[1][1]=((a[1][1]*b[1][1])%mod+(a[1][0]*b[0][1]))%mod;
                                                return ans;
             
                                            }
                                            for(int i=0;i<n;i++){
                                                for(int j=0;j<m;j++){
                                                    for(int k=0;k<b.length;k++){
                                                        ans[i][j]=(ans[i][j]+(a[i][k]*b[k][j])%mod)%mod;
                                                    }
                                                }
                                            }
                                            return ans; 
                                        }
                                         static class name implements Comparable<name> {
                                            long l,b,h;
                                            public name(long   x,long y,long z){
                                                {
                                                    l=x;
                                                    b=y;        
                                                }
                                                
                                                
                                                h=z;
                                            }
                                            public int compareTo(name o){
                                                return -(int)(l*b-o.l*o.b);
                                            }
                                            
                                        }
                                        public static class s {
                                            static BufferedReader reader;
                                            static StringTokenizer tokenizer;
                                        
                                            /** call this method to initialize reader for InputStream */
                                            static void init(InputStream input) {
                                                reader = new BufferedReader(
                                                            new InputStreamReader(input) );
                                                tokenizer = new StringTokenizer("");
                                            }   
                                        
                                            /** get next word */
                                            static String ns() throws IOException {
                                                while ( ! tokenizer.hasMoreTokens() ) {
                                                    //TODO add check for eof if necessary
                                                    tokenizer = new StringTokenizer(
                                                        reader.readLine() );
                                                }
                                                return tokenizer.nextToken();
                                            }
                                        
                                            static int ni() throws IOException {
                                                return Integer.parseInt( ns() );
                                            }
                                        
                                            static double nd() throws IOException {
                                                return Double.parseDouble( ns() );
                                            }
                                            static long nl() throws IOException {
                                                return Long.parseLong( ns() );
                                            }
                                        }
                                    }