codeforces 782B - The Meeting Place Cannot Be Changed

time limit per test

5 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

The main road in Bytecity is a straight line from south to north. Conveniently, there are coordinates measured in meters from the southernmost building in north direction.

At some points on the road there are n friends, and i-th of them is standing at the point xi meters and can move with any speed no greater than vi meters per second in any of the two directions along the road: south or north.

You are to compute the minimum time needed to gather all the n friends at some point on the road. Note that the point they meet at doesn't need to have integer coordinate.

Input

The first line contains single integer n (2 ≤ n ≤ 60 000) — the number of friends.

The second line contains n integers x1, x2, ..., xn (1 ≤ xi ≤ 109) — the current coordinates of the friends, in meters.

The third line contains n integers v1, v2, ..., vn (1 ≤ vi ≤ 109) — the maximum speeds of the friends, in meters per second.

Output

Print the minimum time (in seconds) needed for all the n friends to meet at some point on the road.

Your answer will be considered correct, if its absolute or relative error isn't greater than 10 - 6. Formally, let your answer be a, while jury's answer be b. Your answer will be considered correct if  holds.

Examples

input

3
7 1 3
1 2 1

output

2.000000000000

input

4
5 10 3 2
2 3 2 4

output

1.400000000000

 #include<cstdio>
 struct type{
     int x;
     int v;
 }p[+];
 int n;
 bool check(double time)
 {
     //遍历每个人在time个单位时间后能走到的位置，不断更新重叠的区间[l,r]，只要到最后这个区间一人不为空，就return true
     double l=p[].x-time*p[].v;
     double r=p[].x+time*p[].v;
     for(int i=;i<=n;i++){
         if(p[i].x-time*p[i].v > l) l=p[i].x-time*p[i].v;
         if(p[i].x+time*p[i].v < r) r=p[i].x+time*p[i].v;
         if(l>r) return false;
     }
     return true;
 }
 int main()
 {
     scanf("%d",&n);
     for(int i=;i<=n;i++) scanf("%d",&p[i].x);
     for(int i=;i<=n;i++) scanf("%d",&p[i].v);
     double st=,ed=;
     while(ed-st>1e-){
         double mid=st+(ed-st)/;
         if(check(mid)) ed=mid;
         else st=mid;
     }
     printf("%.12lf\n",ed);
 }