#include <bits/stdc++.h>
using namespace std;
#define int long long
bool good(int t[], int x[], double mid, int n, double& sol){
double L = -1e18;
double R = 1e18;
for(int i=0; i<n; i++){
double cleft = x[i] - (mid - t[i]);
double cright = x[i] + (mid - t[i]);
L = max(L, cleft);
R = min(R, cright);
}
if (L <= R){sol = (L + R) / 2.0; return true;}
return false;
}
int32_t main(){
#ifndef ONLINE_JUDGE
freopen("input.txt","r+",stdin);
#endif
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t; cin>>t;
while(t--){
int n; cin>>n;
int t[n], x[n];
for(int i=0; i<n; i++){
cin>>x[i];
}
for(int i=0; i<n; i++){
cin>>t[i];
}
double l =0, r = 2e18;
double sol = 0;
for(int i=0; i< 100; i++){
double mid = l + (r-l)/2;
if (good(t, x, mid, n, sol)) r = mid;
else l = mid;
}
cout<<sol<<"\n";
}
return 0;
}
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