CF 25.09 B OK

#include <iostream>
#include <cmath>
#include <vector>
#include <queue>
#include <algorithm>
#include <string>
#include <stack>
#include <set>
#include <map>
#define pii pair <int, int>
#define pb(x) push_back(x)
using namespace std;
using ll = long long;
using ld = long double;
using db = double;
void cv(vector <int> &v) {
    for (auto x : v) cout << x << ' ';
    cout << "\n";
}

void cvl(vector <ll> &v) {
    for (auto x : v) cout << x << ' ';
    cout << "\n";
}


void cvv(vector <vector <int> > &v) {
    for (auto x : v) cv(x);
    cout << "\n";
}

void cvb(vector <bool> v) {
    for (bool x : v) cout << x << ' ';
    cout << "\n";
}

void cvs(vector <string>  v) {
    for (auto a : v) {
        cout << a << "\n";
    }
}

void cvp(vector <pii> a) {
    for (auto p : a) {
        cout << p.first << ' ' << p.second << "\n";
    }
    cout << "\n";
}

bool sh = 0;

void slv() {
    int n, A = 2e9, B = -2e9;
    cin >> n;
    vector <int> t(n), x(n);
    for (int &i: x) cin>>i;
    for (int &i: t) cin>>i;
    vector <pii> a(n); //{crd, t}
    for (int i = 0; i < n; ++i) {
        a[i] = {x[i], t[i]};
    }
    sort(a.begin(), a.end());
    vector <int> pf(n), repf(n);
    //pf = max(ti - xi) (+x0);
    //repf = max(tk + xk) - (x0)
    pf[0] = - a[0].first + a[0].second;
    repf[n - 1] = a[n - 1].first + a[n - 1].second;
    for (int i = 1; i < n; ++i) {
        pf[i] = max(pf[i - 1], - a[i].first + a[i].second);
    }
    for (int i = n - 2; i >= 0; --i) {
        repf[i] = max(repf[i + 1], a[i].first + a[i].second);
    }

    if (sh) {
        cout << "a\n";
        cvp(a);
        cout << "pf\n";
        cv(pf);
        cout<<"repf\n";
        cv(repf);
        cout<<"GO x0 \n";
    }

    //min time * 2
    int x0 = 0;//индекс в векторе = i in vector
    int opt = 2 * (repf[1] - a[0].first);
    if (sh) {
        cout << "first opt = " << opt << "\n";
    }
    if (sh) {
        cout << "option end = " << 2 * (pf[n - 2] + a[n - 1].first) << "\n";
    }
    if (opt > 2 * (pf[n - 2] + a[n - 1].first) ) {
        opt = 2 * (pf[n - 2] + a[n - 1].first);
        x0 = n - 1;
        if (sh) {
            cout << "sec opt = " << opt << "\n";
        }
    }
    //check crd[i] = x0
    for (int i = 1; i < n - 1; ++i) {

        int now = max(2 * (pf[i - 1] + a[i].first), 2 * (repf[i + 1] - a[i].first) );
        if (sh) {
            cout << "i = " << i << "\n";
            cout << "now = " << now << "\n";
        }
        if (now < opt) {
            if (sh) {
                cout << "BETTER!\n";
            }
            opt = now;
            x0 = i;
        }
    }
    //теперь проверим

    if (sh) {
        cout << "\nopt = " << opt << "\n";
        cout << "GO x1\n";
    }
    int bestx1 = -1;
    int x1 = -1; //принадлежит [i; i + 1] в векторе
    for (int i = 0; i < n - 1; ++i) {
        //now * 2 = :
        int now = pf[i] + repf[i + 1];
        //x1 * 2 = :
        x1 =  -pf[i] + repf[i + 1] ;
        if(sh) {
            cout << "i = " << i << "\n";
        }
        if (sh) {
            cout << "best x * 2 = " << x1 << "\n";
            cout << "now = " << now << "\n";
        }
        if (x1 <= 2 * a[i].first || x1 >= 2 * a[i + 1].first) {
            if (sh) {
                cout << "skip\n";
            }
            continue; //considered
        }
        if (sh) {
            cout << "check\n";
        }
        if (now < opt) {
            bestx1 = x1;
            opt = now;
            if (sh) {
                cout << "BETTER!\n";
            }
        }
    }

    if (sh) {
        cout << "x0 x1 = " << x0 << ' ' << x1 << "\n";
    }

    x0 = a[x0].first;
    if (bestx1 == -1) {//если x0 подошел
        cout << x0 << "\n";
        return;
    }

    //x1 уже сконвертирован в координату - осталось только поделить на 2
    if (bestx1 % 2 == 0) {
        cout << bestx1 / 2 << "\n";
        return;
    }
    cout << bestx1 / 2 << ".5\n";
}

/*
предпоследний и предпредпоследний

6
5 4 7 2 10 4
3 2 5 1 4 6
*/

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t = 1;
    if (!sh) cin >> t;
    for (int go = 0; go < t; ++ go) {
        slv();
    }
}