/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Egor Kulikov
 */





#include <bits/stdc++.h>

using namespace std;

#define all(v) (v).begin(), (v).end()

using ll = long long;
using ull = unsigned long long;
using li = __int128;
using uli = unsigned __int128;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;

void doReplace() {
}

template <typename T, typename U, typename...Vs>
void doReplace(T& t, const U& u, Vs&& ...vs) {
    t = u;
    doReplace(vs...);
}

template <typename T, typename...Us>
T minim(T& was, const T& cand, Us&& ...us) {
    if (was > cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}

template <typename T, typename...Us>
T maxim(T& was, const T& cand, Us&& ...us) {
    if (was < cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}


template <typename D>
D dPower(D base, ll exponent) {
    if (exponent < 0) {
        return dPower(1 / base, -exponent);
    }
    if (exponent == 0) {
        return 1;
    }
    if ((exponent & 1) == 1) {
        return dPower(base, exponent - 1) * base;
    } else {
        D res = dPower(base, exponent >> 1);
        return res * res;
    }
}


class NumberIterator : iterator<forward_iterator_tag, int> {
public:
    int v;

    NumberIterator(int v) : v(v) {}

    operator int&() { return v; }

    int operator*() { return v; }
};

class range : pii {
public:
    range(int begin, int end) : pii(begin, max(begin, end)) {}

    range(int n) : pii(0, max(0, n)) {}

    NumberIterator begin() {
        return first;
    }

    NumberIterator end() {
        return second;
    }
};


template <typename T>
class arr {
    T* b;
    int n;

    void allocate(int sz) {
#ifdef LOCAL
        if (sz < 0) {
            throw "bad alloc";
        }
#endif
        n = sz;
        if (sz > 0) {
            b = (T*) (::operator new(sz * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr(int n = 0) {
        allocate(n);
#ifdef LOCAL
        view();
#endif
    }

    arr(int n, const T& init) {
        allocate(n);
        for (int i : range(n)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(initializer_list<T> l) : arr(l.size()) {
        if (n > 0) {
            memcpy(b, l.begin(), n * sizeof(T));
        }
    }

    arr(T* b, int n) : arr(b, b + n) {}

    arr(T* b, T* e) : b(b), n(e - b) {}

    int size() const {
        return n;
    }

    T* begin() {
        return b;
    }

    const T* begin() const {
        return b;
    }

    T* end() {
        return b + n;
    }

    const T* end() const {
        return b + n;
    }

    arr<T> clone() const {
        arr<T> res(n);
        copy(b, b + n, res.begin());
        return res;
    }

    T& operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    const T& operator[](int at) const {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    bool operator==(const arr& other) const {
        if (n != other.n) {
            return false;
        }
        for (int i : range(n)) {
            if (b[i] != other.b[i]) {
                return false;
            }
        }
        return true;
    }

    vector<T> view() {
        return vector<T>(b, b + min(n, 50));
    }
};

typedef arr<int> arri;

void decreaseByOne() {}

template <typename T, class...Vs>
void decreaseByOne(arr<T>& array, Vs& ...vs) {
    int n = array.size();
    for (int i : range(n)) {
        array[i]--;
    }
    decreaseByOne(vs...);
}

template <typename T, typename U>
void decreaseByOne(arr<pair<T, U>>& v) {
    for (auto& p : v) {
        p.first--;
        p.second--;
    }
}


template <typename T>
class arr2d {
    T* b;
    int d1;
    int d2;
    int sz;

    void allocate(int n) {
#ifdef LOCAL
        if (n < 0) {
            throw "bad alloc";
        }
#endif
        if (n > 0) {
            b = (T*) (::operator new(n * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr2d(int d1 = 0, int d2 = 0) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
#ifdef LOCAL
        view();
#endif
    }

    arr2d(int d1, int d2, const T& init) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        for (int i : range(sz)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(T* b, int d1, int d2) : b(b), d1(d1), d2(d2), sz(d1 * d2) {}

    int size() const {
        return sz;
    }

    int dim1() const {
        return d1;
    }

    int dim2() const {
        return d2;
    }

    T* begin() {
        return b;
    }

    T* end() {
        return b + sz;
    }

    T& operator()(int i1, int i2) {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    const T& operator()(int i1, int i2) const {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    T& operator[](const pii& p) {
        return operator()(p.first, p.second);
    }

    const T& operator[](const pii& p) const {
        return operator()(p.first, p.second);
    }

    arr<T> operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= d1) {
            throw "Out of bounds";
        }
#endif
        return arr<T>(b + at * d2, d2);
    }

    vector<vector<T>> view() {
        vector<vector<T>> res(min(d1, 50));
        for (int i : range(res.size())) {
            res[i] = (*this)[i].view();
        }
        return res;
    }

    arr2d<T> clone() {
        arr2d<T> res(d1, d2);
        copy(b, b + sz, res.b);
        return res;
    }
};


inline bool isWhitespace(int c) {
    return isspace(c) || c == EOF;
}

class Input {
private:
    bool exhausted = false;
    int bufSize = 4096;
    char* buf = new char[bufSize];
    int bufRead = 0;
    int bufAt = 0;

public:
    inline int get() {
        if (exhausted) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            return EOF;
        }
        return buf[bufAt++];
    }

private:
    template <typename T>
    inline T readInteger() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        T res = 0;
        do {
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c));
        return res * sgn;
    }

    void initArrays(int) {}

    template <typename T, class...Vs>
    void initArrays(int n, arr<T>& array, Vs& ...vs) {
        array = arr<T>(n, T());
        initArrays(n, vs...);
    }

    template <typename T, class...Vs>
    void initArrays(int n, vector<T>&, Vs& ...vs) {
        initArrays(n, vs...);
    }

    void readImpl(int) {}

    template <typename T, class...Vs>
    void readImpl(int i, arr<T>& arr, Vs& ...vs) {
        arr[i] = readType<T>();
        readImpl(i, vs...);
    }

    template <typename T, class...Vs>
    void readImpl(int i, vector<T>& arr, Vs& ...vs) {
        arr.push_back(readType<T>());
        readImpl(i, vs...);
    }

public:
    inline int skipWhitespace() {
        int c;
        while (isWhitespace(c = get()) && c != EOF);
        return c;
    }

    inline int readInt() {
        return readInteger<int>();
    }

    inline ll readLong() {
        return readInteger<ll>();
    }

    string readString() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        do {
            res.push_back(c);
        } while (!isWhitespace(c = get()));
        return res;
    }

    arri readIntArray(int size) {
        return readArray<int>(size);
    }

    arr<ll> readLongArray(int size) {
        return readArray<ll>(size);
    }

    arr<double> readDoubleArray(int size) {
        return readArray<double>(size);
    }

    arr<string> readStringArray(int size) {
        return readArray<string>(size);
    }

    arr<char> readCharArray(int size) {
        return readArray<char>(size);
    }

    template <typename T>
    T readType() {
        throw "Operation not supported";
    }

    template <typename U, typename V>
    pair<U, V> readType() {
        U first = readType<U>();
        V second = readType<V>();
        return make_pair(first, second);
    }

    template <typename T>
    arr<T> readArray(int n) {
        arr<T> res(n, T());
        for (int i : range(n)) {
            res[i] = readType<T>();
        }
        return res;
    }


    template <class...Vs>
    void readArrays(int n, Vs& ...vs) {
        initArrays(n, vs...);
        for (int i : range(n)) {
            readImpl(i, vs...);
        }
    }

    template <typename U, typename V>
    arr<pair<U, V>> readArray(int n) {
        arr<pair<U, V>> res(n);
        for (int i : range(n)) {
            res[i] = readType<U, V>();
        }
        return res;
    }

    template <typename T>
    arr2d<T> readTable(int rows, int cols) {
        arr2d<T> result(rows, cols);
        for (int i : range(rows)) {
            for (int j : range(cols)) {
                result(i, j) = readType<T>();
            }
        }
        return result;
    }

    arr2d<int> readIntTable(int rows, int cols) {
        return readTable<int>(rows, cols);
    }

    arr2d<char> readCharTable(int rows, int cols) {
        return readTable<char>(rows, cols);
    }

    string readLine() {
        int c = get();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        do {
            res.push_back(c);
            c = get();
        } while (c != '\n' && c != '\r' && c != EOF);
        return res;
    }

    inline double readDouble() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        double res = 0;
        do {
            if (tolower(c) == 'e') {
                return sgn * res * dPower(double(10), readInt());
            }
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c) && c != '.');
        if (c == '.') {
            double add = 0;
            int length = 0;
            c = get();
            do {
                if (tolower(c) == 'e') {
                    return sgn * (res + add * dPower(double(10), -length)) * dPower(double(10), readInt());
                }
                if (!isdigit(c)) {
#ifdef LOCAL
                    throw "Number format error";
#endif
                    res += add * dPower(10, -length);
                    return res * sgn;
                }
                add *= 10;
                add += c - '0';
                length++;
                c = get();
            } while (!isWhitespace(c));
            res += add * dPower(double(10), -length);
        }
        return res * sgn;
    }

    inline char readChar() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return 0;
        }
        return c;
    }

    inline bool isExhausted() { return exhausted; }

    inline void setBufSize(int newBufSize) {
        if (newBufSize > bufSize) {
            char* newBuf = new char[newBufSize];
            memcpy(newBuf, buf, bufSize);
            buf = newBuf;
        }
        bufSize = newBufSize;
    }
};

template <>
inline double Input::readType() {
    return readDouble();
}

template <>
inline int Input::readType() {
    return readInt();
}

template <>
inline ll Input::readType() {
    return readLong();
}

template <>
inline char Input::readType() {
    return readChar();
}

template <>
inline string Input::readType() {
    return readString();
}

Input in;


class Output {
private:
    ostream* out;

    template <typename T>
    inline void printSingle(const T& value) {
        *out << value;
    }

    template <typename T>
    void printSingle(const vector<T>& array) {
        size_t n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr<T>& array) {
        int n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr2d<T>& array) {
        size_t n = array.dim1();
        size_t m = array.dim2();
        for (int i : range(n)) {
            for (int j : range(m)) {
                *out << array(i, j);
                if (j + 1 != m) {
                    *out << ' ';
                }
            }
            if (i + 1 != n) {
                *out << '\n';
            }
        }
    }

    template <typename T, typename U>
    inline void printSingle(const pair<T, U>& value) {
        out << value.first << ' ' << value.second;
    }

public:
    bool autoflush;

    Output(ostream& out, bool autoflush) : out(&out), autoflush(autoflush) {
        out << fixed << setprecision(20);
    }

    void setOut(ostream& nOut) {
        out = &nOut;
    }

    inline void print() {}

    template <typename T, typename...Targs>
    inline void print(const T& first, const Targs... args) {
        printSingle(first);
        if (sizeof...(args) != 0) {
            *out << ' ';
            print(args...);
        }
        if (autoflush) {
            flush();
        }
    }

    template <typename...Targs>
    inline void printLine(const Targs... args) {
        print(args...);
        *out << '\n';
        if (autoflush) {
            flush();
        }
    }

    inline void flush() {
        out->flush();
    }

    inline void setPrecision(int digs) {
        *out << fixed << setprecision(digs);
    }
};

Output out(cout, false);
Output err(cerr, true);


template <typename T>
class FenwickTree {
    arr<T> value;

    T get(int to) const {
        minim(to, int(value.size()) - 1);
        T result = 0;
        while (to >= 0) {
            result += value[to];
            to = (to & (to + 1)) - 1;
        }
        return result;
    }

public:
    FenwickTree(int size) {
        value = arr<T>(size, 0);
    }

    void add(int at, T val) {
        while (at < value.size()) {
            value[at] += val;
            at = at | (at + 1);
        }
    }

    T get(int from, int to) const {
        if (from >= to) {
            return 0;
        }
        return get(to - 1) - get(from - 1);
    }

    void clear() {
        fill(all(value), 0);
    }
};


template <typename T>
class que : public queue<T> {
    using parent = queue<T>;
public:
    que() : parent() {}

    que(const que<T>& q) : parent(q) {}

    que(que<T>&& q) noexcept: parent(move(q)) {}

    T pop() {
#ifdef LOCAL
        if (parent::empty()) {
            throw "Pop on empty queue";
        }
#endif
        T res = parent::front();
        parent::pop();
        return res;
    }

    que<T>& operator=(que<T>&& __x) noexcept {
        parent::operator=(__x);
        return *this;
    }

    que<T>& operator=(const que<T>& __x) {
        parent::operator=(__x);
        return *this;
    }
};

using qi = que<int>;


template <typename T>
inline void unique(vector<T>& v) {
    v.resize(unique(all(v)) - v.begin());
}

arri createOrder(int n) {
    arri order(n);
    for (int i = 0; i < n; i++) {
        order[i] = i;
    }
    return order;
}

arri inverse(const arri& p) {
    arri res(p.size());
    for (int i : range(p.size())) {
        res[p[i]] = i;
    }
    return res;
}

template <typename T, typename Iterator>
inline void addAll(vector<T>& v, Iterator begin, Iterator end) {
    v.insert(v.end(), begin, end);
}

template <class Collection, typename Iterator>
inline void addAll(Collection& v, Iterator begin, Iterator end) {
    v.insert(begin, end);
}

template <typename Iterator>
arri getQty(Iterator begin, Iterator end, int length) {
    arri res(length, 0);
    for (Iterator it = begin; it != end; it++) {
        res[*it]++;
    }
    return res;
}

template <typename Iterator>
arri getQty(Iterator begin, Iterator end) {
    return getQty(begin, end, *max_element(begin, end) + 1);
}

template <class Collection>
void collect(Collection&) {}

template <class Collection, class Other, class ...Vs>
void collect(Collection& all, Other& a, Vs& ...vs) {
    addAll(all, all(a));
    collect(all, vs...);
}

void replace(const vi&) {}

template <class ...Vs>
void replace(const vi& all, vi& a, Vs& ...vs) {
    for (int& i : a) {
        i = lower_bound(all(all), i) - all.begin();
    }
    replace(all, vs...);
}

template <class ...Vs>
void replace(const vi& all, arri& a, Vs& ...vs) {
    for (int& i : a) {
        i = lower_bound(all(all), i) - all.begin();
    }
    replace(all, vs...);
}

template <class ...Vs>
vi compress(Vs& ...vs) {
    vi vals;
    collect(vals, vs...);
    sort(all(vals));
    unique(vals);
    replace(vals, vs...);
    return vals;
}


class ERandomPawn {
public:
    void solve() {
        int n = in.readInt();
        auto a = in.readLongArray(n);
        auto b = in.readIntArray(n);

        int at = max_element(all(a)) - a.begin();
        arr<ll> aa(n + 1);
        arri bb(n + 1);
        for (int i : range(n - at)) {
            aa[i] = a[at + i];
            bb[i] = b[at + i];
        }
        for (int i : range(at)) {
            aa[i + n - at] = a[i];
            bb[i + n - at] = b[i];
        }
        aa[n] = a[at];
        bb[n] = b[at];
        a = aa;
        b = bb;
        FenwickTree<ll> sumB(n);
        FenwickTree<ll> sumBI(n);
        for (int i : range(n)) {
            sumB.add(i, b[i]);
            sumBI.add(i, i * b[i]);
        }
        auto f = [&](int i, int left, int right) -> ll {
            int k = right - left;
            int j = i - left;
            ll base = j * a[right] + (k - j) * a[left];
            ll lb = 2 * ll(j) * k * sumB.get(i, right) -
                    2 * j * (sumBI.get(i, right) - left * sumB.get(i, right));
            ll rb = 2 * (k - j) * (sumBI.get(left + 1, i) - left * sumB.get(left + 1, i));
            ll c = base - (lb + rb);
            return c;
        };
        /*set<int> poi;
        for (int i : range(n + 1)) {
            poi.insert(i);
        }
        que<int> toCheck;
        arr<bool> inQueue(n + 1, true);
        for (int i : range(1, n)) {
            toCheck.push(i);
        }
        while (!toCheck.empty()) {
            int i = toCheck.pop();
            inQueue[i] = false;
            poi.erase(i);
            auto it = poi.lower_bound(i);
            int right = *it;
            it--;
            int left = *it;
            ld c = f(i, left, right);
            if (c >= a[i]) {
                if (!inQueue[left]) {
                    inQueue[left] = true;
                    toCheck.push(left);
                }
                if (!inQueue[right]) {
                    inQueue[right] = true;
                    toCheck.push(right);
                }
            } else {
                poi.insert(i);
            }
        }*/

/*        poi.insert(0);
        poi.insert(n);
        arri order(n - 1);
        for (int i : range(1, n)) {
            order[i - 1] = i;
        }
        sort(all(order), [&](int x, int y) -> bool {
            return a[x] > a[y];
        });
//        ld answer = a[0];
        for (int i : order) {
            auto it = poi.lower_bound(i);
            int right = *it;
            it--;
            int left = *it;
            int k = right - left;
            int j = i - left;
            ld base = ld(j) / k * a[right] + ld(k - j) / k * a[left];
            ld lb = 2 * j * k * sumB.get(i, right) -
                        2 * j * (sumBI.get(i, right) - left * sumB.get(i, right));
            ld rb = 2 * (k - j) * (sumBI.get(left + 1, i) - left * sumB.get(left + 1, i));
            ld c = base - (lb + rb) / k;
            if (c < a[i]) {
                poi.insert(i);
//                answer += a[i];
            } else {
//                answer += c;
            }
        }*/
        vi q;
        for (int i : range(n + 1)) {
            while (q.size() >= 2) {
                int last = q.back();
                int before = q[q.size() - 2];
                if (f(last, before, i) > a[last] * (i - before)) {
                    q.pop_back();
                } else {
                    break;
                }
            }
            q.push_back(i);
        }
        set<int> poi;
        addAll(poi, all(q));
        ld answer = 0;
        for (int i : range(n)) {
            if (poi.count(i)) {
                answer += a[i];
            } else {
                auto it = poi.lower_bound(i);
                int right = *it;
                it--;
                int left = *it;
//                int k = right - left;
//                int j = i - left;
//                ld base = ld(j) / k * a[right] + ld(k - j) / k * a[left];
//                ld lb = 2 * j * k * sumB.get(i, right) -
//                        2 * j * (sumBI.get(i, right) - left * sumB.get(i, right));
//                ld rb = 2 * (k - j) * (sumBI.get(left + 1, i) - left * sumB.get(left + 1, i));
//                ld c = base - (lb + rb) / k;
                answer += ld(f(i, left, right)) / (right - left);
            }
        }
        answer /= n;
        out.setPrecision(20);
        out.printLine(answer);
    }
};


int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
#ifdef LOCAL_RELEASE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    auto time = clock();
#endif
    ERandomPawn solver;


    solver.solve();
    fflush(stdout);
#ifdef LOCAL_RELEASE
    cerr << clock() - time << endl;
#endif
    return 0;
}


Measured memory_bytes: 17040