#include <bits/stdc++.h>
#define rep(i,x,y) for(int i=x; i<=y; ++i)
#define repd(i,x,y) for(int i=x; i>=y; --i)
#define mid ((l + r) >> 1)
#define lch (rt << 1)
#define rch (rt << 1 | 1)

using namespace std;

using i64 = long long;

/*
    PAY ATTENTION TO CONSTRUCT FUNCTION OF CLASS INFO!!!
*/
template<class Info>
struct SegmentTree {
    int n;
    std::vector<Info> info;
    SegmentTree() : n(0) {}
    SegmentTree(int n_, Info v_ = Info()) {
        init(n_, v_);
    }
    template<class T>
    SegmentTree(std::vector<T> init_) {
        init(init_);
    }
    void init(int n_, Info v_ = Info()) {
        init(std::vector(n_, v_));
    }
    template<class T>
    void init(std::vector<T> init_) {
        n = init_.size();
        info.assign(4 << std::__lg(n), Info());
        std::function<void(int, int, int)> build = [&](int p, int l, int r) {
            if (r - l == 1) {
                info[p] = init_[l];
                return;
            }
            int m = (l + r) / 2;
            build(2 * p, l, m);
            build(2 * p + 1, m, r);
            pull(p);
        };
        build(1, 0, n);
    }
    void pull(int p) {
        info[p] = info[2 * p] + info[2 * p + 1];
    }
    void modify(int p, int l, int r, int x, const Info &v) {
        if (r - l == 1) {
            info[p] = v;
            return;
        }
        int m = (l + r) / 2;
        if (x < m) {
            modify(2 * p, l, m, x, v);
        } else {
            modify(2 * p + 1, m, r, x, v);
        }
        pull(p);
    }
    void modify(int p, const Info &v) {
        modify(1, 0, n, p, v);
    }
    Info rangeQuery(int p, int l, int r, int x, int y) {
        if (l >= y || r <= x) {
            return Info();
        }
        if (l >= x && r <= y) {
            return info[p];
        }
        int m = (l + r) / 2;
        return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
    }
    Info rangeQuery(int l, int r) {
        return rangeQuery(1, 0, n, l, r);
    }
    template<class F>
    int findFirst(int p, int l, int r, int x, int y, F &&pred) {
        if (l >= y || r <= x) {
            return -1;
        }
        if (l >= x && r <= y && !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findFirst(2 * p, l, m, x, y, pred);
        if (res == -1) {
            res = findFirst(2 * p + 1, m, r, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findFirst(int l, int r, F &&pred) {
        return findFirst(1, 0, n, l, r, pred);
    }
    template<class F>
    int findLast(int p, int l, int r, int x, int y, F &&pred) {
        if (l >= y || r <= x) {
            return -1;
        }
        if (l >= x && r <= y && !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findLast(2 * p + 1, m, r, x, y, pred);
        if (res == -1) {
            res = findLast(2 * p, l, m, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findLast(int l, int r, F &&pred) {
        return findLast(1, 0, n, l, r, pred);
    }
};

constexpr int inf = 1E9;

struct Info
{
    int x = -inf;
    pair<int, int> id {-1, -1};
} ;

Info operator+(Info a, Info b)
{
    if (a.x > b.x) return a;
    return b;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n;
    cin >> n;
    vector<int> a(n), b(n);
    rep(i,0,n-1) cin >> a[i];
    rep(i,0,n-1) cin >> b[i];
    if (n&1)
    {
        n++;
        a.push_back(0);
        b.push_back(0);
    }

    vector<int> id(n);
    iota(id.begin(), id.end(), 0);
    sort(id.begin(), id.end(),
        [&](int i, int j) {
            return a[i] == a[j] ? i < j : a[i] < a[j];
        });
    vector<int> pa(n);
    rep(i,0,n-1) pa[id[i]] = i;
    sort(id.begin(), id.end(),
        [&](int i, int j) {
            return b[i] == b[j] ? i < j : b[i] < b[j];
        });
    vector<int> pb(n);
    rep(i,0,n-1) pb[id[i]] = i;

    set<pair<int, int>> sA, sB;
    rep(i,0,n-1) sA.insert({a[i], i}), sB.insert({b[i], i});

    SegmentTree<Info> segA(n), segB(n);
    SegmentTree<Info> segA2(n), segB2(n);
    i64 ans = 0;
    for (int i = 0; i < n; i += 2)
    {
        int A2 = next(sA.begin()) -> first;
        int B2 = next(sB.begin()) -> first;
        int Ab = inf;
        int aB = inf;
        Info qA, qB, qA2, qB2;
        if (sA.begin() -> second != sB.begin() -> second)
        {
            int A = sA.begin() -> second;
            int B = sB.begin() -> second;
            
            qA = segA.rangeQuery(0, pb[B]);
            qB = segB.rangeQuery(0, pa[A]);
            
            qA2 = segA2.rangeQuery(pb[B], n);
            qB2 = segB2.rangeQuery(pa[A], n);

            Ab = min(sA.begin() -> first + sB.begin() -> first - qA.x, sA.begin() -> first - qA2.x);
            aB = min(sA.begin() -> first + sB.begin() -> first - qB.x, sB.begin() -> first - qB2.x);
        }

        int v = min({A2, B2, Ab, aB});
        ans += v;
        if (v == A2)
        {
            int x = sA.begin() -> second; sA.erase(sA.begin());
            int y = sA.begin() -> second; sA.erase(sA.begin());
            sB.erase({b[x], x}), sB.erase({b[y], y});
            segA.modify(min(pb[x], pb[y]), {v, make_pair(x, y)});
            segA2.modify(min(pb[x], pb[y]), {v - min(b[x], b[y]), make_pair(x, y)});
        }
        else if (v == B2)
        {
            int x = sB.begin() -> second; sB.erase(sB.begin());
            int y = sB.begin() -> second; sB.erase(sB.begin());
            sA.erase({a[x], x}), sA.erase({a[y], y});
            segB.modify(min(pa[x], pa[y]), {v, make_pair(x, y)});
            segB2.modify(min(pa[x], pa[y]), {v - min(a[x], a[y]), make_pair(x, y)});
        }
        else if (v == Ab)
        {
            int x = sA.begin() -> second; sA.erase(sA.begin()), sB.erase({b[x], x});
            int y = sB.begin() -> second; sB.erase(sB.begin()), sA.erase({a[y], y});

            auto [nx, ny] = b[y] - qA.x < -qA2.x ? qA.id : qA2.id;
            if (pb[nx] > pb[ny]) swap(nx, ny);
            segA.modify(min(pb[nx], pb[ny]), Info());
            segA2.modify(min(pb[nx], pb[ny]), Info());

            segA.modify(min(pb[x], pb[ny]), {a[x], make_pair(x, ny)});
            segB.modify(min(pa[y], pa[nx]), {max(b[y], b[nx]), make_pair(y, nx)});

            segA2.modify(min(pb[x], pb[ny]), {a[x] - min(b[x], b[ny]), make_pair(x, ny)});
            segB2.modify(min(pa[y], pa[nx]), {max(b[y], b[nx]) - min(a[y], a[nx]), make_pair(y, nx)});
        }
        else
        {
            int x = sB.begin() -> second; sB.erase(sB.begin()), sA.erase({a[x], x});
            int y = sA.begin() -> second; sA.erase(sA.begin()), sB.erase({b[y], y});

            auto [nx, ny] = a[y] - qB.x < -qB2.x ? qB.id : qB2.id;
            if (pa[nx] > pa[ny]) swap(nx, ny);
            segB.modify(min(pa[nx], pa[ny]), Info());
            segB2.modify(min(pa[nx], pa[ny]), Info());

            segB.modify(min(pa[x], pa[ny]), {b[x], make_pair(x, ny)});
            segA.modify(min(pb[y], pb[nx]), {max(a[y], a[nx]), make_pair(y, nx)});

            segB2.modify(min(pa[x], pa[ny]), {b[x] - min(a[x], a[ny]), make_pair(x, ny)});
            segA2.modify(min(pb[y], pb[nx]), {max(a[y], a[nx]) - min(b[y], b[nx]), make_pair(y, nx)});
        }
    }
    cout << ans << '\n';
    return 0;
}