// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #define oj_local(x, y) (y) #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #define oj_local(x, y) (x) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template V &operator--(V &v) { for (auto &x : v) --x; return v; } template V &operator++(V &v) { for (auto &x : v) ++x; return v; } bool next_product(vector &v, int m) { repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0; return false; } bool next_product(vector &v, vector const& s) { repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0; return false; } template int sort_unique(vec &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } template auto prefix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(s.back() + *l++); return s; } template auto suffix_sum(It l, It r) { vector s = { 0 }; while (l != r) s.emplace_back(*--r + s.back()); reverse(s.begin(), s.end()); return s; } template T pop(vector &a) { auto x = a.back(); a.pop_back(); return x; } template T pop(priority_queue &a) { auto x = a.top(); a.pop(); return x; } template T pop(queue &a) { auto x = a.front(); a.pop(); return x; } template T pop_front(deque &a) { auto x = a.front(); a.pop_front(); return x; } template T pop_back(deque &a) { auto x = a.back(); a.pop_back(); return x; } template T pop_front(set &a) { auto x = *a.begin(); a.erase(a.begin()); return x; } template T pop_back(set &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } template T pop_front(multiset &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; } template T pop_back(multiset &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } // <<< // >>> modint template class modint { static_assert(md < (1u<<31), ""); using M = modint; using i64 = int64_t; uint32_t x; public: static constexpr uint32_t mod = md; constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { } constexpr i64 val() const { return x; } constexpr explicit operator i64() const { return x; } constexpr bool operator==(M r) const { return x == r.x; } constexpr bool operator!=(M r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; } constexpr M& operator/=(M r) { return *this *= r.inv(); } constexpr M operator+(M r) const { return M(*this) += r; } constexpr M operator-(M r) const { return M(*this) -= r; } constexpr M operator*(M r) const { return M(*this) *= r; } constexpr M operator/(M r) const { return M(*this) /= r; } friend constexpr M operator+(i64 x, M y) { return M(x)+y; } friend constexpr M operator-(i64 x, M y) { return M(x)-y; } friend constexpr M operator*(i64 x, M y) { return M(x)*y; } friend constexpr M operator/(i64 x, M y) { return M(x)/y; } constexpr M inv() const { assert(x > 0); return pow(md-2); } constexpr M pow(i64 n) const { assert(not (x == 0 and n == 0)); if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } #ifdef LOCAL friend string to_s(M r) { return to_s(r.val(), mod); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; // <<< //constexpr int64_t MOD = 998244353; constexpr int64_t MOD = 1e9+7; using mint = modint; mint sign(int n) { return n & 1 ? -1 : +1; } // >>> mod table template struct ModTable { vector fact, finv; void calc(int n) { int old = fact.size(); if (n < old) return; n += 1000; fact.resize(n+1); finv.resize(n+1); if (old == 0) { fact[0] = fact[1] = finv[0] = finv[1] = 1; old = 2; } for (auto i = old; i <= n; i++) fact[i] = fact[i-1] * i; finv[n] = mint(1) / fact[n]; for (auto i = n-1; i >= old; i--) finv[i] = finv[i+1] * (i+1); } }; ModTable mod_tab; mint fact(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.fact[n]; } mint finv(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.finv[n]; } mint comb(int n, int k) { if (n < 0 || k < 0 || n < k) return 0; mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[k] * mod_tab.finv[n-k]; } mint perm(int n, int k) { assert(k >= 0); assert(n >= k); mod_tab.calc(n); return mod_tab.fact[n] * mod_tab.finv[n-k]; } // <<< // >>> pair + - * += -= *= template constexpr auto operator+(pair const& p, pair const& q) { return make_pair(p.first + q.first, p.second + q.second); } template constexpr auto operator-(pair const& p, pair const& q) { return make_pair(p.first - q.first, p.second - q.second); } template constexpr auto operator*(pair const& p, C const& k) { return make_pair(p.first * k, p.second * k); } template constexpr auto operator*(C const& k, pair const& p) { return make_pair(k * p.first, k * p.second); } template constexpr auto& operator+=(pair& p, pair const& q) { return p = p + q; } template constexpr auto& operator-=(pair& p, pair const& q) { return p = p - q; } template constexpr auto operator*=(pair& p, C const& k) { return p = p * k; } // <<< // >>> BIT 2D template struct BIT2D { vector> pos; vector xs, ys; vector bit; vector idx; bool built = false; BIT2D() {} void add_point(Int x, Int y) { pos.emplace_back(x, y); built = false; } void build() { auto make_unique = [&](auto &v) { v.resize(unique(v.begin(), v.end())-v.begin()); }; sort(pos.begin(), pos.end()); make_unique(pos); for (auto [x, y] : pos) xs.push_back(x); make_unique(xs); int n = xs.size(); idx.resize(n+1); vector> z(n); int i = 0; for (auto [x, y] : pos) { if (xs[i] < x) i++; z[i].push_back(y); } for (i = 0; i < n; i++) { make_unique(z[i]); int j = i | (i + 1); if (j >= n) continue; int A = z[j].size(), B = z[i].size(); z[j].reserve(A + B); copy(z[i].begin(), z[i].end(), back_inserter(z[j])); inplace_merge(z[j].begin(), z[j].begin() + A, z[j].end()); } for (i = 0; i < n; i++) { copy(z[i].begin(), z[i].end(), back_inserter(ys)); idx[i+1] = ys.size(); } bit.resize(idx.back()); built = true; } void add(Int x, Int y, T const& val) { assert(built); int i = lower_bound(xs.begin(), xs.end(), x) - xs.begin(); assert(i < (int)xs.size() and xs[i] == x); for ( ; i < (int)xs.size(); i |= i + 1) { auto it = lower_bound(ys.begin() + idx[i], ys.begin() + idx[i+1], y); assert(it != ys.end() and *it == y); int j = it - (ys.begin() + idx[i]); for ( ; idx[i] + j < idx[i+1]; j |= j + 1) { bit[idx[i] + j] += val; } } } T sum(Int xr, Int yl, Int yr) const { assert(built); int i = lower_bound(xs.begin(), xs.end(), xr) - xs.begin(); // T s = 0; T s = pair(mint(0), mint(0)); for (i-- ; i >= 0; i = (i & (i + 1)) - 1) { int j = lower_bound(ys.begin() + idx[i], ys.begin() + idx[i+1], yr) - (ys.begin() + idx[i]); for (j-- ; j >= 0; j = (j & (j + 1)) - 1) { s += bit[idx[i] + j]; } j = lower_bound(ys.begin() + idx[i], ys.begin() + idx[i+1], yl) - (ys.begin() + idx[i]); for (j-- ; j >= 0; j = (j & (j + 1)) - 1) { s -= bit[idx[i] + j]; } } return s; } T sum(Int xl, Int xr, Int yl, Int yr) const { return sum(xr, yl, yr) - sum(xl, yl, yr); } T get(Int x, Int y) const { return sum(x, x+1, y, y+1); } vector dat() const { assert(built); vector ret; for (auto [x, y] : pos) ret.push_back(get(x, y)); return ret; } }; // <<< // >>> reord void reord_impl(vector const&) { } template void reord_impl(vector const& idx, C& v, Args&&... args) { auto t = v; rep (i, v.size()) t[i] = v[idx[i]]; swap(v, t); reord_impl(idx, forward(args)...); } template ()(0, 0))> void reord(Comp comp, C& v, Args&&... args) { vector idx(v.size()); iota(idx.begin(), idx.end(), 0); sort(idx.begin(), idx.end(), comp); reord_impl(idx, v, args...); } template void reord(C& v, Args&&... args) { vector idx(v.size()); iota(idx.begin(), idx.end(), 0); sort(idx.begin(), idx.end(), [&](int i, int j) { return v[i] < v[j]; }); reord_impl(idx, v, args...); } template void reordR(C& v, Args&&... args) { vector idx(v.size()); iota(idx.begin(), idx.end(), 0); sort(idx.begin(), idx.end(), [&](int i, int j) { return v[i] > v[j]; }); reord_impl(idx, v, args...); } // <<< int32_t main() { int n; cin >> n; vector a(n), b(n); cin >> a >> b; mint ans[2] = {}; rep (t, 2) { reord(a, b); using P = pair; // cnt, sum; BIT2D

bit; rep (i, n) bit.add_point(a[i]+b[i], a[i]-b[i]); bit.build(); rep (i, n) { auto [cnt, sum] = bit.sum(a[i]+b[i], -INF, a[i]-b[i]); dump(t, i, cnt, sum); ans[t] += a[i]*cnt - sum; bit.add(a[i]+b[i], a[i]-b[i], P(1, a[i])); } swap(a, b); ans[t] *= 2; } cout << ans << '\n'; }