#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif template struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val; MDCONST ModInt() : val(0) {} MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; } MDCONST ModInt(lint v) { _setval(v % md + md); } MDCONST explicit operator bool() const { return val != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); } MDCONST ModInt operator-() const { return ModInt()._setval(md - val); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.inv() % md); } MDCONST bool operator==(const ModInt &x) const { return val == x.val; } MDCONST bool operator!=(const ModInt &x) const { return val != x.val; } MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; } MDCONST ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static std::vector facs, facinvs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } MDCONST lint inv() const { if (this->val < std::min(md >> 1, 1 << 21)) { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val].val; } else { return this->pow(md - 2).val; } } MDCONST ModInt fac() const { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val]; } MDCONST ModInt facinv() const { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val]; } MDCONST ModInt doublefac() const { lint k = (this->val + 1) / 2; return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv(); } MDCONST ModInt nPr(const ModInt &r) const { return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv(); } ModInt sqrt() const { if (val == 0) return 0; if (md == 2) return val; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val, md - x.val)); } }; template std::vector> ModInt::facs = {1}; template std::vector> ModInt::facinvs = {1}; template std::vector> ModInt::invs = {0}; using mint = ModInt<1000000007>; #ifndef ATCODER_INTERNAL_BITOP_HPP #define ATCODER_INTERNAL_BITOP_HPP 1 #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #endif // ATCODER_INTERNAL_BITOP_HPP #ifndef ATCODER_SEGTREE_HPP #define ATCODER_SEGTREE_HPP 1 #include #include #include // #include "atcoder/internal_bit" namespace atcoder { template struct segtree { public: segtree() : segtree(0) {} explicit segtree(int n) : segtree(std::vector(n, e())) {} explicit segtree(const std::vector &v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) const { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) const { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() const { return d[1]; } template int max_right(int l) const { return max_right(l, [](S x) { return f(x); }); } template int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template int min_left(int r) const { return min_left(r, [](S x) { return f(x); }); } template int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; } // namespace atcoder #endif // ATCODER_SEGTREE_HPP // Reference: https://atcoder.github.io/ac-library/document_ja/segtree.html /* usage: struct S { long long su; int nb; }; S e() { return {0, 0}; } S op(S l, S r) { return {l.su + r.su, l.nb + r.nb}; } vector seginit(100000, e()); atcoder::segtree segtree(seginit); */ #include #include #include #include // 逆元を要求しない領域木 template class rangetree { int n; using Pt = std::pair; std::vector _pts; std::vector> _range2yxs; std::vector> segtrees; void _set(int v, Pt p, S val) { auto i = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first})); segtrees[v].set(i, val); } void _add(int v, Pt p, S val) { auto i = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first})); segtrees[v].set(i, op(segtrees[v].get(i), val)); } S _prod(int v, Coordinate yl, Coordinate yr) const { auto comp = [&](const Pt &l, const Pt &r) { return l.first < r.first; }; auto il = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yl, yl}, comp)); auto ir = std::distance( _range2yxs[v].begin(), std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yr, yr}, comp)); return segtrees[v].prod(il, ir); } public: rangetree() = default; void add_point(Coordinate x, Coordinate y) noexcept { _pts.emplace_back(x, y); } void build() { std::sort(_pts.begin(), _pts.end()); _pts.erase(std::unique(_pts.begin(), _pts.end()), _pts.end()); n = _pts.size(); _range2yxs.resize(n * 2); for (int i = 0; i < n; i++) _range2yxs[n + i] = {{_pts[i].second, _pts[i].first}}; for (int i = n - 1; i > 0; i--) { auto &lch = _range2yxs[i * 2]; auto &rch = _range2yxs[i * 2 + 1]; std::merge( lch.begin(), lch.end(), rch.begin(), rch.end(), std::back_inserter(_range2yxs[i])); _range2yxs[i].erase( std::unique(_range2yxs[i].begin(), _range2yxs[i].end()), _range2yxs[i].end()); } for (const auto &v : _range2yxs) segtrees.emplace_back(v.size()); } void set(Coordinate x, Coordinate y, S val) { int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, y})); assert(i < n and _pts[i] == std::make_pair(x, y)); for (i += n; i; i >>= 1) _set(i, {x, y}, val); } void add(Coordinate x, Coordinate y, S val) { int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, y})); assert(i < n and _pts[i] == std::make_pair(x, y)); for (i += n; i; i >>= 1) _add(i, {x, y}, val); } S prod(Coordinate xl, Coordinate xr, Coordinate yl, Coordinate yr) const { auto comp = [](const Pt &l, const Pt &r) { return l.first < r.first; }; int l = n + std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{xl, yr}, comp)); int r = n + std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{xr, yr}, comp)); S ret = e(); while (l < r) { if (l & 1) ret = op(ret, _prod(l++, yl, yr)); if (r & 1) ret = op(ret, _prod(--r, yl, yr)); l >>= 1, r >>= 1; } return ret; } S get(Coordinate x, Coordinate y) const { return prod(x, x + 1, y, y + 1); } }; struct S { int nv; mint xsum, ysum; mint eval1(mint x, mint y) const { return xsum + ysum - nv * (x + y); } mint eval2(mint x, mint y) const { return xsum - ysum - nv * (x - y); } }; S e() { return {0, 0, 0}; } S op(S l, S r) { return {l.nv + r.nv, l.xsum + r.xsum, l.ysum + r.ysum}; } // 0-indexed BIT (binary indexed tree / Fenwick tree) (i : [0, len)) template struct BIT { int n; std::vector data; BIT(int len = 0) : n(len), data(len) {} void reset() { std::fill(data.begin(), data.end(), T(0)); } void add(int pos, T v) { // a[pos] += v pos++; while (pos > 0 and pos <= n) data[pos - 1] += v, pos += pos & -pos; } T sum(int k) const { // a[0] + ... + a[k - 1] T res = 0; while (k > 0) res += data[k - 1], k -= k & -k; return res; } T sum(int l, int r) const { return sum(r) - sum(l); } // a[l] + ... + a[r - 1] template friend OStream &operator<<(OStream &os, const BIT &bit) { T prv = 0; os << '['; for (int i = 1; i <= bit.n; i++) { T now = bit.sum(i); os << now - prv << ',', prv = now; } return os << ']'; } }; int main() { int N; cin >> N; vector A(N), B(N); cin >> A >> B; vector uv; map> v2us; vector us; REP(i, N) { auto u = A[i] - B[i]; auto v = A[i] + B[i]; uv.emplace_back(u, v); v2us[v].push_back(u); us.push_back(u); } dbg(uv); us = sort_unique(us); BIT sum_x(us.size()), sum_y(us.size()), sum_1(us.size()); // rangetree tree; // for (auto [u, v] : uv) tree.add_point(u, v); // tree.build(); // for (auto [u, v] : uv) { // tree.add(u, v, S{1, u, v}); // } mint ret0 = 0, ret1 = 0; constexpr lint INF = 1LL << 60; for (const auto &[v, uuu] : v2us) { for (lint u : uuu) { int p = arglb(us, u); ret0 += sum_1.sum(0, p) * mint(u + v) - sum_x.sum(0, p) - sum_y.sum(0, p); ret1 += sum_1.sum(p + 1, us.size()) * mint(-u + v) + sum_x.sum(p + 1, us.size()) - sum_y.sum(p + 1, us.size()); } for (lint u : uuu) { int p = arglb(us, u); sum_x.add(p, u); sum_y.add(p, v); sum_1.add(p, 1); } } // for (auto [u, v] : uv) { // ret0 += tree.prod(u + 1, INF, v + 1, INF).eval1(u, v); // ret1 += tree.prod(u + 1, INF, -INF, v).eval2(u, v); // } cout << ret0 << ' ' << ret1 << '\n'; }