/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define ISIZE(x) ((int)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // tuple 出力 template ostream &operator<<(ostream &os, tuple &a) { if constexpr (N < std::tuple_size_v>) { os << get(a); if constexpr (N + 1 < std::tuple_size_v>) { os << ' '; } else if constexpr (end_line) { os << '\n'; } return operator<<(os, a); } return os; } template void print_tuple(tuple &a) { operator<<<0, true>(cout, a); } void pprint() { cout << endl; } template void pprint(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail) > 0) cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifndef MYLOCAL #undef DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ assert((cin >> __VA_ARGS__)); template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } template constexpr void operator--(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]--; } template constexpr void operator++(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]++; } /* #endregion */ // #include // using namespace atcoder; /* #region BIT */ template struct BinaryIndexedTree { vector data; BinaryIndexedTree(int sz) { data.assign(++sz, 0); } T sum(int k) const { T ret = 0; for (++k; k > 0; k -= k & -k) ret += data[k]; return (ret); } void add(int k, const T &x) { for (++k; k < SIZE(data); k += k & -k) data[k] += x; } // query for [l, r) // subtraction is required T query(const int l, const int r) const { return sum(r - 1) - sum(l - 1); } }; /* #endregion */ /* #region CoordCompress1D */ // 1次元座圧 template class CoordCompress1D { map coord2zipped; // キーが座標値 vc zipped2coord; // 各要素が座標値 ll sz; T MAX, MIN; public: CoordCompress1D() {} CoordCompress1D(vc coords, const T &MAX = INF, const T &MIN = -INF) : MAX(MAX), MIN(MIN) { sort(ALL(coords)); UNIQ(coords); sz = SIZE(coords); zipped2coord = coords; REP(i, 0, sz) coord2zipped[coords[i]] = i; } // 座標の圧縮(コンストラクタに与えた座標限定) ll zip(const T &coord) const { return coord2zipped.at(coord); } T unzip(const ll &zipped) const { return zipped2coord.at(zipped); } // coord 以上の最小の座標値を返す. // 戻り値は圧縮前なので注意.入力も圧縮前. T coord_geq(const T &coord) const { auto it = lower_bound(ALL(zipped2coord), coord); if (it != zipped2coord.end()) return *it; return MAX; } // coord より大きいの最小の座標値を返す. // 戻り値は圧縮前なので注意.入力も圧縮前. T coord_gt(const T &coord) const { auto it = upper_bound(ALL(zipped2coord), coord); if (it != zipped2coord.end()) return *it; return MAX; } // coord 以下の最小の座標値を返す. // 戻り値は圧縮前なので注意.入力も圧縮前. T coord_leq(const T &coord) const { auto rit = lower_bound(zipped2coord.rbegin(), zipped2coord.rend(), coord, [](ll const lhs, ll const rhs) { return lhs > rhs; }); if (rit != zipped2coord.rend()) return *rit; return MIN; } // coord 未満の最小の座標値を返す. // 戻り値は圧縮前なので注意.入力も圧縮前. T coord_lt(const T &coord) const { auto rit = upper_bound(zipped2coord.rbegin(), zipped2coord.rend(), coord, [](ll const lhs, ll const rhs) { return lhs > rhs; }); if (rit != zipped2coord.rend()) return *rit; return MIN; } ll size() const { return sz; } }; /* #endregion */ // Problem void solve() { VAR(ll, n); vll a(n), b(n); cin >> a, b; // a[i]+b[i] の大きい順に見ていく map mp; // (a[i]+b[i]) -> indices REP(i, 0, n) { ll sum = a[i] + b[i]; mp[sum].push_back(i); } vvll queries; for (auto [k, v] : mp) { queries.push_back(v); } reverse(ALL(queries)); // a[i]-b[i] の区間を考える vll coords(n); REP(i, 0, n) coords[i] = a[i] - b[i]; CoordCompress1D<> cc(coords); ll sz = cc.size(); BinaryIndexedTree bit(sz); ll ans = 0; for (const vll &indices : queries) { // 数える for (const ll &i : indices) { ll zipped = cc.zip(a[i] - b[i]); if (zipped != sz - 1) { ans += bit.query(zipped + 1, sz); } } // 足す for (const ll &i : indices) { ll zipped = cc.zip(a[i] - b[i]); bit.add(zipped, 1); } } pprint(ans); } // entry point int main() { solve(); return 0; }