// BEGIN: main.cpp
#line 1 "main.cpp"
// BEGIN: my_template.hpp
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#endif
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = numeric_limits<double>::infinity();
template <>
constexpr long double infty<long double> =
    numeric_limits<long double>::infinity();

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using pq_max = priority_queue<T>;
template <class T>
using pq_min = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b) - 1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define all(x) (x).begin(), (x).end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  struct iter {
    UINT s;
    iter(UINT s) : s(s) {}
    int operator*() const { return lowbit(s); }
    iter &operator++() {
      s &= s - 1;
      return *this;
    }
    bool operator!=(const iter) const { return s != 0; }
  };
  UINT s;
  all_bit(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename UINT>
struct all_subset {
  static_assert(is_unsigned<UINT>::value);
  struct iter {
    UINT s, t;
    bool ed;
    iter(UINT s) : s(s), t(s), ed(0) {}
    UINT operator*() const { return s ^ t; }
    iter &operator++() {
      (t == 0 ? ed = 1 : t = (t - 1) & s);
      return *this;
    }
    bool operator!=(const iter) const { return !ed; }
  };
  UINT s;
  all_subset(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

constexpr ll TEN[] = {
    1LL,
    10LL,
    100LL,
    1000LL,
    10000LL,
    100000LL,
    1000000LL,
    10000000LL,
    100000000LL,
    1000000000LL,
    10000000000LL,
    100000000000LL,
    1000000000000LL,
    10000000000000LL,
    100000000000000LL,
    1000000000000000LL,
    10000000000000000LL,
    100000000000000000LL,
    1000000000000000000LL,
};

template <typename T, typename U>
T SUM(const U &A) {
  return std::accumulate(A.begin(), A.end(), T{});
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C &c, const T &x) {
  return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C &c, const T &x) {
  return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (llabs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vc<T> cumsum(const vc<U> &A, int off = 1) {
  int N = A.size();
  vc<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vc<int> argsort(const vc<T> &A) {
  vc<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &...others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
// END: my_template.hpp
#line 2 "main.cpp"
// BEGIN: other/io.hpp
#line 1 "other/io.hpp"
#define FASTIO

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memmove(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') {
      minus = 1, c = ibuf[pil++];
    }
  }
  x = 0;
  while ('0' <= c) {
    x = x * 10 + (c & 15), c = ibuf[pil++];
  }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> rd(
    T &x) {
  rd_integer(x);
}

template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> rd(T &x) {
  rd_real(x);
}

template <class T, class U>
void rd(pair<T, U> &p) {
  rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < tuple_size<T>::value) {
    auto &x = get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d : x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d : x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &...t) {
  rd(h), read(t...);
}

// 先に用意（既出なら不要）
inline void wt_range(const char *s, size_t n) {
  size_t i = 0;
  while (i < n) {
    if (por == SZ) flush();
    size_t chunk = min(n - i, (size_t)(SZ - por));
    memcpy(obuf + por, s + i, chunk);
    por += chunk;
    i += chunk;
  }
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const char *s) { wt_range(s, strlen(s)); }
void wt(const string &s) { wt_range(s.data(), s.size()); }

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) {
    obuf[por++] = '-', x = -x;
  }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
inline void wt_real(T x) {
  char buf[64];
  // 有効数字 15 桁、通常/指数を自動選択（printf("%.15g") 相当）
  int n = std::snprintf(buf, sizeof(buf), "%.15g", (double)x);

  // （任意）-0 を 0 に正規化
  if (n == 2 && buf[0] == '-' && buf[1] == '0') {
    buf[0] = '0';
    n = 1;
  }
  wt_range(buf, (size_t)n);
}

template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> wt(
    T x) {
  wt_integer(x);
}

template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> wt(T x) {
  wt_real(x);
}

inline void wt(bool b) { wt(static_cast<char>('0' + (b ? 1 : 0))); }

template <class T, class U>
void wt(const pair<T, U> &val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T &t) {
  if constexpr (N < tuple_size<T>::value) {
    if constexpr (N > 0) wt(' ');
    wt(get<N>(t));
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(const tuple<T...> &tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> &val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> &val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
}  // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;

#if defined(LOCAL)
#define HDR "[DEBUG:", __func__, __LINE__, "]"
#define SHOW(...)                                                         \
  SHOW_IMPL(__VA_ARGS__, SHOW8, SHOW7, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, \
            SHOW1)                                                        \
  (__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, _7, _8, NAME, ...) NAME
#define SHOW1(x) print(HDR, #x, "=", (x)), flush()
#define SHOW2(x, y) print(HDR, #x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) \
  print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
  print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v)                                                  \
  print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
        (v)),                                                                 \
      flush()
#define SHOW6(x, y, z, w, v, u)                                               \
  print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
        (v), #u, "=", (u)),                                                   \
      flush()
#define SHOW7(x, y, z, w, v, u, t)                                            \
  print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
        (v), #u, "=", (u), #t, "=", (t)),                                     \
      flush()
#define SHOW8(x, y, z, w, v, u, t, s)                                         \
  print(HDR, #x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", \
        (v), #u, "=", (u), #t, "=", (t), #s, "=", (s)),                       \
      flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YA(!t); }
// END: other/io.hpp
#line 3 "main.cpp"

// BEGIN: ds/wavelet_matrix/wavelet_matrix_2d_range.hpp
#line 1 "ds/wavelet_matrix/wavelet_matrix_2d_range.hpp"
// BEGIN: ds/wavelet_matrix/wavelet_matrix.hpp
#line 1 "ds/wavelet_matrix/wavelet_matrix.hpp"
// BEGIN: ds/bit_vector.hpp
#line 1 "ds/bit_vector.hpp"
struct Bit_Vector {
  int n;
  bool prepared = 0;
  vc<pair<u64, u32>> dat;
  Bit_Vector(int n = 0) : n(n) { dat.assign((n + 127) >> 6, {0, 0}); }
  void set(int i) {
    assert(!prepared && (0 <= i && i < n));
    dat[i >> 6].fi |= u64(1) << (i & 63);
  }
  void reset() {
    fill(all(dat), pair<u64, u32>{0, 0});
    prepared = 0;
  }
  void build() {
    prepared = 1;
    FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
  }
  // [0, k) 内の 1 の個数
  bool operator[](int i) { return dat[i >> 6].fi >> (i & 63) & 1; }
  int count_prefix(int k, bool f = true) {
    assert(prepared);
    auto [a, b] = dat[k >> 6];
    int ret = b + popcnt(a & ((u64(1) << (k & 63)) - 1));
    return (f ? ret : k - ret);
  }
  int count(int L, int R, bool f = true) { return count_prefix(R, f) - count_prefix(L, f); }
  string to_string() {
    string ans;
    FOR(i, n) ans += '0' + (dat[i / 64].fi >> (i % 64) & 1);
    return ans;
  }
};
// END: ds/bit_vector.hpp
#line 2 "ds/wavelet_matrix/wavelet_matrix.hpp"
// BEGIN: ds/index_compression.hpp
#line 1 "ds/index_compression.hpp"
template <typename T>
struct Index_Compression_DISTINCT_SMALL {
  static_assert(is_same_v<T, int>);
  int mi, ma;
  vc<int> dat;
  vc<int> build(vc<int> X) {
    mi = 0, ma = -1;
    if (!X.empty()) mi = MIN(X), ma = MAX(X);
    dat.assign(ma - mi + 2, 0);
    for (auto& x: X) dat[x - mi + 1]++;
    FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
    for (auto& x: X) { x = dat[x - mi]++; }
    FOR_R(i, 1, len(dat)) dat[i] = dat[i - 1];
    dat[0] = 0;
    return X;
  }
  int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};

template <typename T>
struct Index_Compression_SAME_SMALL {
  static_assert(is_same_v<T, int>);
  int mi, ma;
  vc<int> dat;
  vc<int> build(vc<int> X) {
    mi = 0, ma = -1;
    if (!X.empty()) mi = MIN(X), ma = MAX(X);
    dat.assign(ma - mi + 2, 0);
    for (auto& x: X) dat[x - mi + 1] = 1;
    FOR(i, len(dat) - 1) dat[i + 1] += dat[i];
    for (auto& x: X) { x = dat[x - mi]; }
    return X;
  }
  int operator()(ll x) { return dat[clamp<ll>(x - mi, 0, ma - mi + 1)]; }
};

template <typename T>
struct Index_Compression_SAME_LARGE {
  vc<T> dat;
  vc<int> build(vc<T> X) {
    vc<int> I = argsort(X);
    vc<int> res(len(X));
    for (auto& i: I) {
      if (!dat.empty() && dat.back() == X[i]) {
        res[i] = len(dat) - 1;
      } else {
        res[i] = len(dat);
        dat.eb(X[i]);
      }
    }
    dat.shrink_to_fit();
    return res;
  }
  int operator()(T x) { return LB(dat, x); }
};

template <typename T>
struct Index_Compression_DISTINCT_LARGE {
  vc<T> dat;
  vc<int> build(vc<T> X) {
    vc<int> I = argsort(X);
    vc<int> res(len(X));
    for (auto& i: I) { res[i] = len(dat), dat.eb(X[i]); }
    dat.shrink_to_fit();
    return res;
  }
  int operator()(T x) { return LB(dat, x); }
};

template <typename T, bool SMALL>
using Index_Compression_DISTINCT = typename std::conditional<SMALL, Index_Compression_DISTINCT_SMALL<T>, Index_Compression_DISTINCT_LARGE<T>>::type;
template <typename T, bool SMALL>
using Index_Compression_SAME = typename std::conditional<SMALL, Index_Compression_SAME_SMALL<T>, Index_Compression_SAME_LARGE<T>>::type;

// SAME: [2,3,2] -> [0,1,0]
// DISTINCT: [2,2,3] -> [0,2,1]
// build で列を圧縮してくれる. そのあと
// (x): lower_bound(X,x) をかえす
template <typename T, bool SAME, bool SMALL>
using Index_Compression = typename std::conditional<SAME, Index_Compression_SAME<T, SMALL>, Index_Compression_DISTINCT<T, SMALL>>::type;
// END: ds/index_compression.hpp
#line 3 "ds/wavelet_matrix/wavelet_matrix.hpp"
// BEGIN: alg/monoid/add.hpp
#line 1 "alg/monoid/add.hpp"

template <typename E>
struct Monoid_Add {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
// END: alg/monoid/add.hpp
#line 4 "ds/wavelet_matrix/wavelet_matrix.hpp"

// 静的メソッドinverseの存在をチェックするテンプレート
template <typename, typename = std::void_t<>>
struct has_inverse : std::false_type {};

template <typename T>
struct has_inverse<T, std::void_t<decltype(T::inverse(std::declval<typename T::value_type>()))>> : std::true_type {};

struct Dummy_Data_Structure {
  using MX = Monoid_Add<bool>;
  void build(const vc<bool>& A) {}
};

template <typename Y, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix {
  using Mono = typename SEGTREE::MX;
  using T = typename Mono::value_type;
  static_assert(Mono::commute);

  int n, log, K;
  Index_Compression<Y, true, SMALL_Y> IDX;
  vc<Y> ItoY;
  vc<int> mid;
  vc<Bit_Vector> bv;
  vc<SEGTREE> seg;

  Wavelet_Matrix() {}
  Wavelet_Matrix(const vc<Y>& A) { build(A); }
  Wavelet_Matrix(const vc<Y>& A, vc<T>& SUM_Data) { build(A, SUM_Data); }
  template <typename F>
  Wavelet_Matrix(int n, F f) {
    build(n, f);
  }

  template <typename F>
  void build(int m, F f) {
    vc<Y> A(m);
    vc<T> S(m);
    for (int i = 0; i < m; ++i) {
      auto p = f(i);
      A[i] = p.fi, S[i] = p.se;
    }
    build(A, S);
  }

  void build(const vc<Y>& A) { build(A, vc<T>(len(A), Mono::unit())); }
  void build(const vc<Y>& A, vc<T> S) {
    n = len(A);
    vc<int> B = IDX.build(A);
    K = 0;
    for (auto& x: B) chmax(K, x + 1);
    ItoY.resize(K);
    FOR(i, n) ItoY[B[i]] = A[i];
    log = 0;
    while ((1 << log) < K) ++log;
    mid.resize(log), bv.assign(log, Bit_Vector(n));
    vc<int> B0(n), B1(n);
    vc<T> S0(n), S1(n);
    seg.resize(log + 1);
    seg[log].build(S);
    for (int d = log - 1; d >= 0; --d) {
      int p0 = 0, p1 = 0;
      for (int i = 0; i < n; ++i) {
        bool f = (B[i] >> d & 1);
        if (!f) { B0[p0] = B[i], S0[p0] = S[i], p0++; }
        if (f) { bv[d].set(i), B1[p1] = B[i], S1[p1] = S[i], p1++; }
      }
      swap(B, B0), swap(S, S0);
      move(B1.begin(), B1.begin() + p1, B.begin() + p0);
      move(S1.begin(), S1.begin() + p1, S.begin() + p0);
      mid[d] = p0, bv[d].build(), seg[d].build(S);
    }
  }

  // [L,R) x [0,y)
  int prefix_count(int L, int R, Y y) {
    int p = IDX(y);
    if (L == R || p == 0) return 0;
    if (p == K) return R - L;
    int cnt = 0;
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (p >> d & 1) cnt += r0 - l0, L = l1, R = r1;
      if (!(p >> d & 1)) L = l0, R = r0;
    }
    return cnt;
  }

  // [L,R) x [y1,y2)
  int count(int L, int R, Y y1, Y y2) { return prefix_count(L, R, y2) - prefix_count(L, R, y1); }

  // [L,R) x [0,y)
  pair<int, T> prefix_count_and_prod(int L, int R, Y y) {
    int p = IDX(y);
    if (p == 0) return {0, Mono::unit()};
    if (p == K) return {R - L, seg[log].prod(L, R)};
    int cnt = 0;
    T t = Mono::unit();
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (p >> d & 1) { cnt += r0 - l0, t = Mono::op(t, seg[d].prod(l0, r0)), L = l1, R = r1; }
      if (!(p >> d & 1)) L = l0, R = r0;
    }
    return {cnt, t};
  }

  // [L,R) x [y1,y2)
  pair<int, T> count_and_prod(int L, int R, Y y1, Y y2) {
    if constexpr (has_inverse<Mono>::value) {
      auto [c1, t1] = prefix_count_and_prod(L, R, y1);
      auto [c2, t2] = prefix_count_and_prod(L, R, y2);
      return {c2 - c1, Mono::op(Mono::inverse(t1), t2)};
    }
    int lo = IDX(y1), hi = IDX(y2), cnt = 0;
    T t = Mono::unit();
    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      assert(b - a == (1 << d));
      if (hi <= a || b <= lo) return;
      if (lo <= a && b <= hi) {
        cnt += R - L, t = Mono::op(t, seg[d].prod(L, R));
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return {cnt, t};
  }

  // [L,R) x [y1,y2)
  T prefix_prod(int L, int R, Y y) { return prefix_count_and_prod(L, R, y).se; }
  // [L,R) x [y1,y2)
  T prod(int L, int R, Y y1, Y y2) { return count_and_prod(L, R, y1, y2).se; }
  T prod_all(int L, int R) { return seg[log].prod(L, R); }

  Y kth(int L, int R, int k) {
    assert(0 <= k && k < R - L);
    int p = 0;
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (k < r0 - l0) {
        L = l0, R = r0;
      } else {
        k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
      }
    }
    return ItoY[p];
  }

  // y 以上最小 OR infty<Y>
  Y next(int L, int R, Y y) {
    int k = IDX(y);
    int p = K;

    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      if (p <= a || L == R || b <= k) return;
      if (d == 0) {
        chmin(p, a);
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l0, r0, a, c), dfs(dfs, d, l1, r1, c, b);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return (p == K ? infty<Y> : ItoY[p]);
  }

  // y 以下最大 OR -infty<T>
  Y prev(int L, int R, Y y) {
    int k = IDX(y + 1);
    int p = -1;
    auto dfs = [&](auto& dfs, int d, int L, int R, int a, int b) -> void {
      if (b - 1 <= p || L == R || k <= a) return;
      if (d == 0) {
        chmax(p, a);
        return;
      }
      --d;
      int c = (a + b) / 2;
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      dfs(dfs, d, l1, r1, c, b), dfs(dfs, d, l0, r0, a, c);
    };
    dfs(dfs, log, L, R, 0, 1 << log);
    return (p == -1 ? -infty<Y> : ItoY[p]);
  }

  Y median(bool UPPER, int L, int R) {
    assert(0 <= L && L < R && R <= n);
    int k = (UPPER ? (R - L) / 2 : (R - L - 1) / 2);
    return kth(L, R, k);
  }

  pair<Y, T> kth_value_and_prod(int L, int R, int k) {
    assert(0 <= k && k <= R - L);
    if (k == R - L) return {infty<Y>, seg[log].prod(L, R)};
    int p = 0;
    T t = Mono::unit();
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (k < r0 - l0) {
        L = l0, R = r0;
      } else {
        t = Mono::op(t, seg[d].prod(l0, r0)), k -= r0 - l0, L = l1, R = r1, p |= 1 << d;
      }
    }
    t = Mono::op(t, seg[0].prod(L, L + k));
    return {ItoY[p], t};
  }

  T prod_index_range(int L, int R, int k1, int k2) {
    static_assert(has_inverse<Mono>::value);
    T t1 = kth_value_and_prod(L, R, k1).se;
    T t2 = kth_value_and_prod(L, R, k2).se;
    return Mono::op(Mono::inverse(t1), t2);
  }

  // [L,R) x [0,y) での check(y, cnt, prod) が true となる最大の (cnt,prod)
  // ただし y はぴったりのところだけです
  template <typename F>
  tuple<Y, int, T> max_right(F check, int L, int R) {
    int cnt = 0;
    int p = 0;
    T t = Mono::unit();
    assert(check(-infty<Y>, 0, Mono::unit()));
    if (check(infty<Y>, R - L, seg[log].prod(L, R))) { return {infty<Y>, R - L, seg[log].prod(L, R)}; }
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      int cnt1 = cnt + r0 - l0;
      int p1 = p | 1 << d;
      T t1 = Mono::op(t, seg[d].prod(l0, r0));
      int y1 = (p1 < len(ItoY) ? ItoY[p1] : infty<Y>);
      if (check(y1, cnt1, t1)) {
        p = p1, cnt = cnt1, t = t1, L = l1, R = r1;
      } else {
        L = l0, R = r0;
      }
    }
    int y = (p < len(ItoY) ? ItoY[p] : infty<Y>);
    return {y, cnt, t};
  }

  void set(int i, T t) {
    assert(0 <= i && i < n);
    int L = i, R = i + 1;
    seg[log].set(L, t);
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (l0 < r0) L = l0, R = r0;
      if (l0 == r0) L = l1, R = r1;
      seg[d].set(L, t);
    }
  }
  void multiply(int i, T t) {
    assert(0 <= i && i < n);
    int L = i, R = i + 1;
    seg[log].multiply(L, t);
    for (int d = log - 1; d >= 0; --d) {
      int l0 = bv[d].count_prefix(L, 0), r0 = bv[d].count_prefix(R, 0);
      int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0;
      if (l0 < r0) L = l0, R = r0;
      if (l0 == r0) L = l1, R = r1;
      seg[d].multiply(L, t);
    }
  }
  void add(int i, T t) { multiply(i, t); }
};
// END: ds/wavelet_matrix/wavelet_matrix.hpp
#line 2 "ds/wavelet_matrix/wavelet_matrix_2d_range.hpp"

template <typename XY, bool SMALL_X, bool SMALL_Y, typename SEGTREE = Dummy_Data_Structure>
struct Wavelet_Matrix_2D_Range {
  // 点群を X 昇順に並べる.
  Wavelet_Matrix<XY, SMALL_Y, SEGTREE> WM;
  using Mono = typename SEGTREE::MX;
  using T = typename Mono::value_type;
  static_assert(Mono::commute);

  Index_Compression<XY, false, SMALL_X> IDX_X;

  int n;
  vc<int> new_idx;

  template <typename F>
  Wavelet_Matrix_2D_Range(int n, F f) {
    build(n, f);
  }

  template <typename F>
  void build(int m, F f) {
    n = m;
    vc<XY> X(n), Y(n);
    vc<T> S(n);
    FOR(i, n) {
      auto tmp = f(i);
      X[i] = get<0>(tmp), Y[i] = get<1>(tmp), S[i] = get<2>(tmp);
    }
    new_idx = IDX_X.build(X);
    vc<int> I(n);
    FOR(i, n) I[new_idx[i]] = i;
    Y = rearrange(Y, I);
    S = rearrange(S, I);
    WM.build(Y, S);
  }

  int count(XY x1, XY x2, XY y1, XY y2) { return WM.count(IDX_X(x1), IDX_X(x2), y1, y2); }

  // [L,R) x [-inf,y)
  pair<int, T> prefix_count_and_prod(XY x1, XY x2, XY y) { return WM.prefix_count_and_prod(IDX_X(x1), IDX_X(x2), y); }

  // [L,R) x [y1,y2)
  pair<int, T> count_and_prod(XY x1, XY x2, XY y1, XY y2) { return WM.count_and_prod(IDX_X(x1), IDX_X(x2), y1, y2); }

  // [L,R) x [-inf,inf)
  T prod_all(XY x1, XY x2) { return WM.prod_all(IDX_X(x1), IDX_X(x2)); }
  // [L,R) x [-inf,y)
  T prefix_prod(XY x1, XY x2, XY y) { return WM.prefix_prod(IDX_X(x1), IDX_X(x2), y); }
  // [L,R) x [y1,y2)
  T prod(XY x1, XY x2, XY y1, XY y2) { return WM.prod(IDX_X(x1), IDX_X(x2), y1, y2); }

  // [L,R) x [-inf,y) での check(cnt, prod) が true となる最大の (cnt,prod)
  template <typename F>
  pair<int, T> max_right(F check, XY x1, XY x2) {
    return WM.max_right(check, IDX_X(x1), IDX_X(x2));
  }

  // i は最初に渡したインデックス
  void set(int i, T t) { WM.set(new_idx[i], t); }
  // i は最初に渡したインデックス
  void multiply(int i, T t) { WM.multiply(new_idx[i], t); }
  void add(int i, T t) { WM.multiply(new_idx[i], t); }
};// END: ds/wavelet_matrix/wavelet_matrix_2d_range.hpp
#line 5 "main.cpp"
#line 6 "main.cpp"
// BEGIN: ds/fenwicktree/fenwicktree_01.hpp
#line 1 "ds/fenwicktree/fenwicktree_01.hpp"

// BEGIN: ds/fenwicktree/fenwicktree.hpp
#line 1 "ds/fenwicktree/fenwicktree.hpp"
#line 3 "ds/fenwicktree/fenwicktree.hpp"

template <typename Monoid>
struct FenwickTree {
  using G = Monoid;
  using MX = Monoid;
  using E = typename G::value_type;
  int n;
  vector<E> dat;
  E total;

  FenwickTree() {}
  FenwickTree(int n) { build(n); }
  template <typename F>
  FenwickTree(int n, F f) {
    build(n, f);
  }
  FenwickTree(const vc<E>& v) { build(v); }

  void build(int m) {
    n = m;
    dat.assign(m, G::unit());
    total = G::unit();
  }
  void build(const vc<E>& v) {
    build(len(v), [&](int i) -> E { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m;
    dat.clear();
    dat.reserve(n);
    total = G::unit();
    FOR(i, n) { dat.eb(f(i)); }
    for (int i = 1; i <= n; ++i) {
      int j = i + (i & -i);
      if (j <= n) dat[j - 1] = G::op(dat[i - 1], dat[j - 1]);
    }
    total = prefix_sum(m);
  }

  E prod_all() { return total; }
  E sum_all() { return total; }
  E sum(int k) { return prefix_sum(k); }
  E prod(int k) { return prefix_prod(k); }
  E prefix_sum(int k) { return prefix_prod(k); }
  E prefix_prod(int k) {
    chmin(k, n);
    E ret = G::unit();
    for (; k > 0; k -= k & -k) ret = G::op(ret, dat[k - 1]);
    return ret;
  }
  E sum(int L, int R) { return prod(L, R); }
  E prod(int L, int R) {
    chmax(L, 0), chmin(R, n);
    if (L == 0) return prefix_prod(R);
    assert(0 <= L && L <= R && R <= n);
    E pos = G::unit(), neg = G::unit();
    while (L < R) { pos = G::op(pos, dat[R - 1]), R -= R & -R; }
    while (R < L) { neg = G::op(neg, dat[L - 1]), L -= L & -L; }
    return G::op(pos, G::inverse(neg));
  }

  vc<E> get_all() {
    vc<E> res(n);
    FOR(i, n) res[i] = prod(i, i + 1);
    return res;
  }

  void add(int k, E x) { multiply(k, x); }
  void multiply(int k, E x) {
    static_assert(G::commute);
    total = G::op(total, x);
    for (++k; k <= n; k += k & -k) dat[k - 1] = G::op(dat[k - 1], x);
  }
  void set(int k, E x) { add(k, G::op(G::inverse(prod(k, k + 1)), x)); }

  template <class F>
  int max_right(const F check, int L = 0) {
    assert(check(G::unit()));
    E s = G::unit();
    int i = L;
    // 2^k 進むとダメ
    int k = [&]() {
      while (1) {
        if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; }
        if (i == 0) { return topbit(n) + 1; }
        int k = lowbit(i) - 1;
        if (i + (1 << k) > n) return k;
        E t = G::op(s, dat[i + (1 << k) - 1]);
        if (!check(t)) { return k; }
        s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i;
      }
    }();
    while (k) {
      --k;
      if (i + (1 << k) - 1 < len(dat)) {
        E t = G::op(s, dat[i + (1 << k) - 1]);
        if (check(t)) { i += (1 << k), s = t; }
      }
    }
    return i;
  }

  // check(i, x)
  template <class F>
  int max_right_with_index(const F check, int L = 0) {
    assert(check(L, G::unit()));
    E s = G::unit();
    int i = L;
    // 2^k 進むとダメ
    int k = [&]() {
      while (1) {
        if (i % 2 == 1) { s = G::op(s, G::inverse(dat[i - 1])), i -= 1; }
        if (i == 0) { return topbit(n) + 1; }
        int k = lowbit(i) - 1;
        if (i + (1 << k) > n) return k;
        E t = G::op(s, dat[i + (1 << k) - 1]);
        if (!check(i + (1 << k), t)) { return k; }
        s = G::op(s, G::inverse(dat[i - 1])), i -= i & -i;
      }
    }();
    while (k) {
      --k;
      if (i + (1 << k) - 1 < len(dat)) {
        E t = G::op(s, dat[i + (1 << k) - 1]);
        if (check(i + (1 << k), t)) { i += (1 << k), s = t; }
      }
    }
    return i;
  }

  template <class F>
  int min_left(const F check, int R) {
    assert(check(G::unit()));
    E s = G::unit();
    int i = R;
    // false になるところまで戻る
    int k = 0;
    while (i > 0 && check(s)) {
      s = G::op(s, dat[i - 1]);
      k = lowbit(i);
      i -= i & -i;
    }
    if (check(s)) {
      assert(i == 0);
      return 0;
    }
    // 2^k 進むと ok になる
    // false を維持して進む
    while (k) {
      --k;
      E t = G::op(s, G::inverse(dat[i + (1 << k) - 1]));
      if (!check(t)) { i += (1 << k), s = t; }
    }
    return i + 1;
  }

  int kth(E k, int L = 0) {
    return max_right([&k](E x) -> bool { return x <= k; }, L);
  }
};
// END: ds/fenwicktree/fenwicktree.hpp
#line 4 "ds/fenwicktree/fenwicktree_01.hpp"

struct FenwickTree_01 {
  using MX = Monoid_Add<int>;
  int N, n;
  vc<u64> dat;
  FenwickTree<Monoid_Add<int>> bit;
  FenwickTree_01() {}
  FenwickTree_01(int n) { build(n); }
  template <typename F>
  FenwickTree_01(int n, F f) {
    build(n, f);
  }

  void build(int m) {
    N = m;
    n = ceil<int>(N + 1, 64);
    dat.assign(n, u64(0));
    bit.build(n);
  }
  void build(vc<int> dat) {
    build(len(dat), [&](int i) -> int { return dat[i]; });
  }

  template <typename F>
  void build(int m, F f) {
    N = m;
    n = ceil<int>(N + 1, 64);
    dat.assign(n, u64(0));
    FOR(i, N) { dat[i / 64] |= u64(f(i)) << (i % 64); }
    bit.build(n, [&](int i) -> int { return popcnt(dat[i]); });
  }

  int sum_all() { return bit.sum_all(); }
  int sum(int k) { return prefix_sum(k); }
  int prefix_sum(int k) {
    int ans = bit.sum(k / 64);
    ans += popcnt(dat[k / 64] & ((u64(1) << (k % 64)) - 1));
    return ans;
  }
  int sum(int L, int R) {
    if (L == 0) return prefix_sum(R);
    int ans = 0;
    ans -= popcnt(dat[L / 64] & ((u64(1) << (L % 64)) - 1));
    ans += popcnt(dat[R / 64] & ((u64(1) << (R % 64)) - 1));
    ans += bit.sum(L / 64, R / 64);
    return ans;
  }
  int prod(int L, int R) { return sum(L, R); }

  void add(int k, int x) {
    if (x == 1) add(k);
    elif (x == -1) remove(k);
    else assert(0);
  }
  void multiply(int k, int x) { add(k, x); }

  void add(int k) {
    dat[k / 64] |= u64(1) << (k % 64);
    bit.add(k / 64, 1);
  }
  void remove(int k) {
    dat[k / 64] &= ~(u64(1) << (k % 64));
    bit.add(k / 64, -1);
  }

  int kth(int k, int L = 0) {
    if (k >= sum_all()) return N;
    k += popcnt(dat[L / 64] & ((u64(1) << (L % 64)) - 1));
    L /= 64;
    int mid = 0;
    auto check = [&](auto e) -> bool {
      if (e <= k) chmax(mid, e);
      return e <= k;
    };
    int idx = bit.max_right(check, L);
    if (idx == n) return N;
    k -= mid;
    u64 x = dat[idx];
    int p = popcnt(x);
    if (p <= k) return N;
    k = binary_search([&](int n) -> bool { return (p - popcnt(x >> n)) <= k; }, 0, 64, 0);
    return 64 * idx + k;
  }

  int next(int k) {
    int idx = k / 64;
    k %= 64;
    u64 x = dat[idx] & ~((u64(1) << k) - 1);
    if (x) return 64 * idx + lowbit(x);
    idx = bit.kth(0, idx + 1);
    if (idx == n || !dat[idx]) return N;
    return 64 * idx + lowbit(dat[idx]);
  }

  int prev(int k) {
    if (k == N) --k;
    int idx = k / 64;
    k %= 64;
    u64 x = dat[idx];
    if (k < 63) x &= (u64(1) << (k + 1)) - 1;
    if (x) return 64 * idx + topbit(x);
    idx = bit.min_left([&](auto e) -> bool { return e <= 0; }, idx) - 1;
    if (idx == -1) return -1;
    return 64 * idx + topbit(dat[idx]);
  }
};// END: ds/fenwicktree/fenwicktree_01.hpp
#line 7 "main.cpp"

void solve() {
  LL(N);
  vi L(N), R(N);
  FOR(i, N) read(L[i], R[i]);

  // Wavelet_Matrix_2D_Range<int, 1, 1, FenwickTree<Monoid_Add<int>>> WM(
  //     N, [&](int i) -> tuple<int, int, int> { return {L[i], R[i], 0}; });
  Wavelet_Matrix_2D_Range<int, 1, 1, FenwickTree_01> WM(
      N, [&](int i) -> tuple<int, int, int> { return {L[i], R[i], 0}; });

  ll ANS = 0;
  FOR(i, N) {
    ANS += WM.prod(0, L[i], R[i] + 1, infty<int>);
    WM.add(i, 1);
  }
  print(ANS);
}

signed main() { solve(); }
// END: main.cpp