#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

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

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 vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = 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 FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#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); }
// (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, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#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 <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  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 (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<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>
vector<int> argsort(const vector<T> &A) {
  vector<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;
}
#endif
#line 1 "library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};

struct has_read_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.read(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __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); }
#line 3 "main.cpp"

#line 2 "library/mod/modint_common.hpp"

struct has_mod_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {0, 1};
  assert(0 <= n);
  if (n >= mod) n %= mod;
  while (len(dat) <= n) {
    int k = len(dat);
    int q = (mod + k - 1) / k;
    dat.eb(dat[k * q - mod] * mint(q));
  }
  return dat[n];
}

template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  assert(0 <= n);
  if (n >= mod) return 0;
  static vector<mint> dat = {1, 1};
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint(len(dat)));
  return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
  return dat[n];
}

template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
  return (mint(1) * ... * fact_inv<mint>(xs));
}

template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
  return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}

template <typename mint>
mint C_dense(int n, int k) {
  static vvc<mint> C;
  static int H = 0, W = 0;
  auto calc = [&](int i, int j) -> mint {
    if (i == 0) return (j == 0 ? mint(1) : mint(0));
    return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
  };
  if (W <= k) {
    FOR(i, H) {
      C[i].resize(k + 1);
      FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    FOR(i, H, n + 1) {
      C[i].resize(W);
      FOR(j, W) { C[i][j] = calc(i, j); }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  if (dense) return C_dense<mint>(n, k);
  if (!large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
  assert(n >= 0);
  assert(0 <= k && k <= n);
  if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / C<mint, 1>(n, k);
}

// [x^d] (1-x) ^ {-n} の計算
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
  assert(n >= 0);
  if (d < 0) return mint(0);
  if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
  return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "library/mod/modint.hpp"

template <int mod>
struct modint {
  static_assert(mod < (1 << 30));
  int val;
  constexpr modint(const ll val = 0) noexcept
      : val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}
  bool operator<(const modint &other) const {
    return val < other.val;
  } // To use std::map
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= mod) val -= mod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += mod - p.val) >= mod) val -= mod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = (int)(1LL * val * p.val % mod);
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint(-val); }
  modint operator+(const modint &p) const { return modint(*this) += p; }
  modint operator-(const modint &p) const { return modint(*this) -= p; }
  modint operator*(const modint &p) const { return modint(*this) *= p; }
  modint operator/(const modint &p) const { return modint(*this) /= p; }
  bool operator==(const modint &p) const { return val == p.val; }
  bool operator!=(const modint &p) const { return val != p.val; }
  modint inverse() const {
    int a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint(u);
  }
  modint pow(ll n) const {
    assert(n >= 0);
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
#ifdef FASTIO
  void write() { fastio::printer.write(val); }
  void read() { fastio::scanner.read(val); }
#endif
  static constexpr int get_mod() { return mod; }
  // (n, r), r は 1 の 2^n 乗根
  static constexpr pair<int, int> ntt_info() {
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 880803841) return {23, 211};
    if (mod == 998244353) return {23, 31};
    if (mod == 1045430273) return {20, 363};
    if (mod == 1051721729) return {20, 330};
    if (mod == 1053818881) return {20, 2789};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 2 "library/alg/monoid/min.hpp"

template <typename E>
struct Monoid_Min {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
  static constexpr X unit() { return infty<E>; }
  static constexpr bool commute = true;
};
#line 2 "library/alg/monoid/max.hpp"

template <typename E>
struct Monoid_Max {
  using X = E;
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return max(x, y); }
  static constexpr X unit() { return -infty<E>; }
  static constexpr bool commute = true;
};
#line 7 "main.cpp"

#line 2 "library/ds/segtree/segtree.hpp"

template <class Monoid>
struct SegTree {
  using MX = Monoid;
  using X = typename MX::value_type;
  using value_type = X;
  vc<X> dat;
  int n, log, size;

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

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat.assign(size << 1, MX::unit());
    FOR(i, n) dat[size + i] = f(i);
    FOR_R(i, 1, size) update(i);
  }

  X get(int i) { return dat[size + i]; }
  vc<X> get_all() { return {dat.begin() + size, dat.begin() + size + n}; }

  void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
  void set(int i, const X& x) {
    assert(i < n);
    dat[i += size] = x;
    while (i >>= 1) update(i);
  }

  void multiply(int i, const X& x) {
    assert(i < n);
    i += size;
    dat[i] = Monoid::op(dat[i], x);
    while (i >>= 1) update(i);
  }

  X prod(int L, int R) {
    assert(0 <= L && L <= R && R <= n);
    X vl = Monoid::unit(), vr = Monoid::unit();
    L += size, R += size;
    while (L < R) {
      if (L & 1) vl = Monoid::op(vl, dat[L++]);
      if (R & 1) vr = Monoid::op(dat[--R], vr);
      L >>= 1, R >>= 1;
    }
    return Monoid::op(vl, vr);
  }

  X prod_all() { return dat[1]; }

  template <class F>
  int max_right(F check, int L) {
    assert(0 <= L && L <= n && check(Monoid::unit()));
    if (L == n) return n;
    L += size;
    X sm = Monoid::unit();
    do {
      while (L % 2 == 0) L >>= 1;
      if (!check(Monoid::op(sm, dat[L]))) {
        while (L < size) {
          L = 2 * L;
          if (check(Monoid::op(sm, dat[L]))) { sm = Monoid::op(sm, dat[L++]); }
        }
        return L - size;
      }
      sm = Monoid::op(sm, dat[L++]);
    } while ((L & -L) != L);
    return n;
  }

  template <class F>
  int min_left(F check, int R) {
    assert(0 <= R && R <= n && check(Monoid::unit()));
    if (R == 0) return 0;
    R += size;
    X sm = Monoid::unit();
    do {
      --R;
      while (R > 1 && (R % 2)) R >>= 1;
      if (!check(Monoid::op(dat[R], sm))) {
        while (R < size) {
          R = 2 * R + 1;
          if (check(Monoid::op(dat[R], sm))) { sm = Monoid::op(dat[R--], sm); }
        }
        return R + 1 - size;
      }
      sm = Monoid::op(dat[R], sm);
    } while ((R & -R) != R);
    return 0;
  }

  // prod_{l<=i<r} A[i xor x]
  X xor_prod(int l, int r, int xor_val) {
    static_assert(Monoid::commute);
    X x = Monoid::unit();
    for (int k = 0; k < log + 1; ++k) {
      if (l >= r) break;
      if (l & 1) { x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]); }
      if (r & 1) { x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]); }
      l /= 2, r /= 2, xor_val /= 2;
    }
    return x;
  }
};
#line 1 "library/ds/offline_query/add_remove_query.hpp"
/*
・時刻 t に x を追加する
・時刻 t に x を削除する
があるときに、
・時刻 [l, r) に x を追加する
に変換する。
クエリが時系列順に来ることが分かっているときは monotone = true の方が高速。
*/
template <typename X, bool monotone>
struct Add_Remove_Query {
  map<X, int> MP;
  vc<tuple<int, int, X>> dat;
  map<X, vc<int>> ADD;
  map<X, vc<int>> RM;

  void add(int time, X x) {
    if (monotone) return add_monotone(time, x);
    ADD[x].eb(time);
  }
  void remove(int time, X x) {
    if (monotone) return remove_monotone(time, x);
    RM[x].eb(time);
  }

  // すべてのクエリが終わった現在時刻を渡す
  vc<tuple<int, int, X>> calc(int time) {
    if (monotone) return calc_monotone(time);
    vc<tuple<int, int, X>> dat;
    for (auto&& [x, A]: ADD) {
      vc<int> B;
      if (RM.count(x)) {
        B = RM[x];
        RM.erase(x);
      }
      if (len(B) < len(A)) B.eb(time);
      assert(len(A) == len(B));

      sort(all(A));
      sort(all(B));
      FOR(i, len(A)) {
        assert(A[i] <= B[i]);
        if (A[i] < B[i]) dat.eb(A[i], B[i], x);
      }
    }
    assert(len(RM) == 0);
    return dat;
  }

private:
  void add_monotone(int time, X x) {
    assert(!MP.count(x));
    MP[x] = time;
  }
  void remove_monotone(int time, X x) {
    auto it = MP.find(x);
    assert(it != MP.end());
    int t = (*it).se;
    MP.erase(it);
    if (t == time) return;
    dat.eb(t, time, x);
  }
  vc<tuple<int, int, X>> calc_monotone(int time) {
    for (auto&& [x, t]: MP) {
      if (t == time) continue;
      dat.eb(t, time, x);
    }
    return dat;
  }
};
#line 10 "main.cpp"

#line 2 "library/alg/monoid/assign.hpp"

template <typename X, X none_val>
struct Monoid_Assign {
  using value_type = X;
  static X op(X x, X y) { return (y == none_val ? x : y); }
  static constexpr X unit() { return none_val; }
  static constexpr bool commute = false;
};
#line 2 "library/ds/rollback_array.hpp"

template <typename T>
struct Rollback_Array {
  int N;
  vc<T> dat;
  vc<pair<int, T>> history;

  Rollback_Array() {}
  Rollback_Array(vc<T> x) : N(len(x)), dat(x) {}
  Rollback_Array(int N) : N(N), dat(N) {}
  template <typename F>
  Rollback_Array(int N, F f) : N(N) {
    dat.reserve(N);
    FOR(i, N) dat.eb(f(i));
  }

  int time() { return len(history); }
  void rollback(int t) {
    FOR_R(i, t, time()) {
      auto& [idx, v] = history[i];
      dat[idx] = v;
    }
    history.resize(t);
  }
  T get(int idx) { return dat[idx]; }
  void set(int idx, T x) {
    history.eb(idx, dat[idx]);
    dat[idx] = x;
  }

  vc<T> get_all() {
    vc<T> res(N);
    FOR(i, N) res[i] = get(i);
    return res;
  }
};
#line 13 "main.cpp"

template <typename ActedMonoid>
struct Rollback_Lazy_SegTree {
  using AM = ActedMonoid;
  using MX = typename AM::Monoid_X;
  using MA = typename AM::Monoid_A;
  using X = typename MX::value_type;
  using A = typename MA::value_type;
  int n, log, size;
  Rollback_Array<X> dat;
  Rollback_Array<A> laz;

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

  void build(int m) {
    build(m, [](int i) -> X { return MX::unit(); });
  }
  void build(const vc<X>& v) {
    build(len(v), [&](int i) -> X { return v[i]; });
  }
  template <typename F>
  void build(int m, F f) {
    n = m, log = 1;
    while ((1 << log) < n) ++log;
    size = 1 << log;
    dat = Rollback_Array<X>(vc<X>(size << 1, MX::unit()));
    laz = Rollback_Array<A>(vc<A>(size, MA::unit()));
    FOR(i, n) dat.set(size + i, f(i));
    FOR_R(i, 1, size) update(i);
  }

  void update(int k) { dat.set(k, MX::op(dat.get(2 * k), dat.get(2 * k + 1))); }
  void set(int p, X x) {
    assert(0 <= p && p < n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    dat.set(p, x);
    for (int i = 1; i <= log; i++) update(p >> i);
  }
  void multiply(int p, const X& x) {
    assert(0 <= p && p < n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    dat.set(p, MX::op(dat.get(p), x));
    for (int i = 1; i <= log; i++) update(p >> i);
  }

  X get(int p) {
    assert(0 <= p && p < n);
    p += size;
    for (int i = log; i >= 1; i--) push(p >> i);
    return dat.get(p);
  }

  vc<X> get_all() {
    auto tmp = dat.get_all();
    FOR(k, 1, size) push(k);
    return {tmp.begin() + size, tmp.begin() + size + n};
  }

  X prod(int l, int r) {
    assert(0 <= l && l <= r && r <= n);
    if (l == r) return MX::unit();
    l += size, r += size;
    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l) push(l >> i);
      if (((r >> i) << i) != r) push((r - 1) >> i);
    }
    X xl = MX::unit(), xr = MX::unit();
    while (l < r) {
      if (l & 1) xl = MX::op(xl, dat.get(l++));
      if (r & 1) xr = MX::op(dat.get(--r), xr);
      l >>= 1, r >>= 1;
    }
    return MX::op(xl, xr);
  }

  X prod_all() { return dat.get(1); }

  void apply(int l, int r, A a) {
    assert(0 <= l && l <= r && r <= n);
    if (l == r) return;
    l += size, r += size;
    for (int i = log; i >= 1; i--) {
      if (((l >> i) << i) != l) push(l >> i);
      if (((r >> i) << i) != r) push((r - 1) >> i);
    }
    int l2 = l, r2 = r;
    while (l < r) {
      if (l & 1) apply_at(l++, a);
      if (r & 1) apply_at(--r, a);
      l >>= 1, r >>= 1;
    }
    l = l2, r = r2;
    for (int i = 1; i <= log; i++) {
      if (((l >> i) << i) != l) update(l >> i);
      if (((r >> i) << i) != r) update((r - 1) >> i);
    }
  }

  template <typename F>
  int max_right(const F check, int l) {
    assert(0 <= l && l <= n);
    assert(check(MX::unit()));
    if (l == n) return n;
    l += size;
    for (int i = log; i >= 1; i--) push(l >> i);
    X sm = MX::unit();
    do {
      while (l % 2 == 0) l >>= 1;
      if (!check(MX::op(sm, dat.get(l)))) {
        while (l < size) {
          push(l);
          l = (2 * l);
          if (check(MX::op(sm, dat.get(l)))) { sm = MX::op(sm, dat.get(l++)); }
        }
        return l - size;
      }
      sm = MX::op(sm, dat.get(l++));
    } while ((l & -l) != l);
    return n;
  }

  template <typename F>
  int min_left(const F check, int r) {
    assert(0 <= r && r <= n);
    assert(check(MX::unit()));
    if (r == 0) return 0;
    r += size;
    for (int i = log; i >= 1; i--) push((r - 1) >> i);
    X sm = MX::unit();
    do {
      r--;
      while (r > 1 && (r % 2)) r >>= 1;
      if (!check(MX::op(dat.get(r), sm))) {
        while (r < size) {
          push(r);
          r = (2 * r + 1);
          if (check(MX::op(dat.get(r), sm))) { sm = MX::op(dat.get(r--), sm); }
        }
        return r + 1 - size;
      }
      sm = MX::op(dat.get(r), sm);
    } while ((r & -r) != r);
    return 0;
  }

  pair<int, int> time() { return {dat.time(), laz.time()}; }
  void rollback(pair<int, int> t) { dat.rollback(t.fi), laz.rollback(t.se); }

private:
  void apply_at(int k, A a) {
    ll sz = 1 << (log - topbit(k));
    dat.set(k, AM::act(dat.get(k), a, sz));
    if (k < size) laz.set(k, MA::op(laz.get(k), a));
  }
  void push(int k) {
    if (laz.get(k) == MA::unit()) return;
    apply_at(2 * k, laz.get(k)), apply_at(2 * k + 1, laz.get(k));
    laz.set(k, MA::unit());
  }
};

using mint = modint998;

struct Data {
  int cnt, max;
  mint sum;
};

struct Mono {
  using value_type = Data;
  using X = value_type;
  static X op(X x, X y) {
    if (x.cnt == 0) return y;
    if (y.cnt == 0) return x;
    return Data{x.cnt + y.cnt, max(x.max, y.max), x.sum + y.sum};
  }
  static constexpr X unit() { return Data{0, -infty<int>, 0}; }
  static constexpr bool commute = 1;
};

struct ActedMonoid {
  using Monoid_X = Mono;
  using Monoid_A = Monoid_Assign<int, -1>;
  using X = typename Monoid_X::value_type;
  using A = typename Monoid_A::value_type;
  static X act(const X& x, const A& a, const ll& size) {
    if (a == -1) return x;
    return Data{x.cnt, a, mint(x.cnt) * mint(a)};
  }
};

// 全部 x = t の形
mint solve_1(vi X1, vi X2, vi Y1, vi Y2) {
  // X しか関係ない
  vi X = {1, 1000000000 + 1};
  for (auto&& x: X1) X.eb(x);
  for (auto&& x: X2) X.eb(x);
  UNIQUE(X);
  for (auto&& x: X1) x = LB(X, x);
  for (auto&& x: X2) x = LB(X, x);
  ll K = len(X) - 1;
  vc<int> DX(K);
  FOR(k, K) DX[k] = X[k + 1] - X[k];
  ll N = len(X1);

  mint ANS = 0;

  /*
  ・x が小さい区間について、Lmax, Rmin
  ・x が大きい区間について、Lmax, Rmin

  R -> Lmax, R->Rmin
  L -> Lmax, L->Rmin
  */
  SegTree<Monoid_Max<int>> segRL(K + 1);
  SegTree<Monoid_Min<int>> segRR(K + 1);
  SegTree<Monoid_Max<int>> segLL(K + 1);
  SegTree<Monoid_Min<int>> segLR(K + 1);

  FOR(i, N) {
    int a = X1[i], b = X2[i];
    segRL.multiply(b, a);
    segRR.multiply(b, b);
    segLR.multiply(a, b);
    segLL.multiply(a, a);
  }

  FOR(b, K) {
    int a1 = segRL.prod(0, b + 1);
    int a2 = segRR.prod(0, b + 1);
    int b1 = segLL.prod(b + 1, K + 1);
    int b2 = segLR.prod(b + 1, K + 1);

    // (b,b,b)
    if (a1 == -infty<int> && b1 == -infty<int>) {
      mint x = DX[b];
      ANS += x * (x - 1) * (x - 2) * inv<mint>(6);
    }
    // (b,b,c)
    if (a1 == -infty<int> && b1 < b2) {
      int lo = max<int>(b1, b + 1);
      int hi = min<int>(b2, K);
      mint x = DX[b];
      x = x * (x - 1) * inv<mint>(2);
      ANS += x * mint(X[hi] - X[lo]);
    }
    // (a,b,b)
    if (b1 == -infty<int> && a1 < a2) {
      int lo = max<int>(a1, 0);
      int hi = min<int>(a2, b);
      mint x = DX[b];
      x = x * (x - 1) * inv<mint>(2);
      ANS += x * mint(X[hi] - X[lo]);
    }
    // (a,b,c)
    chmax(a1, 0), chmin(a2, b);
    chmax(b1, b + 1), chmin(b2, K);
    if (a1 < a2 && b1 < b2) {
      ANS += mint(DX[b]) * mint(X[a2] - X[a1]) * mint(X[b2] - X[b1]);
    }
  }
  return ANS;
}

// y = t をひとつ使って、x = t をふたつ使う
mint solve_2(vi X1, vi X2, vi Y1, vi Y2) {
  const int N = len(X1);
  vi X = {1, 1000000000 + 1};
  for (auto&& x: X1) X.eb(x);
  for (auto&& x: X2) X.eb(x);
  UNIQUE(X);
  for (auto&& x: X1) x = LB(X, x);
  for (auto&& x: X2) x = LB(X, x);

  vi Y = {1, 1000000000 + 1};
  for (auto&& x: Y1) Y.eb(x);
  for (auto&& x: Y2) Y.eb(x);
  UNIQUE(Y);
  for (auto&& x: Y1) x = LB(Y, x);
  for (auto&& x: Y2) x = LB(Y, x);

  ll N1 = len(X) - 1, N2 = len(Y) - 1;

  vc<int> DX(N1), DY(N2);
  FOR(i, N1) DX[i] = X[i + 1] - X[i];
  FOR(i, N2) DY[i] = Y[i + 1] - Y[i];

  Add_Remove_Query<int, false> ARQ;
  FOR(i, N) {
    ARQ.add(0, i);
    ARQ.remove(Y1[i], i);
    ARQ.add(Y2[i], i);
    ARQ.remove(N2, i);
  }

  // rollback_dfs
  auto upd = ARQ.calc(N2);
  vc<mint> ANS(N2);
  vc<int> I(len(upd));
  iota(all(I), 0);

  vc<int> LO(N1), HI(N1);
  FOR(i, N1) LO[i] = 1 + i, HI[i] = N1;
  int r_min = N1, l_max = 0;

  vc<mint> C2(N1);
  FOR(i, N1) C2[i] = mint(DX[i]) * mint(DX[i] - 1) * inv<mint>(2);
  C2 = cumsum<mint>(C2);

  Rollback_Lazy_SegTree<ActedMonoid> seg_1(N1, [&](int i) -> Data {
    Data x;
    x.cnt = DX[i];
    x.max = X[i + 1];
    x.sum = mint(x.cnt) * mint(X[i + 1]);
    return x;
  });

  Rollback_Lazy_SegTree<ActedMonoid> seg_2(N1, [&](int i) -> Data {
    Data x;
    x.cnt = DX[i];
    x.max = X[N1];
    x.sum = mint(x.cnt) * mint(X[N1]);
    return x;
  });

  auto dfs = [&](auto& dfs, vc<int>& upd_query_I, int begin, int end) -> void {
    if (begin == end) return;
    // snapshot
    // vc<int> LO_memo = LO, HI_memo = HI;
    auto seg_1_time = seg_1.time();
    auto seg_2_time = seg_2.time();
    int r_min_memo = r_min;
    int l_max_memo = l_max;

    vc<int> IL, IR;
    int mid = (begin + end) / 2;
    for (auto&& i: upd_query_I) {
      auto [a, b, idx] = upd[i];
      if (a <= begin && end <= b) {
        int x1 = X1[idx], x2 = X2[idx];
        // FOR(p, x1) { chmax(LO[p], x1), chmin(HI[p], x2); }
        seg_2.apply(x2, N1, 0);

        // LO[p] < x1 となる範囲を探索
        int k = 0;
        k = seg_1.max_right([&](Data d) -> bool { return d.max < X[x1]; }, 0);
        seg_1.apply(0, k, X[x1]);
        k = seg_2.max_right([&](Data d) -> bool { return d.max < X[x2]; }, 0);
        if (k < x1) seg_2.apply(k, x1, X[x2]);
        chmin(r_min, x2), chmax(l_max, x1);
      } else {
        if (a < mid) IL.eb(i);
        if (mid < b) IR.eb(i);
      }
    }
    if (begin + 1 == end) {
      // 求値クエリ
      int qid = begin;
      /*
      int s = 0;
      while (s < len(LO) && LO[s] > HI[s]) ++s;
      */
      int s = binary_search(
          [&](int s) -> bool {
            if (s >= r_min) return true;
            int lo = seg_1.prod(s, s + 1).max;
            int hi = seg_2.prod(s, s + 1).max;
            return lo <= hi;
          },
          r_min, -1);

      if (s < r_min) {
        mint hi_sum = seg_2.prod(s, r_min).sum;
        mint lo_sum = seg_1.prod(s, r_min).sum;
        ANS[qid] += hi_sum - lo_sum;
      }
      /*
      if (s < r_min) {
        FOR(i, s, r_min) {
          assert(LO[i] <= HI[i]);
          mint x = X[HI[i]] - X[LO[i]];
          ANS[qid] += x * mint(DX[i]);
        }
      }
      */
      if (l_max <= r_min) ANS[qid] += C2[r_min] - C2[l_max];
    } else {
      dfs(dfs, IL, begin, mid);
      dfs(dfs, IR, mid, end);
    }
    // rollback
    // LO = LO_memo, HI = HI_memo;
    seg_1.rollback(seg_1_time);
    seg_2.rollback(seg_2_time);
    r_min = r_min_memo;
    l_max = l_max_memo;
  };
  dfs(dfs, I, 0, N2);
  mint ans = 0;
  FOR(i, N2) ans += mint(DY[i]) * ANS[i];
  return ans;
}

void solve() {
  LL(N);
  vi X1(N), X2(N), Y1(N), Y2(N);
  FOR(i, N) { read(X1[i]), read(Y1[i]), read(X2[i]), read(Y2[i]); }
  FOR(i, N) X2[i]++, Y2[i]++;
  mint ANS = 0;
  ANS += solve_1(X1, X2, Y1, Y2);
  ANS += solve_2(X1, X2, Y1, Y2);
  ANS += solve_1(Y1, Y2, X1, X2);
  ANS += solve_2(Y1, Y2, X1, X2);
  print(ANS);
}

signed main() {
  INT(T);
  FOR(T) solve();
  return 0;
}