#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;
using u128 = unsigned __int128;
using f128 = __float128;

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); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(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 2 "library/ds/segtree/dynamic_segtree_sparse.hpp"

// 常にほとんどの要素が unit であることが保証されるような動的セグ木
// したがって、default_prod の類は持たせられず、acted monoid も一般には扱えない
// 永続化しない場合のノード数を O(N) に抑えることができるのが利点
template <typename Monoid, bool PERSISTENT, int NODES>
struct Dynamic_SegTree_Sparse {
  using MX = Monoid;
  using X = typename MX::value_type;

  struct Node {
    ll idx;
    Node *l, *r;
    X prod, x;
  };

  const ll L0, R0;
  Node *pool;
  int pid;
  using np = Node *;

  Dynamic_SegTree_Sparse(ll L0, ll R0) : L0(L0), R0(R0), pid(0) {
    pool = new Node[NODES];
  }

  np new_root() { return nullptr; }

  np new_node(ll idx, const X x) {
    pool[pid].idx = idx;
    pool[pid].l = pool[pid].r = nullptr;
    pool[pid].x = pool[pid].prod = x;
    return &(pool[pid++]);
  }

  X prod(np root, ll l, ll r) {
    assert(L0 <= l && l <= r && r <= R0);
    if (l == r) return MX::unit();
    X x = MX::unit();
    prod_rec(root, L0, R0, l, r, x);
    return x;
  }

  X prod_all(np root) { return prod(root, L0, R0); }

  np set(np root, ll i, const X &x) {
    assert(L0 <= i && i < R0);
    return set_rec(root, L0, R0, i, x);
  }

  np multiply(np root, ll i, const X &x) {
    assert(L0 <= i && i < R0);
    return multiply_rec(root, L0, R0, i, x);
  }

  template <typename F>
  ll max_right(np root, F check, ll L) {
    assert(L0 <= L && L <= R0 && check(MX::unit()));
    X x = MX::unit();
    return max_right_rec(root, check, L0, R0, L, x);
  }

  template <typename F>
  ll min_left(np root, F check, ll R) {
    assert(L0 <= R && R <= R0 && check(MX::unit()));
    X x = MX::unit();
    return min_left_rec(root, check, L0, R0, R, x);
  }

  void reset() { pid = 0; }

  vc<pair<ll, X>> get_all(np root) {
    vc<pair<ll, X>> res;
    auto dfs = [&](auto &dfs, np c) -> void {
      if (!c) return;
      dfs(dfs, c->l);
      res.eb(c->idx, c->x);
      dfs(dfs, c->r);
    };
    dfs(dfs, root);
    return res;
  }

  X get(np root, ll idx) {
    auto dfs = [&](auto &dfs, np c) -> X {
      if (!c) return Monoid::unit();
      if (idx == c->idx) return c->x;
      if (idx < (c->idx)) return dfs(dfs, c->l);
      return dfs(dfs, c->r);
    };
    return dfs(dfs, root);
  }

private:
  void update(np c) {
    c->prod = c->x;
    if (c->l) c->prod = MX::op(c->l->prod, c->prod);
    if (c->r) c->prod = MX::op(c->prod, c->r->prod);
  }

  np copy_node(np c) {
    if (!c || !PERSISTENT) return c;
    pool[pid].idx = c->idx;
    pool[pid].l = c->l;
    pool[pid].r = c->r;
    pool[pid].x = c->x;
    pool[pid].prod = c->prod;
    return &(pool[pid++]);
  }

  np set_rec(np c, ll l, ll r, ll i, X x) {
    if (!c) {
      c = new_node(i, x);
      return c;
    }
    c = copy_node(c);
    if (c->idx == i) {
      c->x = x;
      update(c);
      return c;
    }
    ll m = (l + r) / 2;
    if (i < m) {
      if (c->idx < i) swap(c->idx, i), swap(c->x, x);
      c->l = set_rec(c->l, l, m, i, x);
    }
    if (m <= i) {
      if (i < c->idx) swap(c->idx, i), swap(c->x, x);
      c->r = set_rec(c->r, m, r, i, x);
    }
    update(c);
    return c;
  }

  np multiply_rec(np c, ll l, ll r, ll i, X x) {
    if (!c) {
      c = new_node(i, x);
      return c;
    }
    c = copy_node(c);
    if (c->idx == i) {
      c->x = MX::op(c->x, x);
      update(c);
      return c;
    }
    ll m = (l + r) / 2;
    if (i < m) {
      if (c->idx < i) swap(c->idx, i), swap(c->x, x);
      c->l = multiply_rec(c->l, l, m, i, x);
    }
    if (m <= i) {
      if (i < c->idx) swap(c->idx, i), swap(c->x, x);
      c->r = multiply_rec(c->r, m, r, i, x);
    }
    update(c);
    return c;
  }

  void prod_rec(np c, ll l, ll r, ll ql, ll qr, X &x) {
    chmax(ql, l);
    chmin(qr, r);
    if (ql >= qr || !c) return;
    if (l == ql && r == qr) {
      x = MX::op(x, c->prod);
      return;
    }
    ll m = (l + r) / 2;
    prod_rec(c->l, l, m, ql, qr, x);
    if (ql <= (c->idx) && (c->idx) < qr) x = MX::op(x, c->x);
    prod_rec(c->r, m, r, ql, qr, x);
  }

  template <typename F>
  ll max_right_rec(np c, const F &check, ll l, ll r, ll ql, X &x) {
    if (!c || r <= ql) return R0;
    if (check(MX::op(x, c->prod))) {
      x = MX::op(x, c->prod);
      return R0;
    }
    ll m = (l + r) / 2;
    ll k = max_right_rec(c->l, check, l, m, ql, x);
    if (k != R0) return k;
    if (ql <= (c->idx)) {
      x = MX::op(x, c->x);
      if (!check(x)) return c->idx;
    }
    return max_right_rec(c->r, check, m, r, ql, x);
  }

  template <typename F>
  ll min_left_rec(np c, const F &check, ll l, ll r, ll qr, X &x) {
    if (!c || qr <= l) return L0;
    if (check(MX::op(c->prod, x))) {
      x = MX::op(c->prod, x);
      return L0;
    }
    ll m = (l + r) / 2;
    ll k = min_left_rec(c->r, check, m, r, qr, x);
    if (k != L0) return k;
    if (c->idx < qr) {
      x = MX::op(c->x, x);
      if (!check(x)) return c->idx + 1;
    }
    return min_left_rec(c->l, check, l, m, qr, x);
  }
};
#line 2 "library/alg/monoid/add.hpp"

template <typename X>
struct Monoid_Add {
  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;
};
#line 3 "library/ds/fenwicktree/fenwicktree.hpp"

template <typename Monoid>
struct FenwickTree {
  using G = 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));
  }

  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);
  }

  template <class F>
  int max_right(const F check) {
    assert(check(G::unit()));
    int i = 0;
    E s = G::unit();
    int k = 1;
    while (2 * k <= n) k *= 2;
    while (k) {
      if (i + k - 1 < len(dat)) {
        E t = G::op(s, dat[i + k - 1]);
        if (check(t)) { i += k, s = t; }
      }
      k >>= 1;
    }
    return i;
  }

  int kth(E k) {
    return max_right([&k](E x) -> bool { return x <= k; });
  }
};
#line 6 "main.cpp"

void solve() {
  LL(N, Q);
  static Dynamic_SegTree_Sparse<Monoid_Add<int>, false, 4000000> seg(0, 100100);
  seg.reset();

  using np = decltype(seg)::np;
  vc<np> root(N);
  FOR(i, N) root[i] = seg.new_root();

  VEC(int, A, N);
  FOR(i, N) {
    --A[i];
    root[A[i]] = seg.set(root[A[i]], i, 1);
  }
  VEC(ll, val, N);
  FenwickTree<Monoid_Add<ll>> bit(val);

  FOR(Q) {
    LL(t);
    if (t == 1) {
      LL(i, x);
      --i, --x;
      root[A[i]] = seg.multiply(root[A[i]], i, -1);
      A[i] = x;
      root[A[i]] = seg.multiply(root[A[i]], i, +1);
    }
    if (t == 2) {
      LL(i, x);
      --i;
      bit.add(i, -val[i]);
      val[i] = x;
      bit.add(i, +val[i]);
    }
    if (t == 3) {
      LL(i, k);
      --i;
      VEC(int, color, k);
      for (auto&& x: color) --x;
      auto can = [&](int L, int R) -> int {
        int res = 0;
        for (auto&& c: color) res += seg.prod(root[c], L, R);
        return res == R - L;
      };
      int L = i, R = i + 1;
      FOR_R(k, 20) {
        int nR = R + (1 << k);
        if (nR <= N && can(R, nR)) R = nR;
        int nL = L - (1 << k);
        if (nL >= 0 && can(nL, L)) L = nL;
      }
      // print("LR", L, R);
      print(bit.sum(L, R));
    }
  }
}

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