#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// 参考 https://codeforces.com/blog/entry/96344
// bmi,bmi2,lzcnt は ucup でコンパイルエラー
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")

#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>
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};
}

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

#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) {
  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 (abs(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>
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"
#define FASTIO
#include <unistd.h>

// 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() {
  memcpy(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;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

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

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

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>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

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 < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(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::read;
using fastio::print;
using fastio::flush;

#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); }
#line 3 "main.cpp"

#line 1 "library/ds/bit_vector.hpp"
struct Bit_Vector {
  vc<pair<u32, u32>> dat;
  Bit_Vector(int n) { dat.assign((n + 63) >> 5, {0, 0}); }

  void set(int i) { dat[i >> 5].fi |= u32(1) << (i & 31); }

  void build() {
    FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
  }

  // [0, k) 内の 1 の個数
  int rank(int k, bool f = 1) {
    auto [a, b] = dat[k >> 5];
    int ret = b + popcnt(a & ((u32(1) << (k & 31)) - 1));
    return (f ? ret : k - ret);
  }
};
#line 2 "library/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;
};
#line 3 "library/ds/wavelet_matrix/wavelet_matrix.hpp"

// 座圧するかどうかを COMPRESS で指定する
// xor 的な使い方をする場合には、コンストラクタで log を渡すこと
template <typename T, bool COMPRESS, typename Monoid = Monoid_Add<T>>
struct Wavelet_Matrix {
  using MX = Monoid;
  using X = typename MX::value_type;
  static_assert(MX::commute);
  int N, lg;
  vector<int> mid;
  vector<Bit_Vector> bv;
  vc<T> key;
  bool set_log;
  vvc<X> cumsum;

  Wavelet_Matrix() {}

  // 和を使わないなら、SUM_data は空でよい
  Wavelet_Matrix(vc<T> A, vc<X> SUM_data = {}, int log = -1) {
    build(A, SUM_data, log);
  }

  void build(vc<T> A, vc<X> SUM_data = {}, int log = -1) {
    N = len(A), lg = log, set_log = (log != -1);
    bool MAKE_SUM = !(SUM_data.empty());
    vc<X>& S = SUM_data;
    if (COMPRESS) {
      assert(!set_log);
      key.reserve(N);
      vc<int> I = argsort(A);
      for (auto&& i: I) {
        if (key.empty() || key.back() != A[i]) key.eb(A[i]);
        A[i] = len(key) - 1;
      }
      key.shrink_to_fit();
    }
    if (lg == -1) lg = __lg(max<ll>(MAX(A), 1)) + 1;
    mid.resize(lg);
    bv.assign(lg, Bit_Vector(N));
    if (MAKE_SUM) cumsum.assign(1 + lg, vc<X>(N + 1, MX::unit()));
    S.resize(N);
    vc<T> A0(N), A1(N);
    vc<X> S0(N), S1(N);
    FOR_R(d, -1, lg) {
      int p0 = 0, p1 = 0;
      if (MAKE_SUM) {
        FOR(i, N) { cumsum[d + 1][i + 1] = MX::op(cumsum[d + 1][i], S[i]); }
      }
      if (d == -1) break;
      FOR(i, N) {
        bool f = (A[i] >> d & 1);
        if (!f) {
          if (MAKE_SUM) S0[p0] = S[i];
          A0[p0++] = A[i];
        }
        if (f) {
          if (MAKE_SUM) S1[p1] = S[i];
          bv[d].set(i), A1[p1++] = A[i];
        }
      }
      mid[d] = p0;
      bv[d].build();
      swap(A, A0), swap(S, S0);
      FOR(i, p1) A[p0 + i] = A1[i], S[p0 + i] = S1[i];
    }
  }

  // xor した結果で [a, b) に収まるものを数える
  int count(int L, int R, T a, T b, T xor_val = 0) {
    return prefix_count(L, R, b, xor_val) - prefix_count(L, R, a, xor_val);
  }

  int count(vc<pair<int, int>> segments, T a, T b, T xor_val = 0) {
    int res = 0;
    for (auto&& [L, R]: segments) res += count(L, R, a, b, xor_val);
    return res;
  }

  // xor した結果で、[L, R) の中で k>=0 番目と prefix sum
  pair<T, X> kth_value_and_sum(int L, int R, int k, T xor_val = 0) {
    assert(!cumsum.empty());
    if (xor_val != 0) assert(set_log);
    assert(0 <= k && k <= R - L);
    if (k == R - L) { return {infty<T>, sum_all(L, R)}; }
    int cnt = 0;
    X sm = MX::unit();
    T ret = 0;
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      if (cnt + c > k) {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      } else {
        X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
        cnt += c, ret |= T(1) << d, sm = MX::op(sm, s);
        if (!f) L += mid[d] - l0, R += mid[d] - r0;
        if (f) L = l0, R = r0;
      }
    }
    sm = MX::op(sm, get(0, L, L + k - cnt));
    if (COMPRESS) ret = key[ret];
    return {ret, sm};
  }

  // xor した結果で、[L, R) の中で k>=0 番目と prefix sum
  pair<T, X> kth_value_and_sum(vc<pair<int, int>> segments, int k,
                               T xor_val = 0) {
    assert(!cumsum.empty());
    if (xor_val != 0) assert(set_log);
    int total_len = 0;
    for (auto&& [L, R]: segments) total_len += R - L;
    assert(0 <= k && k <= total_len);
    if (k == total_len) { return {infty<T>, sum_all(segments)}; }
    int cnt = 0;
    X sm = MX::unit();
    T ret = 0;
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int c = 0;
      for (auto&& [L, R]: segments) {
        int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
        c += (f ? (R - L) - (r0 - l0) : (r0 - l0));
      }
      if (cnt + c > k) {
        for (auto&& [L, R]: segments) {
          int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
          if (!f) L = l0, R = r0;
          if (f) L += mid[d] - l0, R += mid[d] - r0;
        }
      } else {
        cnt += c, ret |= T(1) << d;
        for (auto&& [L, R]: segments) {
          int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
          X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
          sm = MX::op(sm, s);
          if (!f) L += mid[d] - l0, R += mid[d] - r0;
          if (f) L = l0, R = r0;
        }
      }
    }
    for (auto&& [L, R]: segments) {
      int t = min(R - L, k - cnt);
      sm = MX::op(sm, get(0, L, L + t));
      cnt += t;
    }
    if (COMPRESS) ret = key[ret];
    return {ret, sm};
  }

  // xor した結果で、[L, R) の中で k>=0 番目
  T kth(int L, int R, int k, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    assert(0 <= k && k < R - L);
    int cnt = 0;
    T ret = 0;
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      if (cnt + c > k) {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      } else {
        cnt += c, ret |= T(1) << d;
        if (!f) L += mid[d] - l0, R += mid[d] - r0;
        if (f) L = l0, R = r0;
      }
    }
    if (COMPRESS) ret = key[ret];
    return ret;
  }

  T kth(vc<pair<int, int>> segments, int k, T xor_val = 0) {
    int total_len = 0;
    for (auto&& [L, R]: segments) total_len += R - L;
    assert(0 <= k && k < total_len);
    int cnt = 0;
    T ret = 0;
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int c = 0;
      for (auto&& [L, R]: segments) {
        int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
        c += (f ? (R - L) - (r0 - l0) : (r0 - l0));
      }
      if (cnt + c > k) {
        for (auto&& [L, R]: segments) {
          int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
          if (!f) L = l0, R = r0;
          if (f) L += mid[d] - l0, R += mid[d] - r0;
        }
      } else {
        cnt += c, ret |= T(1) << d;
        for (auto&& [L, R]: segments) {
          int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
          if (!f) L += mid[d] - l0, R += mid[d] - r0;
          if (f) L = l0, R = r0;
        }
      }
    }
    if (COMPRESS) ret = key[ret];
    return ret;
  }

  // xor した結果で、[L, R) の中で中央値。
  // LOWER = true：下側中央値、false：上側中央値
  T median(bool UPPER, int L, int R, T xor_val = 0) {
    int n = R - L;
    int k = (UPPER ? n / 2 : (n - 1) / 2);
    return kth(L, R, k, xor_val);
  }

  T median(bool UPPER, vc<pair<int, int>> segments, T xor_val = 0) {
    int n = 0;
    for (auto&& [L, R]: segments) n += R - L;
    int k = (UPPER ? n / 2 : (n - 1) / 2);
    return kth(segments, k, xor_val);
  }

  // xor した結果で [k1, k2) 番目であるところの SUM_data の和
  X sum(int L, int R, int k1, int k2, T xor_val = 0) {
    X add = prefix_sum(L, R, k2, xor_val);
    X sub = prefix_sum(L, R, k1, xor_val);
    return MX::op(add, MX::inverse(sub));
  }

  X sum_all(int L, int R) { return get(lg, L, R); }

  X sum_all(vc<pair<int, int>> segments) {
    X sm = MX::unit();
    for (auto&& [L, R]: segments) { sm = MX::op(sm, get(lg, L, R)); }
    return sm;
  }

  // check(cnt, prefix sum) が true となるような最大の (cnt, sum)
  template <typename F>
  pair<int, X> max_right(F check, int L, int R, T xor_val = 0) {
    assert(check(0, MX::unit()));
    if (xor_val != 0) assert(set_log);
    if (check(R - L, get(lg, L, R))) return {R - L, get(lg, L, R)};
    int cnt = 0;
    X sm = MX::unit();
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
      if (check(cnt + c, MX::op(sm, s))) {
        cnt += c, sm = MX::op(sm, s);
        if (f) L = l0, R = r0;
        if (!f) L += mid[d] - l0, R += mid[d] - r0;
      } else {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      }
    }
    int k = binary_search(
        [&](int k) -> bool {
          return check(cnt + k, MX::op(sm, get(0, L, L + k)));
        },
        0, R - L);
    cnt += k;
    sm = MX::op(sm, get(0, L, L + k));
    return {cnt, sm};
  }

private:
  inline X get(int d, int L, int R) {
    assert(!cumsum.empty());
    return MX::op(MX::inverse(cumsum[d][L]), cumsum[d][R]);
  }

  // xor した結果で [0, x) に収まるものを数える
  int prefix_count(int L, int R, T x, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    x = (COMPRESS ? LB(key, x) : x);
    if (x == 0) return 0;
    if (x >= (1 << lg)) return R - L;
    int cnt = 0;
    FOR_R(d, lg) {
      bool add = (x >> d) & 1;
      bool f = ((xor_val) >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int kf = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      if (add) {
        cnt += kf;
        if (f) { L = l0, R = r0; }
        if (!f) { L += mid[d] - l0, R += mid[d] - r0; }
      } else {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      }
    }
    return cnt;
  }

  // xor した結果で [0, k) 番目のものの和
  X prefix_sum(int L, int R, int k, T xor_val = 0) {
    return kth_value_and_sum(L, R, k, xor_val).se;
  }

  // xor した結果で [0, k) 番目のものの和
  X prefix_sum(vc<pair<int, int>> segments, int k, T xor_val = 0) {
    return kth_value_and_sum(segments, k, xor_val).se;
  }
};
#line 5 "main.cpp"

bool check(vc<int> A) {
  vc<int> X(len(A));
  FOR(i, len(A)) X[i] = (1 + i) * A[i];
  bool ok = 1;
  FOR(i, len(A) - 1) if (X[i] > X[i + 1]) ok = 0;
  return ok;
}

bool mycheck(vc<int> A) {
  FOR(i, len(A)) {
    ll x = abs(i + 1 - A[i]);
    if (x >= 2) return 0;
  }
  return 1;
}

void solve() {
  LL(N);
  VEC(int, A, N);
  Wavelet_Matrix<int, false> WM(A);
  vc<int> pos(N + 1, -1);
  FOR(i, N) pos[A[i]] = i;

  // i,i+1 の swap だけ回避できる
  //

  vi dp(N + 1, infty<ll>);
  dp[0] = 0;
  FOR(i, N) {
    // i+1 を置く
    // i+1 の左にある i+1 より大きいもの
    {
      int p = pos[i + 1];
      ll cost = WM.count(0, p, i + 1, N + 1);
      chmin(dp[i + 1], dp[i] + cost);
    }

    // i+2, i+1 を書く
    if (i + 2 <= N) {
      int p = pos[i + 2];
      int q = pos[i + 1];
      ll cost = WM.count(0, p, i + 2, N + 1);
      cost += WM.count(0, q, i + 1, N + 1);
      if (p < q) --cost;
      chmin(dp[i + 2], dp[i] + cost);
    }
  }
  print(dp[N]);
}

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

In file included from /usr/include/c++/13/string:43,
                 from /usr/include/c++/13/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:52,
                 from library/my_template.hpp:10:
/usr/include/c++/13/bits/allocator.h: In destructor ‘constexpr std::__cxx11::basic_string<char>::_Alloc_hider::~_Alloc_hider()’:
/usr/include/c++/13/bits/allocator.h:184:7: error: inlining failed in call to ‘always_inline’ ‘constexpr std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = char]’: target specific option mismatch
  184 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/13/string:54:
/usr/include/c++/13/bits/basic_string.h:181:14: note: called from here
  181 |       struct _Alloc_hider : allocator_type // TODO check __is_final
      |              ^~~~~~~~~~~~