結果

問題 No.2257 Swim and Sleep
ユーザー NyaanNyaan
提出日時 2023-03-24 23:02:52
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 19,809 bytes
コンパイル時間 3,360 ms
コンパイル使用メモリ 298,388 KB
最終ジャッジ日時 2025-02-11 17:40:24
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
other AC * 3 WA * 6 RE * 8
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ソースコード

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/**
 *  date : 2023-03-24 23:02:42
 */
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}
  using pair<T, U>::first;
  using pair<T, U>::second;
  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
  return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}
template <typename F>
vector<int> mkord(int N,F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}
vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}
template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}
template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
}  // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}
istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;
}  // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;
  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }
  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(r * mod == 1, "invalid, r * mod != 1");
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  u32 a;
  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};
  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }
  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }
  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }
  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }
  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }
  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  
  constexpr mint inverse() const { return pow(mod - 2); }
  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }
  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }
  
  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }
  static constexpr u32 get_mod() { return mod; }
};
template <typename T>
struct Binomial {
  vector<T> f, g, h;
  Binomial(int MAX = 0) {
    assert(T::get_mod() != 0 && "Binomial<mint>()");
    f.resize(1, T{1});
    g.resize(1, T{1});
    h.resize(1, T{1});
    while (MAX >= (int)f.size()) extend();
  }
  void extend() {
    int n = f.size();
    int m = n * 2;
    f.resize(m);
    g.resize(m);
    h.resize(m);
    for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
    g[m - 1] = f[m - 1].inverse();
    h[m - 1] = g[m - 1] * f[m - 2];
    for (int i = m - 2; i >= n; i--) {
      g[i] = g[i + 1] * T(i + 1);
      h[i] = g[i] * f[i - 1];
    }
  }
  T fac(int i) {
    if (i < 0) return T(0);
    while (i >= (int)f.size()) extend();
    return f[i];
  }
  T finv(int i) {
    if (i < 0) return T(0);
    while (i >= (int)g.size()) extend();
    return g[i];
  }
  T inv(int i) {
    if (i < 0) return -inv(-i);
    while (i >= (int)h.size()) extend();
    return h[i];
  }
  T C(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r) * finv(r);
  }
  inline T operator()(int n, int r) { return C(n, r); }
  template <typename I>
  T multinomial(const vector<I>& r) {
    static_assert(is_integral<I>::value == true);
    int n = 0;
    for (auto& x : r) {
      if (x < 0) return T(0);
      n += x;
    }
    T res = fac(n);
    for (auto& x : r) res *= finv(x);
    return res;
  }
  template <typename I>
  T operator()(const vector<I>& r) {
    return multinomial(r);
  }
  T C_naive(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    T ret = T(1);
    r = min(r, n - r);
    for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
    return ret;
  }
  T P(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r);
  }
  // [x^r] 1 / (1-x)^n
  T H(int n, int r) {
    if (n < 0 || r < 0) return T(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
//
using namespace Nyaan;
using mint = LazyMontgomeryModInt<998244353>;
// using mint = LazyMontgomeryModInt<1000000007>;
using vm = vector<mint>;
using vvm = vector<vm>;
Binomial<mint> C;
using namespace Nyaan;
bool naive2(ll A, ll B, V<string> g, int rec = 5) {
  assert(sz(g) == A);
  each(v, g) assert(sz(v) == B);
  if (rec == 0) return true;
  V<string> h(A, string(B, ' '));
  rep(i, A) rep(j, B) {
    if (g[i][j] == 'U') h[(i - 1 + A) % A][j] = 'U';
    if (g[i][j] == 'D') h[(i + 1 + A) % A][j] = 'D';
    if (g[i][j] == 'L') h[i][(j - 1 + B) % B] = 'L';
    if (g[i][j] == 'R') h[i][(j + 1 + B) % B] = 'R';
  }
  rep(i, A) rep(j, B) if (h[i][j] == ' ') return false;
  return naive2(A, B, h, rec - 1);
}
mint naive(ll A, ll B, V<pair<pl, char>> ps) {
  V<string> g(A, string(B, ' '));
  each(p, ps) g[p.fi.fi][p.fi.se] = p.se;
  mint ans = 0;
  auto dfs = [&](auto rc, int idx) -> void {
    if (idx == A * B) {
      if (naive2(A, B, g)) {
        trc2(g);
        ans += 1;
      }
      return;
    }
    if (g[idx / B][idx % B] == ' ') {
      each(c, string("LRUD")) {
        g[idx / B][idx % B] = c;
        rc(rc, idx + 1);
      }
      g[idx / B][idx % B] = ' ';
    } else {
      rc(rc, idx + 1);
    }
  };
  dfs(dfs, 0);
  return ans;
}
// 90 度 / 180 度回る
void rotate(ll& A, ll& B, V<pair<pl, char>>& ps, bool is_90) {
  // ..#    #.
  // ... -> ..
  //        ..
  // U -> L -> D -> R -> U ...
  string S = "ULDRUL";
  if (is_90) {
    each(p, ps) {
      ll x = p.fi.fi, y = p.fi.se;
      char c = p.se;
      p.fi.fi = B - 1 - y;
      p.fi.se = x;
      p.se = S[S.find(c) + 1];
    }
    swap(A, B);
  } else {
    each(p, ps) {
      p.fi.fi = A - 1 - p.fi.fi;
      if (p.se == 'U') {
        p.se = 'D';
      } else if (p.se == 'D') {
        p.se = 'U';
      }
    }
  }
}
mint calc(ll A, ll B, V<pair<pl, char>> ps) {
  if (A == 2 and B == 2) return naive(A, B, ps);
  mint ans = 0;
  // -> ->
  rep(_, 2) {
    if (B % 2 == 1) {
      int ok = 1;
      map<int, char> mp;
      each(p, ps) {
        ll x = p.fi.fi;
        char c = p.se;
        if (c != 'L' and c != 'R') {
          ok = 0;
          break;
        }
        if (mp.count(x) == 0) {
          mp[x] = c;
        } else if (mp[x] != c) {
          ok = 0;
        }
      }
      if (ok) ans += mint{2}.pow(A - sz(mp));
    } else {
      map<int, string> mp2;
      int ok = 1;
      each(p, ps) {
        ll x = p.fi.fi;
        ll y = p.fi.se;
        char c = p.se;
        if (c != 'L' and c != 'R') ok = 0;
        if (!ok) break;
        if (mp2.count(x) == 0) mp2[x] = "..";
        if (mp2[x][y % 2] == '.') {
          mp2[x][y % 2] = c;
        } else if (mp2[x][y % 2] != c) {
          ok = 0;
        }
      }
      if (ok) {
        ll al = 2 * A;
        each2(__, s, mp2) {
          if (s[0] != '.') al--;
          if (s[1] != '.') al--;
        }
        ans += mint{2}.pow(al);
      }
    }
    rotate(A, B, ps, 1);
  }
  // ■
  if (A % 2 == 0 and B % 2 == 0) {
    rep(_, 2) {
      // RD
      // UL
      V<string> v{"RD", "UL"};
      int ok = 1;
      each(p, ps) {
        if (v[p.fi.fi % 2][p.fi.se % 2] != p.se) ok = 0;
      }
      if (ok) ans += 1;
      rep(t, 4) {
        if (t % 2 == 0) {
          each(p, ps) {
            p.fi.fi += 1;
            p.fi.fi %= A;
          }
        } else {
          each(p, ps) {
            p.fi.se += 1;
            p.fi.se %= B;
          }
        }
      }
    }
  }
  // R と U しかない -> 斜めのラインに同じ文字があればいい？
  if (gcd(A, B) != 1) {
    ll g = gcd(A, B);
    rep(_, 2) {
      rep(t, 4) {
        int ok = 1;
        // 差の 法が 0, 1, ..., g-1 で場合分け
        map<ll, char> mp;
        int allr = 1, allu = 1;
        each(p, ps) {
          ll x = p.fi.fi;
          ll y = p.fi.se;
          char c = p.se;
          if (c != 'R' and c != 'U') ok = 0;
          if (c == 'R') allu = 0;
          if (c == 'U') allr = 0;
          ll d = ((x - y) % g + g) % g;
          if (mp.count(d) == 0) {
            mp[d] = c;
          } else if (mp[d] != c) {
            ok = 0;
          }
        }
        if (ok) {
          ans += mint{2}.pow(g - sz(mp));
          if (allr) ans -= 1;
          if (allu) ans -= 1;
        }
        if (ok) trc(ps, g - sz(mp));
        rotate(A, B, ps, 1);
      }
      break;
      //      rotate(A, B, ps, 0);
    }
  }
  return ans;
}
namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;
// [0, 2^64 - 1)
u64 rng() {
  static u64 _x =
      u64(chrono::duration_cast<chrono::nanoseconds>(
              chrono::high_resolution_clock::now().time_since_epoch())
              .count()) *
      10150724397891781847ULL;
  _x ^= _x << 7;
  return _x ^= _x >> 9;
}
// [l, r]
i64 rng(i64 l, i64 r) {
  assert(l <= r);
  return l + rng() % (r - l + 1);
}
// [l, r)
i64 randint(i64 l, i64 r) {
  assert(l < r);
  return l + rng() % (r - l);
}
// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
  assert(l <= r && n <= r - l);
  unordered_set<i64> s;
  for (i64 i = n; i; --i) {
    i64 m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<i64> ret;
  for (auto& x : s) ret.push_back(x);
  return ret;
}
// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}
}  // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
void test() {
  rep(t, 100) {
    ll H = 3;
    ll W = 4;
    V<pair<pl, char>> ps;
    string S = "LRUD";
    rep(i, H) rep(j, W) {
      if (rng(0, 2) == 0) ps.emplace_back(pl{i, j}, S[rng(0, 3)]);
    }
    trc2(H, W);
    trc2(ps);
    auto an = naive(H, W, ps);
    auto a2 = calc(H, W, ps);
    if (an != a2) {
      trc2(H, W);
      trc2(ps);
      trc2(an, a2);
      exit(1);
    }
  }
}
void q() {
#ifdef NyaanLocal
  test();
  cerr << "OK" << endl;
  exit(0);
#endif
  inl(A, B, K);
  V<pair<pl, char>> ps(K);
  in(ps);
  swap(A, B);
  each2(p, _, ps) swap(p.fi, p.se);
  if (A <= 2 or B <= 2) {
#ifdef NyaanDebug
    trc("owari");
    return;
#else
    exit(1);
#endif
  }
  out(calc(A, B, ps));
}
void Nyaan::solve() {
  int t = 1;
  in(t);
  while (t--) q();
}
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