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QOJ

ID题目提交者结果用时内存语言文件大小提交时间测评时间
#295751#7559. Bocchi the RockwxhtzdyAC ✓953ms93400kbC++2015.4kb2023-12-31 21:09:482023-12-31 21:09:48

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你现在查看的是最新测评结果

  • [2023-12-31 21:09:48]
  • 评测
  • 测评结果:AC
  • 用时:953ms
  • 内存:93400kb
  • [2023-12-31 21:09:48]
  • 提交

answer

#include <bits/stdc++.h>

using namespace std;

template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}

template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}

template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

/*
using ModType = int;

struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

// make it understandable one day...
namespace fft {

typedef double dbl;

struct num {
  dbl x, y;
  num() { x = y = 0; }
  num(dbl x_, dbl y_) : x(x_), y(y_) {}
};

inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
inline num operator*(num a, num b) { return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x); }
inline num conj(num a) { return num(a.x, -a.y); }

int base = 1;
vector<num> roots = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};

const dbl PI = static_cast<dbl>(acosl(-1.0));

void ensure_base(int nbase) {
  if (nbase <= base) {
    return;
  }
  rev.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++) {
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  }
  roots.resize(1 << nbase);
  while (base < nbase) {
    dbl angle = 2 * PI / (1 << (base + 1));
//      num z(cos(angle), sin(angle));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      roots[i << 1] = roots[i];
//        roots[(i << 1) + 1] = roots[i] * z;
      dbl angle_i = angle * (2 * i + 1 - (1 << base));
      roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));
    }
    base++;
  }
}

void fft(vector<num>& a, int n = -1) {
  if (n == -1) {
    n = (int) a.size();
  }
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++) {
    if (i < (rev[i] >> shift)) {
      swap(a[i], a[rev[i] >> shift]);
    }
  }
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        num z = a[i + j + k] * roots[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}

vector<num> fa, fb;

vector<int64_t> square(const vector<int>& a) {
  if (a.empty()) {
    return {};
  }
  int need = (int) a.size() + (int) a.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if ((sz >> 1) > (int) fa.size()) {
    fa.resize(sz >> 1);
  }
  for (int i = 0; i < (sz >> 1); i++) {
    int x = (2 * i < (int) a.size() ? a[2 * i] : 0);
    int y = (2 * i + 1 < (int) a.size() ? a[2 * i + 1] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz >> 1);
  num r(1.0 / (sz >> 1), 0.0);
  for (int i = 0; i <= (sz >> 2); i++) {
    int j = ((sz >> 1) - i) & ((sz >> 1) - 1);
    num fe = (fa[i] + conj(fa[j])) * num(0.5, 0);
    num fo = (fa[i] - conj(fa[j])) * num(0, -0.5);
    num aux = fe * fe + fo * fo * roots[(sz >> 1) + i] * roots[(sz >> 1) + i];
    num tmp = fe * fo;
    fa[i] = r * (conj(aux) + num(0, 2) * conj(tmp));
    fa[j] = r * (aux + num(0, 2) * tmp);
  }
  fft(fa, sz >> 1);
  vector<int64_t> res(need);
  for (int i = 0; i < need; i++) {
    res[i] = llround(i % 2 == 0 ? fa[i >> 1].x : fa[i >> 1].y);
  }
  return res;
}

vector<int64_t> multiply(const vector<int>& a, const vector<int>& b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  if (a == b) {
    return square(a);
  }
  int need = (int) a.size() + (int) b.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int) fa.size()) {
    fa.resize(sz);
  }
  for (int i = 0; i < sz; i++) {
    int x = (i < (int) a.size() ? a[i] : 0);
    int y = (i < (int) b.size() ? b[i] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz);
  num r(0, -0.25 / (sz >> 1));
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
    fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
    fa[i] = z;
  }
  for (int i = 0; i < (sz >> 1); i++) {
    num A0 = (fa[i] + fa[i + (sz >> 1)]) * num(0.5, 0);
    num A1 = (fa[i] - fa[i + (sz >> 1)]) * num(0.5, 0) * roots[(sz >> 1) + i];
    fa[i] = A0 + A1 * num(0, 1);
  }
  fft(fa, sz >> 1);
  vector<int64_t> res(need);
  for (int i = 0; i < need; i++) {
    res[i] = llround(i % 2 == 0 ? fa[i >> 1].x : fa[i >> 1].y);
  }
  return res;
}

vector<int> multiply_mod(const vector<int>& a, const vector<int>& b, int m) {
  if (a.empty() || b.empty()) {
    return {};
  }
  int eq = (a.size() == b.size() && a == b);
  int need = (int) a.size() + (int) b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int) fa.size()) {
    fa.resize(sz);
  }
  for (int i = 0; i < (int) a.size(); i++) {
    int x = (a[i] % m + m) % m;
    fa[i] = num(x & ((1 << 15) - 1), x >> 15);
  }
  fill(fa.begin() + a.size(), fa.begin() + sz, num {0, 0});
  fft(fa, sz);
  if (sz > (int) fb.size()) {
    fb.resize(sz);
  }
  if (eq) {
    copy(fa.begin(), fa.begin() + sz, fb.begin());
  } else {
    for (int i = 0; i < (int) b.size(); i++) {
      int x = (b[i] % m + m) % m;
      fb[i] = num(x & ((1 << 15) - 1), x >> 15);
    }
    fill(fb.begin() + b.size(), fb.begin() + sz, num {0, 0});
    fft(fb, sz);
  }
  dbl ratio = 0.25 / sz;
  num r2(0, -1);
  num r3(ratio, 0);
  num r4(0, -ratio);
  num r5(0, 1);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num a1 = (fa[i] + conj(fa[j]));
    num a2 = (fa[i] - conj(fa[j])) * r2;
    num b1 = (fb[i] + conj(fb[j])) * r3;
    num b2 = (fb[i] - conj(fb[j])) * r4;
    if (i != j) {
      num c1 = (fa[j] + conj(fa[i]));
      num c2 = (fa[j] - conj(fa[i])) * r2;
      num d1 = (fb[j] + conj(fb[i])) * r3;
      num d2 = (fb[j] - conj(fb[i])) * r4;
      fa[i] = c1 * d1 + c2 * d2 * r5;
      fb[i] = c1 * d2 + c2 * d1;
    }
    fa[j] = a1 * b1 + a2 * b2 * r5;
    fb[j] = a1 * b2 + a2 * b1;
  }
  fft(fa, sz);
  fft(fb, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) {
    int64_t aa = llround(fa[i].x);
    int64_t bb = llround(fb[i].x);
    int64_t cc = llround(fa[i].y);
    res[i] = static_cast<int>((aa + ((bb % m) << 15) + ((cc % m) << 30)) % m);
  }
  return res;
}

}  // namespace fft

template <typename T>
typename enable_if<is_same<typename Modular<T>::Type, int>::value, vector<Modular<T>>>::type operator*(
    const vector<Modular<T>>& a,
    const vector<Modular<T>>& b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  if (min(a.size(), b.size()) < 150) {
    vector<Modular<T>> c(a.size() + b.size() - 1, 0);
    for (int i = 0; i < (int) a.size(); i++) {
      for (int j = 0; j < (int) b.size(); j++) {
        c[i + j] += a[i] * b[j];
      }
    }
    return c;
  } 
  vector<int> a_mul(a.size());
  for (int i = 0; i < (int) a.size(); i++) {
    a_mul[i] = static_cast<int>(a[i]);
  }
  vector<int> b_mul(b.size());
  for (int i = 0; i < (int) b.size(); i++) {
    b_mul[i] = static_cast<int>(b[i]);
  }
  vector<int> c_mul = fft::multiply_mod(a_mul, b_mul, T::value);
  vector<Modular<T>> c(c_mul.size());
  for (int i = 0; i < (int) c.size(); i++) {
    c[i] = c_mul[i];
  }
  return c;
}

template <typename T>
typename enable_if<is_same<typename Modular<T>::Type, int>::value, vector<Modular<T>>>::type& operator*=(
    vector<Modular<T>>& a,
    const vector<Modular<T>>& b) {
  return a = a * b;
}

int ckadd(int a, int b) {
  return a + b >= md ? a + b - md : a + b;
}

vector<int> add_mod(vector<int> a, vector<int> b) {
  if (a.size() < b.size()) {
    swap(a, b);
  }
  vector<int> res = a;
  for (int i = 0; i < (int) b.size(); i++) {
    res[i] = ckadd(res[i], b[i]);
  }
  return res;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<vector<int>> pt(n, vector<int>(2));
  vector<vector<int>> arc(n, vector<int>(2));
  for (int i = 0; i < 2 * n; i++) {
    if (i % 2 == 0) {
      if (s[i] == '?') {
        arc[i / 2][0] = arc[i / 2][1] = 1;
      } else {
        arc[i / 2][s[i] == 'P' ? 1 : 0] = 1;
      }
    } else {
      if (s[i] == '?') {
        pt[i / 2][0] = pt[i / 2][1] = 1;
      } else {
        pt[i / 2][s[i] == 'R' ? 1 : 0] = 1;
      }
    }
  }
  vector<vector<vector<vector<int>>>> st(4 * n, vector<vector<vector<int>>>(2, vector<vector<int>>(2)));
  function<void(int, int, int)> Build = [&](int x, int l, int r) {
    if (l == r) {
      if (arc[l][0]) {
        st[x][0][0] = vector<int>{0, pt[l][0] + pt[l][1]};
        st[x][0][1] = vector<int>{pt[l][1], pt[l][0], 0};
      }
      if (arc[l][1]) {
        st[x][1][0] = vector<int>{0, pt[l][0], pt[l][1]};
        st[x][1][1] = vector<int>{0, pt[l][0] + pt[l][1]};
      }
      return;
    }
    int mid = l + r >> 1;
    Build(x << 1, l, mid);
    Build(x << 1 | 1, mid + 1, r);
    for (int a = 0; a < 2; a++) {
      for (int b = 0; b < 2; b++) {
        for (int c = 0; c < 2; c++) {
          st[x][b][c] = add_mod(fft::multiply_mod(st[x << 1][b][a], st[x << 1 | 1][a][c], md), st[x][b][c]);
        }
      }
    }
  };
  Build(1, 0, n - 1);
  vector<int> res = add_mod(st[1][0][0], st[1][1][1]);
  if (res.size() > n) {
    cout << res[n] << '\n';
  } else {
    cout << 0 << '\n';
  }
  return 0;
}

詳細信息

Test #1:

score: 100
Accepted
time: 1ms
memory: 3696kb

input:

2
????

output:

12

result:

ok 1 number(s): "12"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3508kb

input:

3
??YR?B

output:

4

result:

ok 1 number(s): "4"

Test #3:

score: 0
Accepted
time: 0ms
memory: 3736kb

input:

5
YBYRPBYRYB

output:

0

result:

ok 1 number(s): "0"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3560kb

input:

10
PRPBPRPRPRPBYB?R?BY?

output:

3

result:

ok 1 number(s): "3"

Test #5:

score: 0
Accepted
time: 1ms
memory: 3740kb

input:

10
?R?R?BYB?R?R?B?B?BYR

output:

96

result:

ok 1 number(s): "96"

Test #6:

score: 0
Accepted
time: 0ms
memory: 3752kb

input:

10
YRPRYRY???P?YB?BYRY?

output:

32

result:

ok 1 number(s): "32"

Test #7:

score: 0
Accepted
time: 1ms
memory: 3744kb

input:

10
PBYBPRPBYRPBYRYBPRPB

output:

0

result:

ok 1 number(s): "0"

Test #8:

score: 0
Accepted
time: 0ms
memory: 3744kb

input:

10
PBPRPRYBYRYRYB?B?RYB

output:

0

result:

ok 1 number(s): "0"

Test #9:

score: 0
Accepted
time: 0ms
memory: 3728kb

input:

10
PRP?PBPRYR??Y?YRPB?R

output:

12

result:

ok 1 number(s): "12"

Test #10:

score: 0
Accepted
time: 0ms
memory: 3752kb

input:

10
?RYB??P??B?B?B???RPR

output:

416

result:

ok 1 number(s): "416"

Test #11:

score: 0
Accepted
time: 267ms
memory: 73280kb

input:

50000
YBPBYRPRPRPRPBPRPBPBPBYRPRPBPBYRPBPRYBYBPBPBPRPBPBYRYBYRPBYRYRPBYRYRYRPBYBYRPBPBYBYBPBYRPBPBYBYBYRPBPRYBPBYBPRPRYBPRPBYBPRPBYRPBYBPRYBPBPBYRYBYBYBPRYBYRPRPRPRPRYRYBPBPBPBPRPRYBYRYBPRPRPRPBYBPBPRYRPRPBYRPBYRYRPBYBYBPBYRYRPBPRYBPRYBPBPBYRPBPBYBYBPRPBYBYBYRYRPBPRPRPRPRPRYBPBPBPRYBYRPRPRYBYRPRPBYR...

output:

0

result:

ok 1 number(s): "0"

Test #12:

score: 0
Accepted
time: 277ms
memory: 73292kb

input:

50000
YRPBPBYRYRYRYBYBYRPBPBPBPBPBYRYBPBPRYBPBYRYRPRYBYBYBYRPRPBPBPRYRPBYBYBPBYRYRPRPBPBPBPRYBYBYRYRPRPRYBPRPBYRPBPRYRPRYBPRYBYBYRYRYBYRYRYBYRPBPBPBYBPBPRPBPRYRPRYBYBPBPRPBPBPRPRPBYRYRPBPBPBYRPBYBYBYRPBPRPBPRYBPRPRYBPRPBPBYRYRYRYBYRPRPRYBYBYBPBPRPBPRYRYRPRPRPBPBPRPRPBYBYRPRPRPBYBYRPBYBPRPRPRPRPRPBPB...

output:

0

result:

ok 1 number(s): "0"

Test #13:

score: 0
Accepted
time: 262ms
memory: 73216kb

input:

50000
PRPRYBPBYBYBPBYRPBYRYBPBPBPRPRPBYBYRPRPRPRPRPRYRYBYRPBPBPRYRPRPBPRPBPRPRPRPBYRYRYRPBYBYRYRPRPRPRPRYBYBYBYBPBPRPBPBPRYRPRYRPRPRYRPRPBPBYRYBPRPRYRPBPBYBYBPBYRPBPRYRPRYRYBPBPBPRPBPRPRPRYBPBPBYBYBPRYRPRYRPBYRYBYRYRPBYBPBPRPRYRPRYBYRPRPRYBYBYBPBYRYRYRYRYRYRPBYBYRYRYBYRPRYRPBPBYBYRYBPBYBPRYBPBYRYBPR...

output:

0

result:

ok 1 number(s): "0"

Test #14:

score: 0
Accepted
time: 244ms
memory: 73236kb

input:

50000
YRPRPBPRYRYRPRYBPBYRPRPBYRYRYRPBPBYRPRYBYBYBPRYRPBPRPBPBYRPRPRPBPBYBYBPRPRPRYRYRYBYRPBYBPBPRYBPRYBYBYBPBYBYBPBPBPRYRPRPBYRYBYRPRYBYRPRYRPRPRYRPBYRYRYBYRYRPRYRYRPBPRPBYRYRPBYRPBPBPBPRPBYBYBPRYBPBPBYRYRYBYRPRPBPRYBPRPBYRPBYBYBPBPRPBYRYRPRPBPRPBPBYRPRPBYRPRPRYRYRPBYBYBPBPBYBPBYBYRYBYRPBPBPBPRYRPB...

output:

0

result:

ok 1 number(s): "0"

Test #15:

score: 0
Accepted
time: 269ms
memory: 73492kb

input:

50000
YBPBYRPRYRPRPBPBYBYRPBYRPBPRPRPBPBPBYRYBYRPBYRYRPBYRPRPRYBPRYRYBYBPRPRYBYBPRPRPRYRPRYBPRPBYRPBYRPBYRPRPBPBPRPBPBYRYBPRPBPBPBPBYRYRPRPRYBYRPRYBYBYBYBYRYRPBPRYRYRPRYBPRPBPRPRPRPRPBPRPBYBPBPBPBYRPBYBPBPRPBYRPRPRYRYBYRPRPBPRYBYRPBPRPBPRYRPRYBYRYBYBPRPRPRPBYRPBPBYRYRPBPRYBPRYBPRYBPRYBYRPBYBPBPBYRPR...

output:

0

result:

ok 1 number(s): "0"

Test #16:

score: 0
Accepted
time: 32ms
memory: 11124kb

input:

5000
PR?BPB?BY?PRY??RPB?R??YBY?P?YRPBYBPRP?YBYBYRPRPB?BPBPR?RYR??Y??RYR?BPRYR?RPRP?Y?PRY?Y?YB??PBYRYR?RPB?BPB?BY?P?Y?YBY??RPB?BPRPBY???PRP?YB?R?RP?PR?BPB???R?B?RP?PBYB?BPRYBP?P??B?RPRP???P???PRYB?RYRP?Y??RPR?BP?PR?BPBPRYR?B??PB??YBPB?B?BY?YB?RY?PR?RYB???BYBP?Y??RYRYB?RYBYBPBYRYBP?YBYR?RPBYBY?YRP??R?...

output:

101508706

result:

ok 1 number(s): "101508706"

Test #17:

score: 0
Accepted
time: 31ms
memory: 10936kb

input:

5000
Y?P?PBYBYBPBYB?RYBPRPB?B??YRY??RP?PB??P??BYR?B?BP??R?R?R?BYBP??BY?Y?PBY?Y?YR?RY?PRPR?R?RPR?RPR?BYR?B?B?RPRPR?RP?Y?YRP?Y??RYB????YRY?YR?BP?YB?B??Y??B?RPBYR?RP????B?RPR??????P?PRPR?RP?PR?????BP?P?YB?BYRP?PBP?YBYB?RPR?R?B?BYRYR?RPBPBY??BYBPRYRPBPB?R?RPR?BYBP?YRY?PR?BPR?RY????BYBYB?RYRP???Y???PBY?Y...

output:

748282195

result:

ok 1 number(s): "748282195"

Test #18:

score: 0
Accepted
time: 34ms
memory: 10972kb

input:

5000
P?PRPRPBP??RYB??YBPBYRYB?BP?YB?B?BY??R?BYRP??BPRY?YBYB?RY????B??????PB?RP?P??R?BPB?BY?PR?RPBPBPR?BY?YB?BYBYRYBYRYBY?Y??RP?YR?R?R?BY?PBY??RYBPBYBYBY?PBY?P?YB?RYR???RY?YBY?YRYRY?PBY?P?PBYRPRY?PBP???PBYRPRY?Y?P?P?Y?PR???B?B?RP???PBY?P?PR???BP?PR????P?YB??YR??YRYBYR?B?BP??BPB??P?Y?PRYRY?YB??YR?RY?Y...

output:

24097861

result:

ok 1 number(s): "24097861"

Test #19:

score: 0
Accepted
time: 39ms
memory: 11100kb

input:

5000
??PBPRYBPR??PRP?PRYBY???P?YRPBYBY?YR?RYR??Y?P?YRPR?BPBY?PRPRYB?RYBY?P?????YBPBYBY?Y??BY?PB???BP?P?Y???YR??YBP???YRYB?BPBPRP???PRY??B???BPB???R?RP?PB???BYRP?YB?BP??RP?PBYRPRPR??P??RY????B?????RP?YBYBPRYBYB?RYRYBP??RPB??YRPBY?PBPBP?YRYBPR?BPRYBPB???BYR?RY?PB?RYRY??BYRP?Y?YRP?PRPR????Y?PRPRYBP?YBP...

output:

447561693

result:

ok 1 number(s): "447561693"

Test #20:

score: 0
Accepted
time: 28ms
memory: 10900kb

input:

5000
P?P?P??????BPR?RY?PR??Y?Y??BPR??PB?B??PRP?YB???RPRPRPBY??R??PRYBYR?RPR?BP??R?B?RYRPRP??B?BYRY??R?RP???P?PRP??RY??RY?YBY???????P?Y?PBPRYBPRYRY?P?PB?BPR??P?Y?Y?Y?PR?RPB??Y??BYRP?PRPRY??R?RYBPR??YBP??B?RPRYBPR?BP??BYBYBPRYRPBPRPRY?Y?YBYRPBP?PB??Y?P??????R?BPBYR???BPR?B?R???BYR?BP?P?Y?YRY?PR??YBYB?...

output:

987042679

result:

ok 1 number(s): "987042679"

Test #21:

score: 0
Accepted
time: 18ms
memory: 9768kb

input:

5000
PRPBPRPRYRPRPBYBPBPBYRPBPBPBYRYRYBPBYRPRYBPBPRYBPBYRPRYBYRYRPBPBPBPBYRPBYRYBYRPRYBPBPBPRYBPRYBYBPRPBPBYRYBPRPBYRYRPRYBPRPRPBYRPBYRYRPRPRYRYRYBYBPBPBPBPRPRPBPRPRYRPBYRYRYRPBPRPRYRPRPBYBYBPBPRPRYRPBPRYBPRYBPRPRYRPRYRPBPRYBPRPRYBYRPBYRPRYBPRPRYBYRPRYRYBPRYBPRPBPRPRPRYBYRYRYRYRPBPRPBPRPBPRPBPRYRYBY...

output:

0

result:

ok 1 number(s): "0"

Test #22:

score: 0
Accepted
time: 14ms
memory: 10064kb

input:

5000
PRYRYBPBPRYRYRYRPBPBYBYRPBPBYRPRPRYBYRPRYRPBPRYBPBYRPRYRYRYBPBPBYBPBYBPBYRYRYRYRYBYRPRPBYRYBPRYBYBPRPRPBYRYRYRPBYBPBPRPRYRPRPBPRYBYBPBPBYBPBPBPRPBYRYRYRYRPRYBYBPBYBYBPBYBYRPRYRPRPRYBYRYBYRYRYBYBYRPBPRYRYRPRPRPRPRYRPRYRYRPBYBYRPBYBPBPRYBPBYBPBPRYRYRPBPRPRPBPRYRPRYBPBYRPRYBPBYRYBPRPRYRYBYBPRPBYBP...

output:

0

result:

ok 1 number(s): "0"

Test #23:

score: 0
Accepted
time: 14ms
memory: 10136kb

input:

5000
PBYRYRYBYBPBYBYBPBYBYRPRYBYRPRPBYRYBPRYBPRPRYRYRPBYRYRPRYRYBPBYBPBPRPBPRPBPBP?YRPBYBYBPRPRPBPRYRPRYBPRYRYBYRPRYBYBPBYRPBPBYBYRYBPRPBYRYBPBYBYRYRYRPRPRYBYBPRYRPRYBYBYBPRYBPBYRYBPBPRPRPBYBYRYBYRPRYBYBYBYBYBPBYRPRPRPRPRYBYRPRYRYRYBYRPBYRPBPRPRYBPBYBYRPRYBPRYBPRPRPRPBYRPRPBYRYBY?PRYRYRYBPRYRYBYRYBY...

output:

172032

result:

ok 1 number(s): "172032"

Test #24:

score: 0
Accepted
time: 44ms
memory: 11176kb

input:

5000
????YRPB??PB??Y?Y??R??P?PRY?P??B??PBPBP???PRP??RY??RP?YRYB?R?BY?P??B?B??Y??R?RYRYRP???P?YBPR?R????YBP???P????R?R?BPR??Y?Y?YBP?Y??RY???PR??????P?P?Y??B?R?????B??Y?Y??BY??B?B???RYR???R?RY??RP?PR?RY?PB??Y?P?P???P??B?R??YR?BYRY??????R??Y??RYRPBYR??Y?P?P??B?RP?Y??B?BPBP?P???Y??B?RY?YBYB?RYRYRYBYB???...

output:

589400951

result:

ok 1 number(s): "589400951"

Test #25:

score: 0
Accepted
time: 79ms
memory: 12136kb

input:

5000
???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????...

output:

312356960

result:

ok 1 number(s): "312356960"

Test #26:

score: 0
Accepted
time: 390ms
memory: 78200kb

input:

50000
YR?BPR?BP??B??YBY?PRY?PRYB??PB?BPBY??R???RPR??Y?Y???PR???BPBPRPRY?Y?P?Y?P?YR??YR?RP?YRP??B?B???R??YR?BPR?B?R?R??Y?YBYRPR?BPBPRPRPB??YBPR??PR??Y??RYBY??RPRPB??YBPR??PBY?PBPBPRPRPRYRYB??YR?BYRP?P??RYR?R?R?RPBP?Y?YR??YBYR??YRYR???BPRPR???BP??B?BPBYBYBYR?B?RPRPBP?P?YBPB?R?BPBPR?BP?PRYRPB?BY?Y??B?B...

output:

61578469

result:

ok 1 number(s): "61578469"

Test #27:

score: 0
Accepted
time: 499ms
memory: 80688kb

input:

50000
Y??RPRP?PBYR?BPRPBYB??YBP?PBPB?????B?BYRYBPBYBPRPRYBP?P?YB?B??PBY?PB?R?RPR?RYBY?Y?PBY????B??YBYRPRY??BYR??PRPBP?P?P?Y?YBPRPBYBPRP???Y?P??RPBYBPBY??BY?Y?YRPB??Y?PBYB??P?Y?PRYBY?YBY??R?B??PR???BYRYB?RPBPBPBPR?RP??BYRYB?BP?PRP?P?YBPRP?PBYR???R?RPBP?P?YB?RPR?RYRP??B?RYRYRYBP??B???BYRYRPB??YRPRYBPB...

output:

21239954

result:

ok 1 number(s): "21239954"

Test #28:

score: 0
Accepted
time: 470ms
memory: 79608kb

input:

50000
YR??PB?BP???YRP??BYRPRP?P?PRPRPR?RPRPBYBPBY??B?B?RPRPBYRP??R?B??PR??P?PR?RYBPRPRY????R?R?RY??B?RYB?R?B?BYBPB??YRYRYBY?P?PR?B?RP??RP?YRPRYBPBYB?BYBP????RYRYR?BPRP?YRY?PB???BP??????BPR?RP?YBPB?RY?PBPBP??BYRP?YBYRP?YBYB?RPRYBYBP?YBY?YB?R??PBYBY?PB?R????P??BPRPRPRY???P???PBPRYRYB?RP?YBYRYRY????RP?...

output:

268137953

result:

ok 1 number(s): "268137953"

Test #29:

score: 0
Accepted
time: 402ms
memory: 78512kb

input:

50000
P???PR?RYBPB?RPBYB??YR??PB??YBPBP?Y?P??R?RYBPRPBYB??YB?R????YR?RPRPB?RYB?RPRP???PBYBY?YB?BYR??PR?B???B?R?RPR?RPR??PR?BYBPR????P???P?YRPR??P?PRYRYB?BYBY???P?PB?R??P??RYBPB?R?RYB???B????PRPRYR???BYRYR?B??PBP???PRP?P?YR??YRP??B?BY?Y?PRPRPRYRYRYRPRY?Y??RPBY?YR?BPRPB?R?BYR?BY??BY?P?Y?YBYRYBYRY?P??R...

output:

903429393

result:

ok 1 number(s): "903429393"

Test #30:

score: 0
Accepted
time: 390ms
memory: 78428kb

input:

50000
P??RPBYB?RP?Y??BPBPBPBYRPRPBYRP?YR??P?PBY?Y?????PRYBPBP?Y??BY??BPR?BYB???R?B??YBYRP??BP?YBPRP?YBP?P?Y?PR??YRPBYBPR?BPBY?PRY??RP???PRYBP?YRP?P??R??P?YBPR??P?PRYB?BPRYRYBP??BYB?RP??RPB??PR?R??YBPR?B??YBY?Y???P??BYRP????RYB?RYR?BP?YBP?P???P?PB??PR?RP?PR?R??P?YB?B??P?YRY?Y??RY?P?YBYBYRYRY?YRPBYBYB...

output:

360140728

result:

ok 1 number(s): "360140728"

Test #31:

score: 0
Accepted
time: 262ms
memory: 73204kb

input:

50000
PBYRYRYBYRYBYRPBYRPBPBYBYRYBYBPRPBYRYRYBYRPBPRYBYRYRYRYBYRYRYRPRYBYRPRPRPRYRPBYRPRPBYRPBYRYRPBYRYBPRYRPRYBYBYRYBPRPBYBPRPRPRYRPRYRPRYRPBYBPRPRYRYRPRPRPBYRYRYRPRPBPRPRYRYRYBYRYRYRPBYBYRPBPBYRPRPBPRYBPRPBYBPBPBPBYRYRPRPBYRPBYRYBPRPBYRYBPBPRPRPBYBPRYRPBYBYBYRPRYBYBYBPBYBPBPRYRYRYRPRYBYBYBPBPBYBPR...

output:

0

result:

ok 1 number(s): "0"

Test #32:

score: 0
Accepted
time: 271ms
memory: 73236kb

input:

50000
PRYRPBPRYRYBYRYBYRYRYRPRPBPRPRYBYBPBYRPRYRYRYRYRPBYBPRPRPRPRPRPRYBPRPBYBPBYBYBYRPRPBYBYBYBYBPRPBYBPBPRYRYBYBPBYRYBYRPBYRYRYRYBYBYRYBYRPRPBPBPBPBPBPRPRYBYRYRPBPRPRYBYRPRYRYRYRYRPRPRYRPBPRYRYRPBYBPRPBYRYRYBYRYBPRYBYRYRPRYBYBPRPBYRPBYBYRYRYRYBPBPRPBYBPBYRYBYRPBPBYBPRYBYRYBPBYRYRPBYBPBYBPRPBYBYRYB...

output:

0

result:

ok 1 number(s): "0"

Test #33:

score: 0
Accepted
time: 271ms
memory: 73268kb

input:

50000
PBPRPBYRPRYBYBYRPBPBYRPBPRPBPBPBYRPBYBYRPRYBPRPRYRYBPBPBYRPRYRYRPBYRYRPBPBYRPBPBYRPBYRYBYRYBYBYRYBPRPBYRYRYRPBYRPBYBPRYRYBPRYBYBYRPBPRYRYRYBYRPBPBPBPBPRYBYRPBYBYRYRYBYRYRYBYRPRYRPBYRPBPRYBYRPBPBYRYRPRYRYRYBPBYRPRPRPBPRPRYRPBPBYBPBPBYBYBYBPBYBPRPBYBYRPRPBYBPRPBPRPBYRPBPRYRPRYRYRYBPRPRPRYRPBYBPR...

output:

0

result:

ok 1 number(s): "0"

Test #34:

score: 0
Accepted
time: 584ms
memory: 82952kb

input:

50000
?BY???P????RPB??P???YB?R?BY?YR????PR??P???????P?YRP?PRY?PB??Y?YR???B??Y?YR?BPRYR?B?B?BPRY?Y???PRY?PBYBPRP?Y?PBY?YRP?PR?R??PRYRY?Y?Y?Y?P?PBPB?RP?PRY?P???PRY???P???P???PB?B?B?B?B?BYBP?PR????P??BYRY??????R?B??P?????PBY??R?B??Y?YB??PBPB?B???R?BP??B?BPB?R????YR????YBP?P?YR????Y?PRPB??Y????R?R?RY??B...

output:

908700788

result:

ok 1 number(s): "908700788"

Test #35:

score: 0
Accepted
time: 953ms
memory: 93400kb

input:

50000
??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????...

output:

422064317

result:

ok 1 number(s): "422064317"