/**
 *    author:  tourist
 *    created: 26.01.2020 22:39:03       
**/
#include <bits/stdc++.h>

using namespace std;

template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
  return '"' + s + '"';
}

string to_string(const char* s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

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 const Modular<U>& abs(const Modular<U>& v) { return v; }

  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>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}

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 = (int) 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

template <typename T>
vector<T>& operator+=(vector<T>& a, const vector<T>& b) {
  if (a.size() < b.size()) {
    a.resize(b.size());
  }
  for (int i = 0; i < (int) b.size(); i++) {
    a[i] += b[i];
  }
  return a;
}

template <typename T>
vector<T> operator+(const vector<T>& a, const vector<T>& b) {
  vector<T> c = a;
  return c += b;
}

template <typename T>
vector<T>& operator-=(vector<T>& a, const vector<T>& b) {
  if (a.size() < b.size()) {
    a.resize(b.size());
  }
  for (int i = 0; i < (int) b.size(); i++) {
    a[i] -= b[i];
  }
  return a;
}

template <typename T>
vector<T> operator-(const vector<T>& a, const vector<T>& b) {
  vector<T> c = a;
  return c -= b;
}

template <typename T>
vector<T> operator-(const vector<T>& a) {
  vector<T> c = a;
  for (int i = 0; i < (int) c.size(); i++) {
    c[i] = -c[i];
  }
  return c;
}

template <typename T>
vector<T> operator*(const vector<T>& a, const vector<T>& b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  vector<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;
}

template <typename T>
vector<T>& operator*=(vector<T>& a, const vector<T>& b) {
  return a = a * b;
}

template <typename T>
vector<T> inverse(const vector<T>& a) {
  assert(!a.empty());
  int n = (int) a.size();
  vector<T> b = {1 / a[0]};
  while ((int) b.size() < n) {
    vector<T> a_cut(a.begin(), a.begin() + min(a.size(), b.size() << 1));
    vector<T> x = b * b * a_cut;
    b.resize(b.size() << 1);
    for (int i = (int) b.size() >> 1; i < (int) min(x.size(), b.size()); i++) {
      b[i] = -x[i];
    }
  }
  b.resize(n);
  return b;
}

template <typename T>
vector<T>& operator/=(vector<T>& a, const vector<T>& b) {
  int n = (int) a.size();
  int m = (int) b.size();
  if (n < m) {
    a.clear();
  } else {
    vector<T> d = b;
    reverse(a.begin(), a.end());
    reverse(d.begin(), d.end());
    d.resize(n - m + 1);
    a *= inverse(d);
    a.erase(a.begin() + n - m + 1, a.end());
    reverse(a.begin(), a.end());
  }
  return a;
}

template <typename T>
vector<T> operator/(const vector<T>& a, const vector<T>& b) {
  vector<T> c = a;
  return c /= b;
}

template <typename T>
vector<T>& operator%=(vector<T>& a, const vector<T>& b) {
  int n = (int) a.size();
  int m = (int) b.size();
  if (n >= m) {
    vector<T> c = (a / b) * b;
    a.resize(m - 1);
    for (int i = 0; i < m - 1; i++) {
      a[i] -= c[i];
    }
  }
  return a;
}

template <typename T>
vector<T> operator%(const vector<T>& a, const vector<T>& b) {
  vector<T> c = a;
  return c %= b;
}

template <typename T, typename U>
vector<T> power(const vector<T>& a, const U& b, const vector<T>& c) {
  assert(b >= 0);
  vector<U> binary;
  U bb = b;
  while (bb > 0) {
    binary.push_back(bb & 1);
    bb >>= 1;
  }
  vector<T> res = vector<T>{1} % c;
  for (int j = (int) binary.size() - 1; j >= 0; j--) {
    res = res * res % c;
    if (binary[j] == 1) {
      res = res * a % c;
    }
  }
  return res;
}

template <typename T>
vector<T> derivative(const vector<T>& a) {
  vector<T> c = a;
  for (int i = 0; i < (int) c.size(); i++) {
    c[i] *= i;   	
  }
  if (!c.empty()) {
    c.erase(c.begin());
  }
  return c;
}
 
template <typename T>
vector<T> primitive(const vector<T>& a) {
  vector<T> c = a;
  c.insert(c.begin(), 0);
  for (int i = 1; i < (int) c.size(); i++) {
    c[i] /= i;
  }
  while (!c.empty() && c.back() == 0) {
    c.pop_back();
  }
  return c;
}

template <typename T>
T evaluate(const vector<T>& a, const T& x) {
  T res = 0;
  for (int i = (int) a.size() - 1; i >= 0; i--) {
    res = res * x + a[i];
  }
  return res;
}

struct State {
  vector<Mint> p;
  vector<Mint> q;
  Mint c;
};
     
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<vector<State>> dp(2, vector<State>(3));
  dp[0][2].c = 1;
  dp[1][2].p = {1};
  dp[1][2].c = -1;
  for (int i = 0; i < n; i++) {
    vector<vector<State>> new_dp(2, vector<State>(3));
    for (int parity = 0; parity < 2; parity++) {
      for (int want = 0; want < 3; want++) {
        State& ft = dp[parity][want];
        for (int rot = 0; rot < 2; rot++) {
          if (rot == 0) { // a[i - 1] < a[i]
            if (want == 1) {
              continue;
            }
            int new_parity = parity ^ 1;
            int new_want = 2;
            if (s[i] == 'X') {
              if (new_parity == 1) {
                continue;
              }
              new_want = 0;
            } else {
              if (new_parity == 0) {
                new_want = 1;
              }
            }
            State& to = new_dp[new_parity][new_want];
            to.p += primitive(ft.p) + vector<Mint> {ft.c};
            to.q += primitive(ft.q);
            to.c += -ft.c;
          } else { // a[i - 1] > a[i]
            int new_parity = 0;
            int new_want = (s[i] == 'X' ? 0 : 1);
            if (want == new_want) {
              continue;
            }
            State& to = new_dp[new_parity][new_want];
            to.p += -primitive(ft.p) + vector<Mint> {evaluate(primitive(ft.p), Mint(1))};
            to.q += -primitive(ft.q) + vector<Mint> {evaluate(primitive(ft.q), Mint(1)) - ft.c};
            to.c += ft.c;
          }
        }
      }
    }
    swap(dp, new_dp);
  }
  vector<Mint> ans(3);
  for (int parity = 0; parity < 2; parity++) {
    for (int want = 0; want < 3; want++) {
      State& ft = dp[parity][want];
      debug(parity, want, ft.p, ft.q, ft.c);
      vector<Mint> cur(3);
      cur[0] += ft.c / 2;
      cur[2] -= ft.c / 2;
      for (int shift = 0; shift < 2; shift++) {
        vector<Mint>& r = (shift == 0 ? ft.p : ft.q);
        Mint c0 = 1;
        Mint c1 = 1;
        for (int i = 0; i < (int) r.size(); i++) {
          cur[shift + 0] += c0 * r[i];
          cur[shift + 1] -= c1 * r[i];
          c0 = c0 * (i + 1);
          c1 = c1 * (i + 1) + 1;
        }
      }
      debug(cur);
      for (int i = 0; i < 3; i++) {
        ans[i] += cur[i] * (want == 0 ? 1 : (want == 1 ? -1 : 0));
      }
      debug(ans);
      if (want >= 1) {
        vector<Mint> P = primitive(ft.p);
        ans[0] += evaluate(P, Mint(1)) - evaluate(P, Mint(0));
        vector<Mint> Q = primitive(ft.q);
        ans[1] += evaluate(Q, Mint(1)) - evaluate(Q, Mint(0));
        ans[0] += ft.c;
        ans[1] -= ft.c;
      }
      debug(ans);
    }
  }
  cout << ans[0] << " " << ans[1] << " " << ans[2] << '\n';
  return 0;
}


Measured memory_bytes: 256