/**
 * @brief ユーザ定義リテラル
 * @author えびちゃん
 */

#ifndef H_int_literals
#define H_int_literals

#include <cstddef>
#include <cstdint>

constexpr intmax_t  operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t    operator ""_zu(unsigned long long n) { return n; }
constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }

#endif  /* !defined(H_int_literals) */

/**
 * @brief 多次元 vector の作成
 * @author えびちゃん
 */

#ifndef H_make_vector
#define H_make_vector

#include <cstddef>
#include <type_traits>
#include <vector>

namespace detail {
  template <typename Tp, size_t N>
  std::vector<Tp> make_vector(
      std::vector<size_t>& sizes,
      typename std::enable_if<(N == 1), Tp const&>::type x
  ) {
    return std::vector<Tp>(sizes[0], x);
  }
  template <typename Tp, size_t N>
  auto make_vector(
      std::vector<size_t>& sizes,
      typename std::enable_if<(N > 1), Tp const&>::type x
  ) {
    size_t size = sizes[N-1];
    sizes.pop_back();
    return std::vector<decltype(make_vector<Tp, N-1>(sizes, x))>(
        size, make_vector<Tp, N-1>(sizes, x)
    );
  }
}  // detail::

template <typename Tp, size_t N>
auto make_vector(size_t const(&sizes)[N], Tp const& x = Tp()) {
  std::vector<size_t> s(N);
  for (size_t i = 0; i < N; ++i) s[i] = sizes[N-i-1];
  return detail::make_vector<Tp, N>(s, x);
}

#endif  /* !defined(H_make_vector) */

/**
 * @brief 合同算術用クラス
 * @author えびちゃん
 */

#ifndef H_modint
#define H_modint

#include <cstdint>
#include <type_traits>
#include <utility>

template <intmax_t Modulo>
class modint {
public:
  using value_type = intmax_t;

private:
  static constexpr value_type S_mod = Modulo;
  value_type M_value = 0;
  value_type M_mod;  // runtime value (used if S_mod == 0)

  static constexpr value_type S_inv(value_type n, value_type m) {
    value_type x = 0;
    value_type y = 1;
    value_type a = n;
    value_type b = m;
    for (value_type u = y, v = x; a;) {
      value_type q = b / a;
      std::swap(x -= q*u, u);
      std::swap(y -= q*v, v);
      std::swap(b -= q*a, a);
    }
    if ((x %= m) < 0) x += m;
    return x;
  }

  static value_type S_normalize(value_type n, value_type m) {
    if (n >= m) {
      n %= m;
    } else if (n < 0) {
      if ((n %= m) < 0) n += m;
    }
    return n;
  }

public:
  modint() = default;
  modint(modint const&) = default;
  modint(modint&&) = default;
  template <typename Up = intmax_t, typename std::enable_if<(Modulo > 0), Up>::type* = nullptr>
  modint(value_type n):
    M_value(S_normalize(n, Modulo)) {}
  template <typename Up = intmax_t, typename std::enable_if<(Modulo == 0), Up>::type* = nullptr>
  modint(value_type n, value_type m):
    M_value(S_normalize(n, m)), M_mod(m) {}
  // copying runtime mod
  modint(value_type n, modint const& base):
    M_value(S_normalize(n, base.modulo())), M_mod(base.M_mod) {}

  modint& operator =(modint const&) = default;
  modint& operator =(modint&&) = default;
  modint& operator =(value_type n) {
    M_value = S_normalize(n, modulo());
    return *this;
  }

  modint& operator +=(modint const& that) {
    if ((M_value += that.M_value) >= modulo()) M_value -= modulo();
    return *this;
  }
  modint& operator -=(modint const& that) {
    if ((M_value -= that.M_value) < 0) M_value += modulo();
    return *this;
  }
  modint& operator *=(modint const& that) {
    (M_value *= that.M_value) %= modulo();
    return *this;
  }
  modint& operator /=(modint const& that) {
    (M_value *= S_inv(that.M_value, modulo())) %= modulo();
    return *this;
  }

  modint& operator +=(value_type const& n) {
    if ((M_value += S_normalize(n, modulo())) >= modulo()) M_value -= modulo();
    return *this;
  }
  modint& operator -=(value_type const& n) {
    if ((M_value -= S_normalize(n, modulo())) < 0) M_value += modulo();
    return *this;
  }
  modint& operator *=(value_type const& n) {
    (M_value *= S_normalize(n, modulo())) %= modulo();
    return *this;
  }
  modint& operator /=(value_type const& n) {
    (M_value *= S_inv(S_normalize(n, modulo()), modulo())) %= modulo();
    return *this;
  }

  modint operator +(modint const& that) const { return modint(*this) += that; }
  modint operator -(modint const& that) const { return modint(*this) -= that; }
  modint operator *(modint const& that) const { return modint(*this) *= that; }
  modint operator /(modint const& that) const { return modint(*this) /= that; }
  modint operator +(value_type const& n) const { return modint(*this) += n; }
  modint operator -(value_type const& n) const { return modint(*this) -= n; }
  modint operator *(value_type const& n) const { return modint(*this) *= n; }
  modint operator /(value_type const& n) const { return modint(*this) /= n; }

  modint operator +() const { return *this; }
  modint operator -() const {
    if (M_value == 0) return *this;
    return modint(modulo()-M_value, *this);
  }

  bool operator ==(modint const& that) const {
    return M_value == that.M_value;
  }
  bool operator ==(value_type const& n) const {
    return M_value == S_normalize(n, modulo());
  }
  bool operator !=(modint const& that) const { return !(*this == that); }
  bool operator !=(value_type const& n) const { return !(*this == n); }

  value_type get() const { return M_value; }
  value_type modulo() const { return ((S_mod > 0)? S_mod: M_mod); }
};

template <typename Tp, intmax_t Modulo>
modint<Modulo> operator +(Tp const& lhs, modint<Modulo> const& rhs) {
  return rhs + lhs;
}
template <typename Tp, intmax_t Modulo>
modint<Modulo> operator -(Tp const& lhs, modint<Modulo> const& rhs) {
  return -(rhs - lhs);
}
template <typename Tp, intmax_t Modulo>
modint<Modulo> operator *(Tp const& lhs, modint<Modulo> const& rhs) {
  return rhs * lhs;
}
template <typename Tp, intmax_t Modulo>
modint<Modulo> operator /(Tp const& lhs, modint<Modulo> const& rhs) {
  return modint<Modulo>(lhs, rhs) / rhs;
}
template <typename Tp, intmax_t Modulo>
bool operator ==(Tp const& lhs, modint<Modulo> const& rhs) {
  return rhs == lhs;
}
template <typename Tp, intmax_t Modulo>
bool operator !=(Tp const& lhs, modint<Modulo> const& rhs) {
  return !(lhs == rhs);
}

#ifndef CALL_FROM_TEST
constexpr intmax_t mod = 1000'000'007;
// constexpr intmax_t mod = 998244353;
using mi = modint<mod>;
#endif

#endif  /* !defined(H_modint) */

/**
 * @brief 合同演算の前計算テーブル
 * @author えびちゃん
 */

#ifndef H_modtable
#define H_modtable

#include <vector>

#ifdef CALL_FROM_TEST
#include "ModularArithmetic/modint.cpp"
#endif

template <typename ModInt>
class modtable {
public:
  using value_type = ModInt;
  using size_type = size_t;
  using underlying_type = typename ModInt::value_type;

private:
  std::vector<value_type> M_f, M_i, M_fi;

public:
  modtable() = default;
  modtable(modtable const&) = default;
  modtable(modtable&&) = default;

  // not compatible with runtime mod
  modtable(underlying_type n): M_f(n+1), M_i(n+1), M_fi(n+1) {
    M_f[0] = 1;
    for (underlying_type i = 1; i <= n; ++i)
      M_f[i] = M_f[i-1] * i;

    underlying_type mod = M_f[0].modulo();
    M_i[1] = 1;
    for (underlying_type i = 2; i <= n; ++i)
      M_i[i] = -value_type(mod / i) * M_i[mod % i];

    M_fi[0] = 1;
    for (underlying_type i = 1; i <= n; ++i)
      M_fi[i] = M_fi[i-1] * M_i[i];
  }

  modtable& operator =(modtable const&) = default;
  modtable& operator =(modtable&&) = default;

  value_type inverse(underlying_type n) const { return M_i[n]; }
  value_type factorial(underlying_type n) const { return M_f[n]; }
  value_type factorial_inverse(underlying_type n) const { return M_fi[n]; }

  value_type binom(underlying_type n, underlying_type k) const {
    if (n < 0 || n < k || k < 0) return 0;
    // assumes n < mod
    return M_f[n] * M_fi[k] * M_fi[n-k];
  }
};

#endif  /* !defined(H_modtable) */

#include <cstdio>
#include <algorithm>
#include <string>

int main() {
  size_t n;
  scanf("%zu", &n);

  char buf[262144];
  scanf("%s", buf);
  std::string s = buf;

  if (s.front() == 'W' || s.back() == 'W') return puts("0"), 0;
  // if (std::count(s.begin(), s.end(), 'B') != std::count(s.begin(), s.end(), 'W')) return puts("0"), 0;

  modtable<mi> mt(s.length());

  // ---- [12, 34]
  // -==- [13, 24], [14, 23]
  mi res = 1;
  int opened = 0;
  for (size_t i = 0; i < s.length(); ++i) {
    if (opened % 2 == 0) {
      if (s[i] == 'W') {
        res *= opened;
        --opened;
      } else {
        ++opened;
      }
    } else {
      if (s[i] == 'W') {
        ++opened;
      } else {
        res *= opened;
        --opened;
      }
    }
    if (opened < 0) return puts("0"), 0;
  }

  if (opened) res = 0;
  res *= mt.factorial(n);
  printf("%jd\n", res.get());
}


Measured memory_bytes: 9984