#include #define rep(i,n) for(int i = 0; i < (n); i++) using namespace std; typedef long long ll; template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int getmod() const { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } constexpr bool operator < (const Fp& r) const noexcept { return this->val < r.val; } friend constexpr istream& operator >> (istream& is, Fp& x) noexcept { is >> x.val; x.val %= MOD; if (x.val < 0) x.val += MOD; return is; } friend constexpr ostream& operator << (ostream& os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp& a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; namespace NTT { long long modpow(long long a, long long n, int mod) { long long res = 1; while (n > 0) { if (n & 1) res = res * a % mod; a = a * a % mod; n >>= 1; } return res; } long long modinv(long long a, int mod) { long long b = mod, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } u %= mod; if (u < 0) u += mod; return u; } int calc_primitive_root(int mod) { if (mod == 2) return 1; if (mod == 167772161) return 3; if (mod == 469762049) return 3; if (mod == 754974721) return 11; if (mod == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; long long x = (mod - 1) / 2; while (x % 2 == 0) x /= 2; for (long long i = 3; i * i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) x /= i; } } if (x > 1) divs[cnt++] = x; for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (modpow(g, (mod - 1) / divs[i], mod) == 1) { ok = false; break; } } if (ok) return g; } } int get_fft_size(int N, int M) { int size_a = 1, size_b = 1; while (size_a < N) size_a <<= 1; while (size_b < M) size_b <<= 1; return max(size_a, size_b) << 1; } // number-theoretic transform template void trans(vector &v, bool inv = false) { if (v.empty()) return; int N = (int)v.size(); int MOD = v[0].getmod(); int PR = calc_primitive_root(MOD); static bool first = true; static vector vbw(30), vibw(30); if (first) { first = false; for (int k = 0; k < 30; ++k) { vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD); vibw[k] = modinv(vbw[k], MOD); } } for (int i = 0, j = 1; j < N - 1; j++) { for (int k = N >> 1; k > (i ^= k); k >>= 1); if (i > j) swap(v[i], v[j]); } for (int k = 0, t = 2; t <= N; ++k, t <<= 1) { long long bw = vbw[k]; if (inv) bw = vibw[k]; for (int i = 0; i < N; i += t) { mint w = 1; for (int j = 0; j < t/2; ++j) { int j1 = i + j, j2 = i + j + t/2; mint c1 = v[j1], c2 = v[j2] * w; v[j1] = c1 + c2; v[j2] = c1 - c2; w *= bw; } } } if (inv) { long long invN = modinv(N, MOD); for (int i = 0; i < N; ++i) v[i] = v[i] * invN; } } // for garner static constexpr int MOD0 = 754974721; static constexpr int MOD1 = 167772161; static constexpr int MOD2 = 469762049; using mint0 = Fp; using mint1 = Fp; using mint2 = Fp; static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1); static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2); static const mint2 imod01 = 187290749; // imod1 / MOD0; // small case (T = mint, long long) template vector naive_mul (const vector &A, const vector &B) { if (A.empty() || B.empty()) return {}; int N = (int)A.size(), M = (int)B.size(); vector res(N + M - 1); for (int i = 0; i < N; ++i) for (int j = 0; j < M; ++j) res[i + j] += A[i] * B[j]; return res; } // mint template vector mul (const vector &A, const vector &B) { if (A.empty() || B.empty()) return {}; int N = (int)A.size(), M = (int)B.size(); if (min(N, M) < 30) return naive_mul(A, B); int MOD = A[0].getmod(); int size_fft = get_fft_size(N, M); if (MOD == 998244353) { vector a(size_fft), b(size_fft), c(size_fft); for (int i = 0; i < N; ++i) a[i] = A[i]; for (int i = 0; i < M; ++i) b[i] = B[i]; trans(a), trans(b); vector res(size_fft); for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i]; trans(res, true); res.resize(N + M - 1); return res; } vector a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0); vector a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0); vector a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0); for (int i = 0; i < N; ++i) a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val; for (int i = 0; i < M; ++i) b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val; trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2); for (int i = 0; i < size_fft; ++i) { c0[i] = a0[i] * b0[i]; c1[i] = a1[i] * b1[i]; c2[i] = a2[i] * b2[i]; } trans(c0, true), trans(c1, true), trans(c2, true); static const mint mod0 = MOD0, mod01 = mod0 * MOD1; vector res(N + M - 1); for (int i = 0; i < N + M - 1; ++i) { int y0 = c0[i].val; int y1 = (imod0 * (c1[i] - y0)).val; int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val; res[i] = mod01 * y2 + mod0 * y1 + y0; } return res; } // long long vector mul_ll (const vector &A, const vector &B) { if (A.empty() || B.empty()) return {}; int N = (int)A.size(), M = (int)B.size(); if (min(N, M) < 30) return naive_mul(A, B); int size_fft = get_fft_size(N, M); vector a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0); vector a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0); vector a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0); for (int i = 0; i < N; ++i) a0[i] = A[i], a1[i] = A[i], a2[i] = A[i]; for (int i = 0; i < M; ++i) b0[i] = B[i], b1[i] = B[i], b2[i] = B[i]; trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2); for (int i = 0; i < size_fft; ++i) { c0[i] = a0[i] * b0[i]; c1[i] = a1[i] * b1[i]; c2[i] = a2[i] * b2[i]; } trans(c0, true), trans(c1, true), trans(c2, true); static const long long mod0 = MOD0, mod01 = mod0 * MOD1; vector res(N + M - 1); for (int i = 0; i < N + M - 1; ++i) { int y0 = c0[i].val; int y1 = (imod0 * (c1[i] - y0)).val; int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val; res[i] = mod01 * y2 + mod0 * y1 + y0; } return res; } }; // Binomial coefficient template struct BiCoef { vector fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int MOD = fact_[0].getmod(); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; const int MOD = 998244353; using mint = Fp; int main(){ cin.tie(0); ios::sync_with_stdio(0); int N; string S; cin >> N >> S; int AB = 0; rep(i,N) if(S[i] == 'A' || S[i] == 'B') AB++; cout << BiCoef(N + 1).com(N, AB) << endl; }