#include using namespace std; #include #include using namespace atcoder; using ll = long long; using vll = vector; using vvll = vector; using vvvll = vector; using vb = vector; using vvb = vector; using vvvb = vector; #define all(A) A.begin(),A.end() #define rep(i, n) for (ll i = 0; i < (ll) (n); i++) template bool chmax(T& p, T q, bool C = 1) { if (C == 0 && p == q) { return 1; } if (p < q) { p = q; return 1; } else { return 0; } } template bool chmin(T& p, T q, bool C = 1) { if (C == 0 && p == q) { return 1; } if (p > q) { p = q; return 1; } else { return 0; } } ll modPow(long long a, long long n, long long p) { if (n == 0) return 1; // 0乗にも対応する場合 if (n == 1) return a % p; if (n % 2 == 1) return (a * modPow(a, n - 1, p)) % p; long long t = modPow(a, n / 2, p); return (t * t) % p; } ll cnt = 0; ll gcd(ll(a), ll(b)) { cnt++; if (a == 0)return b; if (b == 0)return a; ll c = a; while (a % b != 0) { c = a % b; a = b; b = c; } return b; } ll sqrtz(ll N) { ll L = 0; ll R = sqrt(N) + 10000; while (abs(R - L) > 1) { ll mid = (R + L) / 2; if (mid * mid <= N)L = mid; else R = mid; } return L; } ll nzkon(ll N, ll K) {// return 0; } using mint = modint998244353; using vm = vector; using vvm = vector; using vvvm = vector; vector fact, factinv, inv; const ll mod = 998244353; void prenCkModp(ll n) { fact.resize(n + 5); factinv.resize(n + 5); inv.resize(n + 5); fact[0] = fact[1] = 1; factinv[0] = factinv[1] = 1; inv[1] = 1; for (ll i = 2; i < n + 5; i++) { fact[i] = (fact[i - 1] * i); inv[i] = (mod - ((inv[mod % i] * (mod / i)))); factinv[i] = (factinv[i - 1] * inv[i]); } } mint nCk(ll n, ll k) { if (n < k || k < 0) return 0; return (fact[n] * ((factinv[k] * factinv[n - k]))); } bool DEB = 0; using vmmat = vector>; void pl(vm& res, vm pk) { ll d = pk.size(); if (d > res.size())res.resize(d); rep(i, d) { res[i] += pk[i]; } } vmmat mul(vmmat A, vmmat B) { ll n = A.size(); vmmat res(n, vvm(n, vm({ 0 }))); rep(i, n)rep(j, n)rep(k, n)pl(res[i][j], convolution(A[i][k], B[k][j])); return res; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); vmmat R = { {{1},{0,1}},{{0},{1}} }; vmmat B = { {{1},{0}},{{0,1},{1}} }; queue Q; ll N; string S; cin >> N >> S; rep(i, N) { Q.push((S[N - i - 1] == 'B' ? B : R)); } while (Q.size() > 1) { queue NQ; while (Q.size() > 1) { auto a = Q.front(); Q.pop(); auto b = Q.front(); Q.pop(); NQ.push(mul(a, b)); } if (!Q.empty()) { auto a = Q.front(); Q.pop(); NQ.push(a); } Q = NQ; } auto V = Q.front(); pl(V[0][0], V[0][1]); pl(V[0][0], V[1][1]); pl(V[0][0], V[1][0]); V[0][0].resize(N + 1); rep(i, N)cout << V[0][0][i + 1].val() << endl; }