#pragma GCC optimize ("Ofast") #pragma GCC optimize ("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } //////////////////////////////////////////////////////////////////////////////// template struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 998244353; using Mint = ModInt; int N; char S[1510]; Mint dp[2][510][510][2]; Mint DP[2][510][510][2]; int main() { for (; ~scanf("%d", &N); ) { scanf("%s", S); const int L = N / 3; memset(dp, 0, sizeof(dp)); memset(DP, 0, sizeof(DP)); dp[0][0][0][0] = 1; for (int i = 0; i < N; ++i) { auto crt = dp[i & 1], nxt = dp[(i + 1) & 1]; auto CRT = DP[i & 1], NXT = DP[(i + 1) & 1]; memset(nxt, 0, sizeof(dp[0])); memset(NXT, 0, sizeof(DP[0])); const bool can0 = (S[i] == '?' || S[i] == '0'); const bool can1 = (S[i] == '?' || S[i] == '1'); const int lim = min({i, N - i, L}); for (int a = 0; a <= lim; ++a) for (int b = 0; b <= lim - a; ++b) { for (int s = 0; s < 2; ++s) if (crt[a][b][s]) { // 0 if (can0 && a + 1 + b <= L) { nxt[a + 1][b][0] += crt[a][b][s]; } // 1 if (can1) { if (!s && a) { nxt[a - 1][b + 1][1] += crt[a][b][s]; } else { nxt[a][b][1] += crt[a][b][s]; } } // 2 if (can0 && b) { NXT[a][b - 1][0] += crt[a][b][s]; } } } for (int a = 0; a <= lim; ++a) for (int b = 0; b <= lim - a; ++b) { for (int s = 0; s < 2; ++s) if (CRT[a][b][s]) { // 1 if (can1) { if (!s && a) { NXT[a - 1][b + 1][1] += CRT[a][b][s]; } else { NXT[a][b][1] += CRT[a][b][s]; } } // 2 if (can0 && b) { NXT[a][b - 1][0] += CRT[a][b][s]; } } } } Mint ans = 0; for (int s = 0; s < 2; ++s) { ans += dp[N & 1][0][0][s]; ans += DP[N & 1][0][0][s]; } printf("%u\n", ans.x); } return 0; }