#include using namespace std ; #define fast_input_output ios::sync_with_stdio(false); cin.tie(nullptr); // #pragma GCC target("avx2") // #pragma GCC optimize("O3") #pragma GCC target("avx") #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") typedef long long ll ; typedef long double ld ; typedef pair P ; typedef tuple TP ; #define chmin(a,b) a = min(a,b) #define chmax(a,b) a = max(a,b) #define bit_count(x) __builtin_popcountll(x) #define gcd(a,b) __gcd(a,b) #define lcm(a,b) a / gcd(a,b) * b #define rep(i,n) for(int i = 0 ; i < n ; i++) #define rrep(i,a,b) for(int i = a ; i < b ; i++) #define repi(it,S) for(auto it = S.begin() ; it != S.end() ; it++) #define pt(a) cout << a << endl #define DEBUG(...) ; cout << #__VA_ARGS__ << endl ; for(auto x : {__VA_ARGS__}) cout << x << " " ; cout << endl ; #define DEBUG_LIST(...) cout << #__VA_ARGS__ << endl ; DEBUG_REP(__VA_ARGS__) ; #define DEBUG_REP(V) cout << "{ " ; repi(itr,V) cout << *itr << ", " ; cout << "}" << endl ; #define debug(a) cout << #a << " " << a << endl #define all(a) a.begin(), a.end() #define endl "\n" const int mod = 998244353 ; template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; modint powmod(modint x , ll n){ modint res = 1 ; while(n > 0){ if(n & 1) (res *= x); (x *= x); n >>= 1 ; } return res ; } int n; string S; int main(){ // fast_input_output cin >> n >> S; vector A(n); rep(i,n) A[i] = S[i] - '0'; modint res = 0; rrep(i,1,n+1){ vector> dp(n+1,vector(2,0)); vector> sp(n+1,vector(2,0)); dp[0][0] = 1; sp[0][0] = 1; rrep(j,1,n+1){ if(j-i>=0){ dp[j][1] += sp[j-1][1]; if(S[j-i] == '1'){ dp[j][1] += sp[j-i][0]; dp[j][0] += sp[j-1][0] - sp[j-i][0]; } else{ dp[j][0] += sp[j-1][0]; } } else{ dp[j][0] += sp[j-1][0]; } sp[j][1] = sp[j-1][1] + dp[j][1]; sp[j][0] = sp[j-1][0] + dp[j][0]; } res += dp[n][1] * powmod(2,i-1); } cout << res << endl; }