#define CP_BUNDLED_SOURCE #ifdef TEMPLATE #else #define TEMPLATE # pragma GCC optimize("O3") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #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 uint=unsigned; using ll=long long; using ull=unsigned long long; using ld=long double; using pii=pair; using pll=pair; using i128=__int128; using u128=unsigned __int128; templateusing vc=vector; templateusing vvc=vc>; templateusing vvvc=vvc>; templateusing smpq=priority_queue,greater>; templateusing bipq=priority_queue; #define rep(i,n) for(ll i=0;i<(ll)(n);i++) #define REP(i,j,n) for(ll i=(j);i<(ll)(n);i++) #define DREP(i,n,m) for(ll i=(n);i>=(m);i--) #define drep(i,n) for(ll i=((n)-1);i>=0;i--) #define rall(x) x.rbegin(),x.rend() #define mp(...) make_pair(__VA_ARGS__) #define pb push_back #define fi first #define se second #define is insert #define bg begin() #define ed end() #define all(x) x.begin(),x.end() void scan(int&a) { cin >> a; } void scan(ll&a) { cin >> a; } void scan(string&a) { cin >> a; } void scan(char&a) { cin >> a; } void scan(uint&a) { cin >> a; } void scan(ull&a) { cin >> a; } void scan(bool&a) { cin >> a; } void scan(ld&a){ cin>> a;} template void scan(vector&a) { for(auto&x:a) scan(x); } void read() {} template void read(Head&head, Tail&... tail) { scan(head); read(tail...); } #define INT(...) int __VA_ARGS__; read(__VA_ARGS__); #define LL(...) ll __VA_ARGS__; read(__VA_ARGS__); #define ULL(...) ull __VA_ARGS__; read(__VA_ARGS__); #define STR(...) string __VA_ARGS__; read(__VA_ARGS__); #define VC(type, name, ...) vector name(__VA_ARGS__); read(name); #define VVC(type, name, size, ...) vector> name(size, vector(__VA_ARGS__)); read(name); templatevoid print(T a) { cout << a; } template void print(vectora) { for(int i=0;i<(int)a.size();i++){if(i)cout<<" ";print(a[i]);}cout< void PRT(T a) { print(a); cout < void PRT(Head head, Tail ... tail) { print(head); cout << " "; PRT(tail...); return; } template bool chmin(T &x, F y){ if(x>y){ x=y; return true; } return false; } template bool chmax(T &x, F y){ if(x T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } void YesNo(bool b){ cout<<(b?"Yes":"No")<stovi(const string&s,const string&S){ vcv(s.size()); rep(i,s.size()){ auto t=S.find(s[i]); assert(t!=string::npos); v[i]=t; } return v; } template T isqrt(T x){ T F=sqrtl(x); while((F+1)*(F+1)<=x)F++; while(F*F>x)F--; return F; } template vvctrans(const vvc&a){ assert(a.size()&&a[0].size()); vvcb(a[0].size(),vc(a.size())); rep(i,a.size())rep(j,a[0].size()){ b[j][i]=a[i][j]; } return b; } template vctrans(const vc&a){ assert(a.size()&&a[0].size()); vcb(a[0].size(),string(a.size(),0)); rep(i,a.size())rep(j,a[0].size()){ b[j][i]=a[i][j]; } return b; } template int popcount(T n){ return __builtin_popcountll(n); } template L sum(vc&a){ return accumulate(all(a),L(0)); } template vcsubset(T S){ vcans; for(T x=S;x>0;x=(x-1)&S)ans.pb(x); ans.pb(0); return ans; } template T max(vc&a){ return *max_element(all(a)); } template T min(vc&a){ return *min_element(all(a)); } #ifndef COMPRESSER_STRUCT #define COMPRESSER_STRUCT template struct compresser{ vcx; compresser(int n=0){x.reserve(n);} compresser(const vc&xs){ x=xs; } void push(T p){built=false;x.pb(p);} bool built=false; void build(){ if(!chmax(built,1))return; sort(all(x)); x.erase(unique(all(x)),x.end()); } int find(T v){ build(); auto itr=lower_bound(all(x),v)-x.begin(); if(itr==x.size()||x[itr]!=v)return -1; return itr; } int find_next(T v){ build(); return lower_bound(all(x),v)-x.begin(); } int size(){ build(); return x.size(); } T operator[](int i)const{ assert(0<=i&&i vc presum(vc &a){ vc ret(a.size()+1); rep(i,a.size())ret[i+1]=ret[i]+a[i]; return ret; } template vc &operator+=(vc &a,F b){ for (auto&v:a)v += b; return a; } template vc &operator-=(vc&a,F b){ for (auto&v:a)v-=b; return a; } template vc &operator*=(vc&a,F b){ for (auto&v:a)v*=b; return a; } template constexpr T pow(T a,T b){ T res=1; while(b){ if(b&1)res*=a; a*=a; b/=2; } return res; } constexpr ll ten(ll a){ return pow(10,a); } templateconstexpr T inf=numeric_limits::max()/2-1; template int tbit(T x){ using U=make_unsigned_t; U y=(U)x; return y?(int)bit_width(y)-1:-1; } template int lbit(T x){ using U=make_unsigned_t; U y=(U)x; return y?(int)countr_zero(y):-1; } template int tbit(T x,int p){ using U=make_unsigned_t; constexpr int W=numeric_limits::digits; U y=(U)x; if(p<0)return -1; if(p>=W-1)return tbit(y); return tbit(y&((U(1)<<(p+1))-1)); } template int lbit(T x,int p){ using U=make_unsigned_t; constexpr int W=numeric_limits::digits; U y=(U)x; if(p<0)return lbit(y); if(p>=W)return -1; return lbit(y&(~U(0)<>(istream&is,i128&x){ string s;is>>s; x=0; int i=0,neg=0; if(s[0]=='-')neg=1,i=1; for(;i<(int)s.size();i++)x=x*10+s[i]-'0'; if(neg)x=-x; return is; } ostream& operator<<(ostream&os,i128 x){ if(x==0)return os<<0; if(x<0)os<<"-"; u128 y=x<0?-(u128)x:(u128)x; string s; while(y)s.pb('0'+y%10),y/=10; reverse(all(s)); return os<sync_with_stdio(0); #ifdef LOCAL cout<0); mod=mod_; m=(i128(1)<<64)/mod; } unsigned reduce(uint64_t x){ assert(mod>0); x-=(((i128)x*m)>>64)*mod; return x struct dynamic_modint{ using u32=uint32_t; using u64=uint64_t; u32 val; dynamic_modint():val(0){} dynamic_modint(ll x){ ll v=x%get_mod(); if(v<0)v+=get_mod(); val=v; } static dynamic_modint raw(int v){ assert(v>=0); dynamic_modint mi; mi.val=v; return mi; } dynamic_modint &operator+=(const dynamic_modint&m){ if((val+=m.val)>=get_mod())val-=get_mod(); return *this; } dynamic_modint &operator-=(const dynamic_modint&m){ if((val+=(get_mod()-m.val))>=get_mod())val-=get_mod(); return *this; } dynamic_modint &operator*=(const dynamic_modint&m){ val=rem(u64(val)*m.val); return *this; } dynamic_modint &operator/=(const dynamic_modint&m){ val=rem(u64(val)*m.inv().val); return *this; } dynamic_modint operator-() const{ return dynamic_modint(val?get_mod()-val:0); } dynamic_modint operator+() const { return *this; } friend dynamic_modint operator+(dynamic_modint lhs, const dynamic_modint& rhs){ return lhs+=rhs; } friend dynamic_modint operator-(dynamic_modint lhs, const dynamic_modint& rhs){ return lhs-=rhs; } friend dynamic_modint operator*(dynamic_modint lhs, const dynamic_modint& rhs){ return lhs*=rhs; } friend dynamic_modint operator/(dynamic_modint lhs,const dynamic_modint&rhs){ return lhs/=rhs; } bool operator==(const dynamic_modint&p) const{ return p.val==val; } bool operator!=(const dynamic_modint&p) const{ return p.val!=val; } dynamic_modint pow(int64_t n) const{ dynamic_modint res(1),mul(val); while(n){ if(n%2)res*=mul; mul*=mul; n/=2; } return res; } friend ostream&operator<<(ostream&os,const dynamic_modint&p){ os<>(istream&is,dynamic_modint&p){ int64_t x; is>>x; p=dynamic_modint(x); return is; } dynamic_modint inv()const{ int64_t a=val,b=get_mod(),u=1,v=0,t; #ifdef LOCAL assert(gcd(a,b)==1); #endif while(b>0){ t=a/b; swap(a-=t*b,b); swap(u-=t*v,v); } return dynamic_modint(u); } inline static u32 rem(u64 x){return barrett_reduction().reduce(x);} static inline int &get_mod(){ static int mod=0; return mod; } static void set_mod(int md){ assert(0 struct binom_has_get_mod:false_type{}; template struct binom_has_get_mod>:true_type{}; template struct binom{ private: static vector&fact_table(){static vectorv={1};return v;} static vector&invfact_table(){static vectorv={1};return v;} static vector&invs_table(){static vectorv={0};return v;} static int&built_mod(){static int mod=-1;return mod;} public: static void build(int n){ auto&_fact=fact_table(); auto&_invfact=invfact_table(); auto&_invs=invs_table(); if constexpr(binom_has_get_mod::value){ auto mod=mint::get_mod(); if(built_mod()!=mod){ _fact={1}; _invfact={1}; _invs={0}; built_mod()=mod; } } if(n<(int)_fact.size())return; int old=_fact.size(); _fact.resize(n+1); _invfact.resize(n+1); _invs.resize(n+1); if constexpr(binom_has_get_mod::value){ auto mod=mint::get_mod(); for(int i=old;i<=n;i++){ _fact[i]=_fact[i-1]*i; if(i==1)_invs[i]=1; else _invs[i]=-_invs[mod%i]*(mod/i); _invfact[i]=_invfact[i-1]*_invs[i]; } }else{ for(int i=old;i<=n;i++){ _fact[i]=_fact[i-1]*i; _invs[i]=mint(1)/i; _invfact[i]=_invfact[i-1]*_invs[i]; } } } static mint fact(int i){ assert(i>=0); build(i); return fact_table()[i]; } static mint invfact(int i){ assert(i>=0); build(i); return invfact_table()[i]; } static mint inv(int i){ assert(i>0); build(i); return invs_table()[i]; } static mint C(int a,int b){//aCb if(b==0)return 1; if(a<0||b<0||a-b<0)return mint(0); build(a); auto&_fact=fact_table(); auto&_invfact=invfact_table(); return _fact[a]*_invfact[b]*_invfact[a-b]; } static mint iC(int a,int b){//1/aCb if(a<0||b<0||a-b<0)return mint(0); build(a); auto&_fact=fact_table(); auto&_invfact=invfact_table(); return _fact[b]*_fact[a-b]*_invfact[a]; } static mint P(int a,int b){ if(a T extgcd(T a, T b, T &x, T &y) { T d = a; if(b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } template pair inv(T x,T m){ T a1,a2; T res=extgcd(x,m,a1,a2); T md=m/res; a1=(a1%md+md)%md; return {a1,md}; } template pair mod_solve(T a,T b,T m){//return x s.t. ax=b mod m a%=m,b%=m;if(a<0)a+=m;if(b<0)b+=m; T g=gcd(gcd(a,b),m); a/=g,b/=g,m/=g; if(gcd(a,m)>1)return {-1,-1}; return {(inv(a,m).first*b)%m,inv(a,m).second}; } //x^2 ≡ b (mod p) ll mod_sqrt(ll b,ll p){ static mt19937 mt(random_device{}()); b%=p;if(b<0)b+=p; if(b==0)return 0; if(p==2){ return b; } assert(p>=3); using mint=dynamic_modint<20260801>;mint::set_mod(p); if(mint(b).pow((p-1)/2)==-1){ return -1; } if(p%4==3){ return mint(b).pow((p+1)/4).val; } ll t=[&](){ ll w; while(1){ ll t=mt()%p; w=t*t-b; if(mint(w).pow((p-1)/2)==mint(-1)){ return t; } } assert(0); }(); mint w=mint(t*t-b); using T=pair; auto ml=[&](T a,T b)->T{ return T{a.first*b.first+a.second*b.second*w,a.second*b.first+a.first*b.second}; }; ll e=(p+1)/2; T ans={1,0}; T gy={t,1}; while(e){ if(e%2)ans=ml(ans,gy); gy=ml(gy,gy); e/=2; } return ans.first.val; } template struct static_modint{ static_assert(0=0); static_modint mi; mi.val=v; return mi; } static_modint &operator+=(const static_modint&m){ if((val+=m.val)>=mod)val-=mod; return *this; } static_modint &operator-=(const static_modint&m){ if((val+=(mod-m.val))>=mod)val-=mod; return *this; } static_modint &operator*=(const static_modint&m){ val=u64(val)*m.val%mod; return *this; } static_modint &operator/=(const static_modint&m){ val=u64(val)*m.inv().val%mod; return *this; } static_modint operator-() const{ return static_modint(mod-val); } static_modint operator+() const { return *this; } friend static_modint operator+(static_modint lhs, const static_modint& rhs){ return lhs+=rhs; } friend static_modint operator-(static_modint lhs, const static_modint& rhs){ return lhs-=rhs; } friend static_modint operator*(static_modint lhs, const static_modint& rhs){ return lhs*=rhs; } friend static_modint operator/(static_modint lhs,const static_modint&rhs){ return lhs/=rhs; } bool operator==(const static_modint&p) const{ return p.val==val; } bool operator!=(const static_modint&p) const{ return p.val!=val; } static_modint pow(int64_t n) const{ static_modint res(1),mul(val); while(n){ if(n%2)res*=mul; mul*=mul; n/=2; } return res; } friend ostream&operator<<(ostream&os,const static_modint&p){ os<>(istream&is,static_modint&p){ int64_t x; is>>x; p=static_modint(x); return is; } static_modint inv()const{ int64_t a=val,b=mod,u=1,v=0,t; #ifdef LOCAL assert(gcd(a,b)==1); #endif while(b>0){ t=a/b; swap(a-=t*b,b); swap(u-=t*v,v); } return static_modint(u); } }; using mint=static_modint<998244353>; using B=binom; void solve(){ INT(n); STR(s); if(s[1]==')'){ PRT(mint(2).pow(n/2)); }else{ mint ans=0; rep(k,n/2+1)ans+=B::C(n/2,k)*B::C(n/2,k); PRT(ans); } } signed main(){ int t=1; // cin >> t; while(t--)solve(); }