#include <vector>
#include <string>
#include <atcoder/convolution>
const int DIGIT = 6;
const int BASE = 1000000;
struct positive_bigint{
  std::vector<int> d;
  positive_bigint(){
  }
  positive_bigint(long long X){
    while (X > 0){
      d.push_back(X % BASE);
      X /= BASE;
    }
  }
  positive_bigint(std::string S){
    if (S == "0"){
      S = "";
    }
    int L = S.size();
    d.resize((L + DIGIT - 1) / DIGIT, 0);
    for (int i = L - 1; i >= 0; i -= 6){
      for (int j = std::max(i - 5, 0); j <= i; j++){
        d[i / DIGIT] *= 10;
        d[i / DIGIT] += S[j] - '0';
      }
    }
    std::reverse(d.begin(), d.end());
  }
  bool empty() const {
    return d.empty();
  }
  int size() const {
    return d.size();
  }
  int& operator [](int i){
    return d[i];
  }
  int operator [](int i) const {
    return d[i];
  }
};
std::string to_string(const positive_bigint &A){
  int N = A.size();
  std::string ans;
  for (int i = N - 1; i >= 0; i--){
    std::string tmp = std::to_string(A[i]);
    if (i < N - 1){
      ans += std::string(DIGIT - tmp.size(), '0');
    }
    ans += tmp;
  }
  if (ans.empty()){
    ans = "0";
  }
  return ans;
}
std::istream& operator >>(std::istream &is, positive_bigint &A){
  std::string S;
  is >> S;
  A = positive_bigint(S);
  return is;
}
std::ostream& operator <<(std::ostream &os, positive_bigint &A){
  os << to_string(A);
  return os;
}
int cmp(const positive_bigint &A, const positive_bigint &B){
  int N = A.size();
  int M = B.size();
  if (N < M){
    return -1;
  } else if (N > M){
    return 1;
  } else {
    for (int i = N - 1; i >= 0; i--){
      if (A[i] < B[i]){
        return -1;
      }
      if (A[i] > B[i]){
        return 1;
      }
    }
    return 0;
  }
}
bool operator ==(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) == 0;
}
bool operator !=(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) != 0;
}
bool operator <(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) < 0;
}
bool operator >(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) > 0;
}
bool operator <=(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) <= 0;
}
bool operator >=(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) >= 0;
}
positive_bigint& operator +=(positive_bigint &A, const positive_bigint &B){
  int N = A.size();
  int M = B.size();
  while (N < M){
    A.d.push_back(0);
    N++;
  }
  for (int i = 0; i < M; i++){
    A[i] += B[i];
  }
  for (int i = 0; i < N - 1; i++){
    if (A[i] >= BASE){
      A[i] -= BASE;
      A[i + 1]++;
    }
  }
  if (N > 0){
    if (A[N - 1] >= BASE){
      A.d.push_back(1);
      A[N - 1] -= BASE;
    }
  }
  return A;
}
positive_bigint operator +(const positive_bigint &A, const positive_bigint &B){
  positive_bigint A2 = A;
  A2 += B;
  return A2;
}
positive_bigint& operator -=(positive_bigint &A, const positive_bigint &B){
  int N = A.size();
  int M = B.size();
  for (int i = 0; i < M; i++){
    A[i] -= B[i];
  }
  for (int i = 0; i < N - 1; i++){
    if (A[i] < 0){
      A[i] += BASE;
      A[i + 1]--;
    }
  }
  while (!A.empty()){
    if (A.d.back() == 0){
      A.d.pop_back();
    } else {
      break;
    }
  }
  return A;
}
positive_bigint operator -(const positive_bigint &A, const positive_bigint &B){
  positive_bigint A2 = A;
  A2 -= B;
  return A2;
}
positive_bigint operator *(const positive_bigint &A, const positive_bigint &B){
  if (A.empty() || B.empty()){
    return 0;
  }
  int N = A.size();
  int M = B.size();
  std::vector<long long> a(N);
  for (int i=  0; i < N; i++){
    a[i] = A[i];
  }
  std::vector<long long> b(M);
  for (int i = 0; i < M; i++){
    b[i] = B[i];
  }
  std::vector<long long> C = atcoder::convolution_ll(a, b);
  for (int i = 0; i < N + M - 2; i++){
    C[i + 1] += C[i] / BASE;
    C[i] %= BASE;
  }
  if (C[N + M - 2] >= BASE){
    C.resize(N + M);
    C[N + M - 1] += C[N + M - 2] / BASE;
    C[N + M - 2] %= BASE;
  }
  positive_bigint ans;
  ans.d.resize(C.size());
  for (int i = 0; i < C.size(); i++){
    ans[i] = C[i];
  }
  return ans;
}
positive_bigint operator *=(positive_bigint &A, const positive_bigint &B){
  A = A * B;
  return A;
}
struct bigint{
  bool neg = false;
  positive_bigint a;
  bigint(){
  }
  bigint(long long X): neg(X < 0), a(abs(X)){
  }
  bigint(const positive_bigint &X, bool neg = false): neg(neg), a(X){
  }
  bigint(const std::string &s){
    if (!s.empty()){
      if (s[0] == '-'){
        neg = true;
        a = positive_bigint(s.substr(1, s.size() - 1));
      } else {
        a = positive_bigint(s);
      }
    }
  }
  bool empty() const {
    return a.empty();
  }
  int size() const {
    return a.size();
  }
  int& operator [](int i){
    return a[i];
  }
};
std::string to_string(const bigint &A){
  std::string ans;
  if (A.neg){
    ans += '-';
  }
  ans += to_string(A.a);
  return ans;
}
std::istream& operator >>(std::istream &is, bigint &A){
  std::string S;
  is >> S;
  if (S != "0"){
    A = bigint(S);
  }
  return is;
}
std::ostream& operator <<(std::ostream &os, bigint A){
  os << to_string(A);
  return os;
}
positive_bigint abs(const bigint &A){
  return A.a;
}
int cmp(const bigint &A, const bigint &B){
  if (!A.neg){
    if (!B.neg){
      return cmp(A.a, B.a);
    } else {
      return 1;
    }
  } else {
    if (!B.neg){
      return -1;
    } else {
      return cmp(B.a, A.a);
    }
  }
}
bool operator ==(const bigint &A, const bigint &B){
  return cmp(A, B) == 0;
}
bool operator !=(const bigint &A, const bigint &B){
  return cmp(A, B) != 0;
}
bool operator <(const bigint &A, const bigint &B){
  return cmp(A, B) < 0;
}
bool operator >(const bigint &A, const bigint &B){
  return cmp(A, B) > 0;
}
bool operator <=(const bigint &A, const bigint &B){
  return cmp(A, B) <= 0;
}
bool operator >=(const bigint &A, const bigint &B){
  return cmp(A, B) >= 0;
}
bigint operator +(const bigint &A){
  return A;
}
bigint operator -(const bigint &A){
  bigint A2 = A;
  if (!A2.empty()){
    A2.neg = !A2.neg;
  }
  return A2;
}
bigint& operator +=(bigint &A, const bigint &B){
  if (A.neg == B.neg){
    A.a += B.a;
  } else {
    int c = cmp(A.a, B.a);
    if (c > 0){
      A.a -= B.a;
    } else if (c < 0){
      A.a = B.a - A.a;
      A.neg = !A.neg;
    } else {
      A = 0;
    }
  }
  return A;
}
bigint operator +(const bigint &A, const bigint &B){
  bigint A2 = A;
  A2 += B;
  return A2;
}
bigint& operator -=(bigint &A, const bigint &B){
  if (A.neg != B.neg){
    A.a += B.a;
  } else {
    int c = cmp(A.a, B.a);
    if (c > 0){
      A.a -= B.a;
    } else if (c < 0){
      A.a = B.a - A.a;
      A.neg = !A.neg;
    } else {
      A = 0;
    }
  }
  return A;
}
bigint operator -(const bigint &A, const bigint &B){
  bigint A2 = A;
  A2 -= B;
  return A2;
}
bigint operator *=(bigint &A, const bigint &B){
  if (A.empty() || B.empty()){
    A = 0;
  } else {
    if (B.neg){
      A.neg = !A.neg;
    }
    A.a *= B.a;
  }
  return A;
}
bigint operator *(const bigint &A, const bigint &B){
  bigint A2 = A;
  A2 *= B;
  return A2;
}

#if 0
__END__
#endif
#include<bits/stdc++.h>
#define fr(i,n) for(int i=0;i<(n);++i)
#define foor(i,a,b) for(int i=(a);i<=(b);++i)
#define rf(i,n) for(int i=(n);i-->0;)
#define roof(i,b,a) for(int i=(b);i>=(a);--i)
#define elsif else if
#define all(x) x.begin(),x.end()
#define Sort(x) sort(all(x))
#define Reverse(x) reverse(all(x))
#define Rev(x) reverse(all(x))
#define Uniq(v) v.erase(unique(all(v)),v.end())
#define PQ priority_queue
#define NP(x) next_permutation(all(x))
#define M_PI 3.14159265358979323846
#define popcount __builtin_popcountll
using namespace std;         using  vb=vector<bool>;using vvb=vector<vb>;
                             using   vi=vector<int>;using vvi=vector<vi>;using vvvi=vector<vvi>;
using  ll=long long;         using   vl=vector< ll>;using vvl=vector<vl>;using vvvl=vector<vvl>;
using ull=unsigned long long;using   vu=vector<ull>;using vvu=vector<vu>;
using dbl=double;            using   vd=vector<dbl>;using vvd=vector<vd>;using vvvd=vector<vvd>;
using str=string;            using   vs=vector<str>;using vvs=vector<vs>;
using pii=pair<int,int>;     using vpii=vector<pii>;using mii=map<int,int>;
using pll=pair< ll, ll>;     using vpll=vector<pll>;using mll=map< ll, ll>;
using pdd=pair<dbl,dbl>;     using vpdd=vector<pdd>;using mdd=map<dbl,dbl>;
using pss=pair<str,str>;     using vpss=vector<pss>;using mss=map<str,str>;
using pil=pair<int, ll>;     using vpil=vector<pil>;using mil=map<int, ll>;
using pli=pair< ll,int>;     using vpli=vector<pli>;using mli=map< ll,int>;
using pdi=pair<dbl,int>;     using vpdi=vector<pdi>;using mdi=map<dbl,int>;
template<typename T>vector<T>&operator<<(vector<T>&v,const T t){v.push_back(t);return v;}
template<typename T>multiset<T>&operator<<(multiset<T>&m,const T t){m.insert(t);return m;}
template<typename T>set<T>&operator<<(set<T>&s,const T t){s.insert(t);return s;}
template<typename T>stack<T>&operator<<(stack<T>&s,const T t){s.push(t);return s;}
template<typename T>stack<T>&operator>>(stack<T>&s,T&t){t=s.top();s.pop();return s;}
template<typename T>queue<T>&operator<<(queue<T>&q,const T t){q.push(t);return q;}
template<typename T>queue<T>&operator>>(queue<T>&q,T&t){t=q.front();q.pop();return q;}
template<typename T,typename U>PQ<T,vector<T>,U>&operator<<(PQ<T,vector<T>,U>&q,const T t){q.push(t);return q;}
template<typename T,typename U>PQ<T,vector<T>,U>&operator>>(PQ<T,vector<T>,U>&q,T&t){t=q.top();q.pop();return q;}
template<typename T,typename U>istream&operator>>(istream&s,pair<T,U>&p){return s>>p.first>>p.second;}
istream&operator>>(istream&s,_Bit_reference b){int a;s>>a;assert(a==0||a==1);b=a;return s;}
template<typename T>istream&operator>>(istream&s,vector<T>&v){fr(i,v.size()){s>>v[i];}return s;}
template<typename T,typename U>ostream&operator<<(ostream&s,const pair<T,U>p){return s<<p.first<<" "<<p.second;}
template<typename T>ostream&operator<<(ostream&s,const vector<T>v){fr(i,v.size()){i?s<<" "<<v[i]:s<<v[i];}return s;}
template<typename T>ostream&operator<<(ostream&s,const deque<T>d){fr(i,d.size()){i?s<<" "<<d[i]:s<<d[i];}return s;}
template<typename T>_Bit_reference operator&=(_Bit_reference b,T t){return b=b&t;}
template<typename T>_Bit_reference operator^=(_Bit_reference b,T t){return b=b^t;}
template<typename T>_Bit_reference operator|=(_Bit_reference b,T t){return b=b|t;}
template<typename T,typename U>pair<T,U>operator+(pair<T,U>a,pair<T,U>b){return {a.first+b.first,a.second+b.second};}
template<typename T,typename U>pair<T,U>operator-(pair<T,U>a,pair<T,U>b){return {a.first-b.first,a.second-b.second};}
template<typename T,typename U>pair<T,U>&operator+=(pair<T,U>&a,pair<T,U>b){return a=a+b;}
template<typename T,typename U>pair<T,U>&operator-=(pair<T,U>&a,pair<T,U>b){return a=a-b;}
void print(void){cout<<"\n";}
void Print(void){cout<<endl;}
template<typename T>void print(T t){cout<<t<<"\n";}
template<typename T>void Print(T t){cout<<t<<endl;}
template<typename T,typename...U>void print(T&&t,U&&...u){cout<<t<<" ";print(forward<U>(u)...);}
template<typename T,typename...U>void Print(T&&t,U&&...u){cout<<t<<" ";Print(forward<U>(u)...);}
bool YN(bool b){print(b?"YES":"NO");return b;}bool PI(bool b){print(b?"POSSIBLE":"IMPOSSIBLE");return b;}
bool Yn(bool b){print(b?"Yes":"No");return b;}bool Pi(bool b){print(b?"Possible":"Impossible");return b;}
bool yn(bool b){print(b?"yes":"no");return b;}bool pi(bool b){print(b?"possible":"impossible");return b;}
const int e5=1e5;
const int e9=1e9;
const int MD=1e9+7;
const int md=998244353;
const ll e18=1e18;
template<typename T>str to_string(const T&n){ostringstream s;s<<n;return s.str();}
template<typename T>bool chmax(T&a,T b){return a<b?(a=b,true):false;}
template<typename T>bool chmin(T&a,T b){return a>b?(a=b,true):false;}
template<typename T,typename U>vector<pair<T,U>>dijkstra(const vector<vector<pair<T,U>>>&E,const U s,const T inf){using P=pair<T,U>;vector<P>d;fr(i,E.size()){d<<P{inf,i};}PQ<P,vector<P>,greater<P>>pq;pq<<(d[s]=P{0,s});while(pq.size()){P a=pq.top();pq.pop();U v=a.second;if(d[v].first>=a.first){for(P e:E[v]){if(d[v].first+e.first<d[e.second].first){d[e.second]=P{d[v].first+e.first,v};pq<<P{d[v].first+e.first,e.second};}}}}return d;}
//template<typename T,typename U>map<U,pair<T,U>>dijkstra(map<U,vector<pair<T,U>>>E,const U s,const T inf){using P=pair<T,U>;map<U,P>d;for(pair<U,vector<P>>e:E){d[e.first]=P{inf,e.first};}PQ<P,vector<P>,greater<P>>pq;pq<<(d[s]=P{0,s});while(pq.size()){P a=pq.top();pq.pop();U v=a.second;if(d[v].first>=a.first){for(P e:E[v]){if(d[v].first+e.first<d[e.second].first){d[e.second]=P{d[v].first+e.first,v};pq<<P{d[v].first+e.first,e.second};}}}}return d;}
//ll maxflow(vector<mil>&E,int s,int t){ll z=0;vi b(E.size(),-1);for(int i=0;;++i){static auto dfs=[&](int v,ll f,auto&dfs)->ll{if(v==t)return f;b[v]=i;for(auto&p:E[v]){if(b[p.first]<i&&p.second){if(ll r=dfs(p.first,min(f,p.second),dfs)){p.second-=r;E[p.first][v]+=r;return r;}}}return 0;};ll x=dfs(s,ll(1e18),dfs);z+=x;if(x==0)return z;}}
template<typename T>T distsq(pair<T,T>a,pair<T,T>b){return (a.first-b.first)*(a.first-b.first)+(a.second-b.second)*(a.second-b.second);}
template<typename T>T max(const vector<T>a){assert(a.size());T m=a[0];for(T e:a){m=max(m,e);}return m;}
template<typename T>T min(const vector<T>a){assert(a.size());T m=a[0];for(T e:a){m=min(m,e);}return m;}
template<typename T>T gcd(const T a,const T b){return a?gcd(b%a,a):b;}
template<typename T>T gcd(const vector<T>a){T g=a[0];for(T e:a){g=gcd(g,e);}return g;}
//template<typename T>vector<T>LCS(vector<T>A,vector<T>B){int N=A.size(),M=B.size();vector<vector<pair<int,pii>>>d(N+1,vector<pair<int,pii>>(M+1));fr(i,N){fr(j,M){if(A[i]==B[j]){d[i+1][j+1]={d[i][j].first+1,{i,j}};}else{d[i+1][j+1]=max(d[i][j+1],d[i+1][j]);}}}vector<T>r;for(pii p={N,M};d[p.first][p.second].first;p=d[p.first][p.second].second){r<<A[d[p.first][p.second].second.first];}Reverse(r);return r;}
//str LCS(str S,str T){vector<char>s=LCS(vector<char>(S.begin(),S.end()),vector<char>(T.begin(),T.end()));return str(s.begin(),s.end());}
//template<typename T>vector<pair<T,T>>ConvexHull(vector<pair<T,T>>V){if(V.size()<=3){return V;}Sort(V);rf(i,V.size()-1)V<<V[i];vector<pair<T,T>>r;for(pair<T,T>p:V){int s=r.size();while(s>=2&&(p.second-r[s-1].second)*(p.first-r[s-2].first)<(p.second-r[s-2].second)*(p.first-r[s-1].first)){r.pop_back();--s;}r<<p;}r.pop_back();return r;}
class UnionFind{vi p,s;void extend(int N){foor(i,p.size(),N){p<<i;s<<1;}}public:UnionFind(void){}UnionFind(int N){extend(N-1);}int find(int i){extend(i);return p[i]=p[i]==i?i:find(p[i]);}void unite(int a,int b){extend(a);extend(b);if((a=find(a))!=(b=find(b))){if(s[a]>s[b]){swap(a,b);}s[b]+=s[a];p[a]=b;}}void unite(pii p){return unite(p.first,p.second);}bool same(int a,int b){extend(a);extend(b);return find(a)==find(b);}bool same(pii p){return same(p.first,p.second);}int size(int x){extend(x);return s[find(x)];}};
//ll MST(vector<pair<ll,pii>>&E){Sort(E);UnionFind uf;ll z=0;for(auto&e:E){if(!uf.same(e.second)){z+=e.first;uf.unite(e.second);}}return z;}
//ll strmod(const str&s,const int m){ll x=0;fr(i,s.size()){x=(x*10+s[i]-48)%m;}return x;}
vvl mul(const vvl&A,const vvl&B,const int m){vvl C;fr(y,A.size()){C<<vl(B[y].size());}fr(y,C.size()){fr(x,C[y].size()){fr(i,A[0].size()){(C[y][x]+=A[y][i]*B[i][x])%=m;}}}return C;}
vvl pow(const vvl&A,const ll n,const int m){vvl B;fr(y,A.size()){B<<vl(A.size());}if(n==0){fr(i,B.size()){B[i][i]=1;}}elsif(n%2){B=mul(A,pow(A,n-1,m),m);}else{vvl C=pow(A,n/2,m);B=mul(C,C,m);}return B;}
ll pow(const ll a,const ll n,const int m){ll t;return n?(n&1?a>=0?a%m:(m-(-a%m))%m:1)*(t=pow(a,n>>1,m),t*t%m)%m:1;}
ll inv(const ll x,const int p){assert(x!=0);return pow(x,p-2,p);}
//ll inv(const ll x){return inv(x,MD);}
vpll fact(const int n,const int p){assert(n<p);vpll v(n+1);v[0].first=1;foor(i,1,n){v[i].first=v[i-1].first*i%p;}v[n].second=inv(v[n].first,p);roof(i,n,1){v[i-1].second=v[i].second*i%p;}return v;}
class Combination{const vpll f;const int M;public:Combination(int n,int m):f(fact(n,m)),M(m){}ll P(int n,int k){return n<0||k<0||n<k?0ll:f[n].first*f[n-k].second%M;}ll C(int n,int k){return k<0||n<k?0ll:P(n,k)*f[k].second%M;}ll H(int n,int k){return n==0&&k==0?1ll:C(n+k-1,k);}ll F(int n){return n<0?0:f[n].first;}};
ll C2(const int n){return(ll)n*~-n/2;}
ll sum(const vi a){ll s=0;for(int e:a){s+=e;}return s;}
ll sum(const vl a){ll s=0;for(ll e:a){s+=e;}return s;}
ll sum(const vb a){ll s=0;for(bool e:a){s+=e;}return s;}
template<typename T>int MSB(T N){int r=-1;for(;N>0;N/=2){++r;}return r;}
template<typename T>class SegmentTree{vector<T>S;T(*const op)(T a,T b);const T zero;const int B;public:SegmentTree(int N,T(*f)(T a,T b),const T zero):S(1<<MSB(N-1)+2,zero),op(f),zero(zero),B(1<<MSB(N-1)+1){}SegmentTree(vector<T>v,T(*f)(T a,T b),const T zero):SegmentTree(v.size(),f,zero){fr(i,v.size()){S[S.size()/2+i]=v[i];}roof(i,S.size()/2-1,1){S[i]=op(S[i*2],S[i*2+1]);}}T calc(int l,int r){l+=B;r+=B;if(l>r){return zero;}if(l==r){return S[l];}T L=S[l],R=S[r];for(;l/2<r/2;l/=2,r/=2){if(l%2==0){L=op(L,S[l+1]);}if(r%2==1){R=op(S[r-1],R);}}return op(L,R);}void replace(int i,T x){for(S[i+=B]=x;i!=1;i/=2){if(i%2){S[i/2]=op(S[i-1],S[i]);}else{S[i/2]=op(S[i],S[i+1]);}}}void add(int i,T x){replace(i,op(S[B+i],x));}T top(){return S[1];}T get(int i){return S[i+B];}};
//ll BITsum(vl&B,int i){ll z=0;while(i>0){z+=B[i];i-=i&-i;}return z;}
//void BITadd(vl&B,int i,ll x){while(i<B.size()){B[i]+=x;i+=i&-i;}}
ll fib(const ll n,const int m){ll a,b,c,d,A,B,C,D;a=1;b=0;c=0;d=1;rf(i,63){A=a*a+b*c;B=a*b+b*d;C=c*a+d*c;D=c*b+d*d;if(n>>i&1){a=A;b=B;c=C;d=D;A=a+b;B=a;C=c+d;D=c;}a=A%m;b=B%m;c=C%m;d=D%m;}return b;}
vi primes(int n){vb b(n+1);vi p;foor(i,2,n){if(!b[i]){p<<i;for(int j=2*i;j<=n;j+=i){b[j]=true;}}}return p;}
//vl primes(ll L,ll R){assert(0<=L);assert(L<=R);int n=sqrt(R);vb b(n+1,true),B(R-L+1,true);for(ll i=2;i<=n;++i){if(b[i]){for(ll j=i+i;j<=n;j+=i){b[j]=false;}for(ll j=R/i*i;j>=max(L,i+i);j-=i){B[j-L]=false;}}}vl P;for(ll i=max(2ll,L);i<=R;++i){if(B[i-L]){P<<i;}}return P;}
vb isprime(const int n){vb v(n+1,true);v[0]=v[1]=false;foor(i,2,n){if(v[i]){for(int j=2*i;j<=n;j+=i){v[j]=false;}}}return v;}
struct LCA{vvi par;vi dep;LCA(vvi&E,int root):par(MSB(E.size())+1,vi(E.size())),dep(E.size()){function<void(int,int)>dfs=[&](int i,int p){for(int j:E[i])if(j!=p){par[0][j]=i;dep[j]=dep[i]+1;dfs(j,i);}};par[0][root]=root;dfs(root,root);fr(i,par.size()-1){fr(j,par[0].size()){par[i+1][j]=par[i][par[i][j]];}}}int operator()(int a,int b){if(dep[a]>dep[b])swap(a,b);for(int t=dep[b]-dep[a],i=0;t;t>>=1,++i){if(t&1){b=par[i][b];}}if(a==b)return a;rf(i,par.size()){if(par[i][a]!=par[i][b]){a=par[i][a];b=par[i][b];}}return par[0][a];}int dist(int a,int b){return dep[a]+dep[b]-2*dep[operator()(a,b)];}};
vpli factor(ll N){vpli r;for(ll i=2;i*i<=N;++i){if(N%i==0){r<<pli{i,0};while(N%i==0){N/=i;++r.back().second;}}}if(N>1){r<<pli{N,1};}return r;}
vl divisors(ll n){vl r;ll m=sqrt(n);foor(i,1,m)if(n%i==0)r<<ll(i);rf(i,r.size()-(m*m==n))r<<n/r[i];return r;}
//vi SuffixArray(str S){int N=S.size();vi rank(N+1),tmp(N+1),sa(N+1);fr(i,N){sa[i]=i;rank[i]=S[i];}sa[N]=N;rank[N]=-1;int k;auto cmp=[&](int&a,int&b)->bool{if(rank[a]!=rank[b])return rank[a]<rank[b];return (a+k<=N?rank[a+k]:-1)<(b+k<=N?rank[b+k]:-1);};for(k=1;k<=N;k*=2){sort(all(sa),cmp);tmp[sa[0]]=0;foor(i,1,N){tmp[sa[i]]=tmp[sa[i-1]]+cmp(sa[i-1],sa[i]);}rank=tmp;}return sa;};
template<typename T,typename U>void sort2(vector<T>&a,vector<U>&b){int N=a.size();assert(b.size()==N);vector<pair<T,U>>v;fr(i,N){v<<pair<T,U>{a[i],b[i]};}Sort(v);fr(i,N){a[i]=v[i].first;b[i]=v[i].second;}}
template<typename T,typename U,typename V>void sort3(vector<T>&a,vector<U>&b,vector<V>&c){int N=a.size();assert(b.size()==N);assert(c.size()==N);vector<pair<T,pair<U,V>>>v;fr(i,N){v.push_back({a[i],{b[i],c[i]}});}Sort(v);fr(i,N){a[i]=v[i].first;b[i]=v[i].second.first;c[i]=v[i].second.second;}}
vi toposo(vvi E){int N=E.size();vi T(N,-1);{vvi R(N);vi v;{vb u(N);function<void(int)>f=[&](int i){if(u[i])return;u[i]=true;for(int j:E[i]){R[j]<<i;f(j);}v<<i;};fr(i,N){f(i);}}{int k=0;function<void(int)>f=[&](int i){T[i]=k;for(int j:R[i]){if(T[j]==-1){f(j);}}};rf(i,v.size()){if(T[v[i]]==-1){f(v[i]);++k;}}}}return T;}
vb SAT2(vvi E){int N=E.size();assert(N%2==0);vi T=toposo(E);vb z(N);fr(i,N/2){if(T[2*i]==T[2*i+1]){return vb{};}z[2*i+(T[2*i]<T[2*i+1])]=true;}return z;}
//ll extgcd(ll a,ll b,ll&x,ll&y){if(b==0){x=1;y=0;return a;}ll d=extgcd(b,a%b,y,x);y-=a/b*x;return d;}
//ll INV(ll a,ll m){ll x,y;extgcd(a,m,x,y);return (x%m+m)%m;}
//ll garner(int m1,int a1,int m2,int a2){if(a1>a2){swap(a1,a2);swap(m1,m2);}return INV(m1,m2)*(a2-a1)%m2*m1+a1;}
//ull mulull(ull a,ull b,ull m){using ld=long double;ll t=a*b-m*ull(ld(a)*ld(b)/ld(m));return t+m*(t<0)-m*(t>=ll(m));}
//ll powll(const ll a,const ll n,const ll m){return n?n%2?mulull(a,powll(a,n-1,m),m):powll(mulull(a,a,m),n/2,m):1;}
//bool MillerRabin(int n){if(n<2){return false;}int d=n-1,s=0;for(;d%2==0;d/=2){++s;}if(s==0){return n==2;}for(int a:{2,7,61})if(a<n){if(pow(a,d,n)!=1){fr(r,s){if(pow(a,d<<r,n)==n-1)break;if(r==s-1)return false;}}}return true;}
//bool MillerRabin(ll n){if(n<1ll<<31){return MillerRabin(int(n));}if(n<2){return false;}ll d=n-1;int s=0;for(;d%2==0;d/=2){++s;}if(s==0){return n==2;}for(int a:{2,325,9375,28178,450775,9780504,1795265022})if(a<n){if(powll(a,d,n)!=1){fr(r,s){if(powll(a,d<<r,n)==n-1)break;if(r==s-1)return false;}}}return true;}
//class Prime{vi P,mf;public:Prime(int N):mf(N+1){foor(i,2,N){if(mf[i]==0){mf[i]=i;P<<i;}for(int j=0;j<P.size()&&i*P[j]<=N&&P[j]<=mf[i];++j){mf[i*P[j]]=P[j];}}}vi list(void){return P;}bool isprime(int x){assert(x<int(mf.size()));return x>=2&&mf[x]==x;}int minfactor(int x){assert(x>=2);assert(x<int(mf.size()));return mf[x];}vpii factor(int x){assert(x>=1);assert(x<int(mf.size()));vpii v;while(x>1){if(v.empty()||v.back().first<mf[x]){v<<pii{mf[x],1};}else{++v.back().second;}x=x/mf[x];}return v;}vi divisors(int x){assert(x>=1);assert(x<int(mf.size()));vi v={1};for(pii p:factor(x)){int n=v.size();fr(i,n){int t=v[i];fr(_,p.second){t*=p.first;v<<t;}}}Sort(v);return v;}};
//int TonelliShanks(const int p,const int a){assert(0<=a&&a<p);if(p==2||a==0)return a;if(pow(a,(p-1)/2,p)!=1)return -1;if(p%4==3)return pow(a,(p+1)/4,p);random_device rand;int q=p-1,m=0;for(;q%2==0;q/=2){++m;}int z;do{z=rand()%p;}while(pow(z,(p-1)/2,p)!=p-1);int c=pow(z,q,p),t=pow(a,q,p),r=pow(a,(q+1)/2,p);for(;m>1;--m){if(pow(t,1<<m-2,p)==1){c=ll(c)*c%p;}else{r=ll(c)*r%p;c=ll(c)*c%p;t=ll(c)*t%p;}}return r;}
vi BFS(vvi&E,int s){vi d(E.size(),-1);d[s]=0;queue<int>q;q<<s;while(q.size()){int i;q>>i;for(int j:E[i]){if(d[j]<0){d[j]=d[i]+1;q<<j;}}}return d;}
//template<typename T>vector<T>slidemax(const vector<T>&v,int k){assert(1<=k&&k<=int(v.size()));--k;vector<T>d(v.size()-k);deque<int>q;fr(j,k){while(q.size()&&v[q.back()]<=v[j]){q.pop_back();}q.push_back(j);}fr(j,v.size()-k){while(q.size()&&v[q.back()]<=v[j+k]){q.pop_back();}q.push_back(j+k);d[j]=v[q.front()];if(q.front()==j){q.pop_front();}}return d;}

int main(){cin.tie(0);ios::sync_with_stdio(false);
	int N;cin>>N;
	str S;cin>>S;
	S="(("s+S+")"s;
	N=S.size();
	vector<pair<bigint,bigint>>v;
	str t;
	fr(i,N){
		char c=S[i];
		char l=i-1>=0?S[i-1]:'(';
		char r=i+1<N?S[i+1]:')';
		if(c=='('){
			v.emplace_back(0,1);
		}elsif(c==')'){
			assert(v.size()>=2);
			v[v.size()-2].second*=v.back().first+v.back().second;
			v.pop_back();
			if(r=='+'||r=='-'){
				v.back().first+=v.back().second;
				v.back().second=1;
			}
		}elsif(c=='-'){
			v.back().second*=-1;
		}elsif('0'<=c&&c<='9'){
			if('0'<=l&&l<='9'){
				t+=c;
			}else{
				t=str(1,c);
			}
			if(!('0'<=r&&r<='9')){
				v.back().second*=t;
			}
			if(r=='+'||r=='-'){
				v.back().first+=v.back().second;
				v.back().second=1;
			}
		}
	}
	assert(v.size()==1);
	print(v[0].second);
	return 0;
}

#if 0
#endif