//#define _GLIBCXX_DEBUG

//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

#include<bits/stdc++.h>
using namespace std;


#ifdef LOCAL
#include <debug_print.hpp>
#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define OUT(...) (static_cast<void>(0))
#endif

#define endl '\n'
#define lfs cout<<fixed<<setprecision(15)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T> using PQ = priority_queue<T>;
template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};  
template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};
template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};
template<typename T>void debug(const vector<T>&v){debug(v,v.size());}
template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}
template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}
template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}
template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}
template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}
template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << "(" << p.first << "," << p.second << ")";}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; return os;}
template<typename T>void rearrange(vector<int>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
template<typename T> vector<int> ascend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i)<make_pair(v[j],j);});
  return ord;
}
template<typename T> vector<int> descend(const vector<T>&v){
  vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);
  sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);});
  return ord;
}
template<typename T> vector<T> inv_perm(const vector<T>&ord){
  vector<T>inv(ord.size());
  for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
  return inv;
}
ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}
ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}
ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}
ll modulo(ll n,ll d){return (n%d+d)%d;};
template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}
template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}
template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};
template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};
template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};
template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};
ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}
ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}
ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
  std::ostream::sentry s(dest);
  if (s) {
    __uint128_t tmp = value < 0 ? -value : value;
    char buffer[128];
    char *d = std::end(buffer);
    do {
      --d;
      *d = "0123456789"[tmp % 10];
      tmp /= 10;
    } while (tmp != 0);
    if (value < 0) {
      --d;
      *d = '-';
    }
    int len = std::end(buffer) - d;
    if (dest.rdbuf()->sputn(d, len) != len) {
      dest.setstate(std::ios_base::badbit);
    }
  }
  return dest;
}
namespace converter{
  int dict[500];
  const string lower="abcdefghijklmnopqrstuvwxyz";
  const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
  const string digit="0123456789";
  const string digit1="123456789";
  void regi_str(const string &t){
    for(int i=0;i<t.size();i++){
      dict[t[i]]=i;
    }
  }
  void regi_int(const string &t){
    for(int i=0;i<t.size();i++){
      dict[i]=t[i];
    }
  }
  vector<int>to_int(const string &s,const string &t){
    regi_str(t);
    vector<int>ret(s.size());
    for(int i=0;i<s.size();i++){
      ret[i]=dict[s[i]];
    }
    return ret;
  }
  vector<int>to_int(const string &s){
    auto t=s;
    sort(t.begin(),t.end());
    t.erase(unique(t.begin(),t.end()),t.end());
    return to_int(s,t);
  }
  
  vector<vector<int>>to_int(const vector<string>&s,const string &t){
    regi_str(t);
    vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));
    for(int i=0;i<s.size();i++){
      for(int j=0;j<s[0].size();j++){
        ret[i][j]=dict[s[i][j]];
      }
    }
    return ret;
  }
  vector<vector<int>>to_int(const vector<string>&s){
    string t;
    for(int i=0;i<s.size();i++){
      t+=s[i];
    }
    sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());
    return to_int(s,t);
  }
  string to_str(const vector<int>&s,const string &t){
    regi_int(t);
    string ret;
    for(auto z:s)ret+=dict[z];
    return ret;
  }
  vector<string> to_str(const vector<vector<int>>&s,const string &t){
    regi_int(t);
    vector<string>ret(s.size());
    for(int i=0;i<s.size();i++){
      for(auto z:s[i])ret[i]+=dict[z];
    }
    return ret;
  }
}
template< typename T = int >
struct edge {
  int to;
  T cost;
  int id;
  edge():to(-1),id(-1){};
  edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}
  operator int() const { return to; }
};

template<typename T>
using Graph = vector<vector<edge<T>>>;
template<typename T>
Graph<T>revgraph(const Graph<T> &g){
  Graph<T>ret(g.size());
  for(int i=0;i<g.size();i++){
    for(auto e:g[i]){
      int to = e.to;
      e.to = i;
      ret[to].push_back(e);
    }
  }
  return ret;
}
template<typename T>
Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){
  Graph<T> ret(n);
  for(int es = 0; es < m; es++){
    int u,v;
    T w=1;
    cin>>u>>v;u-=indexed,v-=indexed;
    if(weighted)cin>>w;
    ret[u].emplace_back(v,w,es);
    if(!directed)ret[v].emplace_back(u,w,es);
  }
  return ret;
}
template<typename T>
Graph<T> readParent(int n,int indexed=1,bool directed=true){
  Graph<T>ret(n);
  for(int i=1;i<n;i++){
    int p;cin>>p;
    p-=indexed;
    ret[p].emplace_back(i);
    if(!directed)ret[i].emplace_back(p);
  }
  return ret;
}
template<typename T>
struct HLD{
  using D=long long;
  int n;
  vector<int>sz;//部分木サイズ
  vector<D>dep;
  vector<int>par;
  vector<int>head;
  Graph<T> &g;//隣接リスト
  vector<edge<T>>edges;//データ構造に乗せるedge列
  vector<int>in,out;//[in,out)で部分木、[ina,inb]でa~bのパス(aが上)
  vector<int>comp;//連結成分の根
  //inは頂点のindexを表す。また、edge列の下側の頂点である
  HLD(Graph<T> &g,int r=-1):g(g),n(g.size()){
    hld_build(r);
  }
  void hld_build(int root = -1){
    in.assign(n,-1);out.assign(n,-1);dep.assign(n,0);
    par.assign(n,-1);head.assign(n,-1);sz.assign(n,-1);comp.assign(n,-1);
    edges.assign(n,edge<T>());
    if(root == -1){//根がどこでも良い場合(森でも可)
      for(int i=0;i<n;i++){
        if(sz[i] == -1){
          head[i] = i;
          dfs_sz(i, 0, i);
          dfs_hld(i);
        }
      }
    }
    else{
      head[root] = root;
      dfs_sz(root, 0, root);
      dfs_hld(root);
    }
  }
  void dfs_sz(int k, D d,int r){
    sz[k] = 1;
    comp[k] = r;
	dep[k] = d;
    for(auto &e: g[k]){
      if(e.to == par[k])continue;
      par[e.to] = k;
      dfs_sz(e.to, d+e.cost, r);
      sz[k] += sz[e.to];
      if(g[k][0].to==par[k]||sz[e.to] > sz[g[k][0].to])swap(e, g[k][0]);
    }
  }
  int time = 0;
  void dfs_hld(int k){
    in[k] = time++;
    for(auto e:g[k]){
      if(e.to == par[k])continue;
      head[e.to] = (e.to == g[k][0].to ? head[k]: e.to);
      edges[time] = e;
      dfs_hld(e.to);
    }
    out[k] = time;
  }
  int lca(int p,int q){
    while(1){
      if(in[p] < in[q])swap(p,q);
      if(head[p] == head[q])return q;
      p = par[head[p]];
    }
  }
  vector<pair<int,int>>query_path(int p,int q,bool isEdge){
    int r=lca(p,q);
    vector<pair<int,int>>ret;
    for(int i=0;i<2;i++){
      if(i == 1)swap(p,q);
      while(1){
        if(isEdge&&p==r)break;
        if(head[p]==head[r]){
          ret.emplace_back(in[r]+(isEdge?1:i),in[p]+1);
          break;
        }
        ret.emplace_back(in[head[p]],in[p]+1);
        p = par[head[p]];
      }
    }
    return ret;
  }
  vector<vector<pair<int,int>>>query_order_path(int p,int q,bool isEdge){
	//非可換クエリ用、配列0を順番を反転したデータ構造に、配列1を通常のデータ構造に
    vector<vector<pair<int,int>>>ret(2);
    int r=lca(p,q);
    for(int i=0;i<2;i++){
      if(i == 1)swap(p,q);
      while(1){
        if(isEdge&&p==r)break;
        if(head[p]==head[r]){
          if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[r]+(isEdge?1:i)));
          else ret[i].emplace_back(in[r]+(isEdge?1:i),in[p]+1);
          break;
        }
        if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[head[p]]));
        else ret[i].emplace_back(in[head[p]],in[p]+1);
        p = par[head[p]];
      }
    }
    reverse(ret[1].begin(), ret[1].end());
    return ret;
  }
  pair<int,int>query_subtree(int p,bool isEdge){
    return make_pair(in[p]+isEdge,out[p]);
  }
  //uのv方向の子 子孫関係は前もって確認すること(in,outを見る)
  int child(int u,int v)const{
    while(1){
      if(head[u]==head[v]){
        v=g[u][0].to;
        break;
      }
      v=head[v];
      if(par[v]==u)break;
      v=par[v];
    }
    return v;
  }
  //uをv方向に一つ進めた頂点
  int move(int u,int v)const{
    assert(u!=v);
    if(in[u]<in[v]&&in[v]<out[u])return child(u,v);
    else return par[u];
  }
  D dist(int u,int v){
    return dep[u]+dep[v]-2*dep[lca(u,v)];
  }
  vector<int>rev_in;
  int climb(int u,int k){
    if(rev_in.empty()){
      rev_in.resize(n);
      for(int i=0;i<n;i++)rev_in[in[i]]=i;
    }
    int nd=max<int>(dep[u]-k, 0);
    while(dep[u]>nd){
      if(dep[head[u]]>nd){
        u=par[head[u]];
      }
      else{
        u=rev_in[in[head[u]]+nd-dep[head[u]]];
      }
    }
    return u;
  }
  int jump(int from,int to, int k){
    int r = lca(from, to);
    int d1 = dep[from] - dep[r];
    int d2 = dep[to] - dep[r];
    if(d1 + d2 < k)return -1;
    else if(k <= d1)return climb(from, k);
    else return climb(to, d1 + d2 - k); 
  }
  template<typename I>
  Graph<T>lca_tree(vector<I>&v){
    auto compare=[&](int x,int y){return in[x]<in[y];};
    sort(v.begin(),v.end(),compare);
    int sz1=v.size();
    for(int i=0;i<sz1-1;i++)v.push_back(lca(v[i],v[i+1]));
    sort(v.begin(),v.end(),compare);
    v.erase(unique(v.begin(),v.end()),v.end());
    int sz2=v.size();
    Graph<T>ret(sz2);
    stack<int>st;
    for(int i=0;i<sz2;i++){
      while(!st.empty()&&out[v[st.top()]]<=in[v[i]])st.pop();
      if(!st.empty()){
        ret[st.top()].emplace_back(i,dep[v[i]]-dep[v[st.top()]]);
        ret[i].emplace_back(st.top(),dep[v[i]]-dep[v[st.top()]]);
      }
      st.push(i);
    }
    return ret;
  }
};
const int VERTEX = 0;
const int HEAVY_LIGHT = -1;
const int LIGHT = -2;
const int HEAVY = -3;
template<typename T>
struct StaticToptree{
  const HLD<T> &hld;
  int count;
  int root;
  vector<int>l,r,p;
  vector<int>aff;
  T edge_identity;
  StaticToptree(const HLD<T> &hld):hld(hld),edge_identity(edge_identity),count(hld.n),l(hld.n*2,-1),r(hld.n*2,-1),p(hld.n*2,-1),aff(hld.n*2,VERTEX){
    int hld_root=min_element(hld.in.begin(),hld.in.end())-hld.in.begin();
    OUT(hld_root);
    root = dfs(hld_root,-1).second;
  }
  //sz,vid
  pair<int,int>dfs(int v,int par){
    int sub=0;
    vector<int>vs;
    vector<int>sz;
    int now=v,pre=par;
    while(1){
      int sum_sz=1;
      //vid,eid
      priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
      for(int i=1;i<hld.g[now].size();i++){
        if(hld.g[now][i].to==pre)continue;
        auto [sz, vid] = dfs(hld.g[now][i].to, now);
        pq.emplace(sz,vid);
        sum_sz+=sz;
      }
      sub+=sum_sz;
      while(pq.size()>=2){
        auto [sx,x]=pq.top();pq.pop();
        auto [sy,y]=pq.top();pq.pop();
        int nv=count++;
        aff[nv]=LIGHT;
        l[nv]=x;
        p[x]=nv;
        r[nv]=y;
        p[y]=nv;
        pq.emplace(sx+sy,nv);
      }
      int last=now;
      if(!pq.empty()){
        auto [sx,x]=pq.top();pq.pop();
        int nv=count++;
        aff[nv]=HEAVY_LIGHT;
        l[nv]=now;
        p[x]=nv;
        r[nv]=x;
        p[now]=nv;
        last=nv;
      }
      vs.push_back(last);
      sz.push_back(sum_sz);
      if(hld.g[now].empty()||hld.g[now][0]==pre)break;
      pre=now;
      now=hld.g[now][0];
    }
    vector<int>csz(sz.size()+1);
    for(int i=0;i<sz.size();i++){
      csz[i+1]=csz[i]+sz[i];
    }
    auto rec=[&](auto &&rec,int ls,int rs)->int{
      {}
      if(ls+1==rs){
        return vs[ls];
      }
      int sum=csz[rs]-csz[ls];
      int lv=-1,rv=-1;
      if(sz[ls]*2>=sum){
        lv=rec(rec,ls,ls+1);
        rv=rec(rec,ls+1,rs);
      }
      else if(sz[rs-1]*2>=sum){
        lv=rec(rec,ls,rs-1);
        rv=rec(rec,rs-1,rs);
      }
      else{
        int ri=min<int>(rs-1,lower_bound(csz.begin(),csz.end(),csz[ls]+(sum+1)/2)-csz.begin());
        int li=max(ls+1,ri-1);
        if(abs((csz[li]-csz[ls])*2-sum)<abs((csz[ri]-csz[ls])*2-sum)){
          ri=li;
        }
        lv=rec(rec,ls,ri);
        rv=rec(rec,ri,rs);
      }
      int nv=count++;
      aff[nv]=HEAVY;
      l[nv]=lv,p[lv]=nv;
      r[nv]=rv,p[rv]=nv;
      return nv;
    };
    int last=rec(rec,0,sz.size());
    return make_pair(sub,last);
  }
};
#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;
}
vector<string>val;
Graph<int>tree;

using State = string::iterator;
template<typename T>
struct Parsing{
  Parsing(){};
  T solve(string &s){
    State itr = s.begin();
    return expr(itr);
  }
  T expr(State &itr){
    T now = term(itr);
    while(1){
      if(*itr == '+' || *itr == '-'){
        char sig=*itr;
        T nxt = term(++itr);
        int idx=tree.size();
        tree.EB();
        tree[idx].EB(now);
        tree[idx].EB(nxt);
        val.PB(string(1,sig));
        now=idx;
      }
      else break;
    }
    return now;
  }
  T term(State &itr){
    T now = fact(itr);
    while(1){
      if(*itr == '*'){
        T nxt = fact(++itr);
        int idx = tree.size();
        tree.emplace_back();
        tree[idx].emplace_back(now);
        tree[idx].emplace_back(nxt);
        val.PB("*");
        now=idx;
      }
      else break;
    }
    return now;
  }
  T fact(State &itr){
    if(*itr=='-'||isdigit(*itr))return number(itr);
    assert(*itr == '(');
    itr++;
    T val = expr(itr);
    assert(*itr == ')');
    itr++;
    return val;
  }
  T number(State &itr){
    string num;
    while(*itr=='-'){
      num += *itr;
      itr++;
    }
    while(isdigit(*itr)){
      num += *itr;
      itr++;
    }
    int idx=tree.size();
    tree.emplace_back();
    val.push_back(num);
    return idx;
  }
};
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n;cin>>n;
  string s;cin>>s;
  Parsing<int>parse;
  int root=parse.solve(s);
  auto pre_tree=tree;
  HLD hld(tree,root);
  StaticToptree st(hld);
  OUT(tree,val);
  OUT(root);
  auto dfs=[&](auto &&f,int k)->pair<bigint,bigint> {
    {}
    auto af=st.aff[k];
    if(af==VERTEX){
      if(val[k]=="+"||val[k]=="-"||val[k]=="*")return MP(-1,-1);
      else return MP(1,val[k]);
    }
    auto lf=f(f,st.l[k]);
    auto rf=f(f,st.r[k]);
    OUT(k,lf,rf,st.l[k],st.r[k]);
    if(af==LIGHT){
      assert(false);
    }
    if(af==HEAVY_LIGHT){
      if(val[st.l[k]]=="+"){
        return MP(1,rf.se);
      }
      else if(val[st.l[k]]=="-"){
        int rr=st.l[k];
        if(pre_tree[rr][0]==tree[rr][0])return MP(1,-rf.se);
        else return MP(-1,rf.se);
      }
      else{
        assert(val[st.l[k]]=="*");
        return MP(rf.se,0);
      }
    }
    if(af==HEAVY){
      return MP(lf.fi*rf.fi,lf.fi*rf.se+lf.se);
    }
  };
  auto ret=dfs(dfs,st.root);
  cout<<ret.se<<endl;
  return 0;
}