#ifdef INCLUDE_MAIN

struct Compare
{
  inline bool operator()( const bigint& n , const bigint& m ) { return n.a.d.size() < m.a.d.size(); }
};

const Compare compare{};

inline void Debug( ... ){}
// inline void Debug( const char& type , const string& s , const int& i_start , const int& i_final ){ cerr << "SyntaxAnalysis " << type << ": " << s.substr( i_start , i_final - i_start + 1 ) << endl; }
// inline void Debug( const char& type , const string& s , const int& i_start , const int& i_final , const bigint& n ){ cerr << "Evaluate " << type << ": " << s.substr( i_start , i_final - i_start + 1 ) << " == " << n << endl; }

bigint& Sum( list<bigint>& a )
{
  a.sort( compare );
  while( a.size() > 1 ){
    auto itr = a.begin();
    bigint temp0 = move( *itr );
    itr = a.erase( itr );
    bigint temp1 = move( *itr );
    itr = a.erase( itr );
    temp0 += temp1;
    a.merge( { move( temp0 ) } , compare );
  }
  return a.front();
}

bigint& Prod( list<bigint>& a )
{
  a.sort( compare );
  while( a.size() > 1 ){
    auto itr = a.begin();
    bigint temp0 = move( *itr );
    itr = a.erase( itr );
    bigint temp1 = move( *itr );
    itr = a.erase( itr );
    temp0 *= temp1;
    a.merge( { move( temp0 ) } , compare );
  }
  return a.front();
}

inline bool Digit( const char& c ) { return '0' <= c && c <= '9'; }
inline bigint Number( const string& s , const int& i_start , const int& i_final ) { return bigint( s.substr( i_start , i_final - i_start + 1 ) ); }

using Data = tuple<char,int,int,int,list<int>>;
CEXPR( char , expression , 'e' );
CEXPR( char , factor , 'f' );
CEXPR( char , number , 'n' );
CEXPR( char , term , 't' );

void SetMatchingParenthesis( const string& s , const int& n , vector<int>& syntax )
{
  CEXPR( int , not_searching , 0 );
  CEXPR( int , searching_num , 1 );
  CEXPR( int , searching_minus , 2 );
  int searching_mode = not_searching;
  list<int> parenthesis{};
  FOR( i , 0 , n ){
    if( s[i] == '(' ){
      assert( searching_mode == not_searching );
      parenthesis.push_back( i );
    } else if( s[i] == ')' ){
      assert( searching_mode == not_searching );
      syntax[syntax[i] = parenthesis.back()] = i;
      parenthesis.pop_back();
    } else if( Digit( s[i] ) ){
      if( searching_mode != searching_num ){
	parenthesis.push_back( i );
	searching_mode = searching_num;
      }
      if( i + 1 == n ? true : ! Digit( s[i+1] ) ){
	syntax[syntax[i] = parenthesis.back()] = i;
	parenthesis.pop_back();
	searching_mode = not_searching;
      }
    } else if( s[i] == '-' ){
      if( searching_mode != searching_minus ){
	parenthesis.push_back( i );
	searching_mode = searching_minus;
      }
      if( i + 1 == n ? true : s[i+1] != '-' ){
	syntax[syntax[i] = parenthesis.back()] = i;
	parenthesis.pop_back();
	searching_mode = not_searching;
      }
    }
  }
}

void Factor( const string& s , const int& i_start , const int& i_final , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , list<int>& child , int& val_num )
{
  child.push_back( val_num );
  int j = i_final;
  int i = syntax[i_final];
  if( i_start == i ){
    while( s[j] == ')' ? syntax[j] == i : false ){
      i++;
      j--;
    }
  }
  stack.push_back( { j == i_final ? number : expression , i , j , val_num , {} } );
  neg.push_back( false );
  val_num++;
}
void Term( const string& s , const int& i_start , const int& i_final , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , list<int>& child , int& val_num )
{
  int j = i_final;
  while( i_start <= j ){
    int i = syntax[j];
    bool temp = false;
    if( i_start < i ? s[i-1] == '-' : false ){
      temp = ( i - syntax[i-1] ) % 2 == 1;
      i = syntax[i-1];
    }
    child.push_back( val_num );
    stack.push_back( { factor , syntax[j] , j , val_num , {} } );
    neg.push_back( temp );
    j = i - 2;
    val_num++;
  }
}
void Expression( const string& s , const int& i_start , const int& i_final , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , list<int>& child , int& val_num )
{
  int j = i_final;
  while( i_start <= j ){
    if( s[j] == '+' ){
      j--;
      continue;
    }
    int i = syntax[j];
    while( i_start < i ){
      if( s[i-1] == '*' ){
	i = syntax[i-2];
      } else if( s[i-1] == '-' ){
	i = syntax[i-1];
      } else {
	break;
      }
    }
    child.push_back( val_num );
    stack.push_back( { term , i , j , val_num , {} } );
    neg.push_back( false );
    j = i - 1;
    val_num++;
  }
}

void SyntaxAnalysis( const string& s , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , int& val_num )
{
  AUTO_ITR( stack );
  while( itr_stack != end_stack ){
    auto& [type,i_start,i_final,self,child] = *itr_stack;
    if( type == expression ){
      Expression( s , i_start , i_final , syntax , stack , neg , child , val_num );
    } else if( type == term ){
      Term( s , i_start , i_final , syntax , stack , neg , child , val_num );
    } else if( type == factor ){
      Factor( s , i_start , i_final , syntax , stack , neg , child , val_num );
    }
    Debug( type , s , i_start , i_final );
    itr_stack++;
  }
}

void Evaluate( const string& s , const vector<int>& syntax , list<Data>& stack , vector<bool>& neg , vector<list<bigint>>& value )
{
  while( !stack.empty() ){
    auto& [type,i_start,i_final,self,child] = stack.back();
    if( type == expression ){
      list<bigint> a{};
      while( !child.empty() ){
	int& temp = child.back();
	bigint& prod = Prod( value[temp] );
	if( neg[temp] ){
	  prod.neg = !prod.neg;
	}
	a.push_back( move( prod ) );
	child.pop_back();
      }
      value[self] = { move( Sum( a ) ) };
    } else if( type == term ){
      while( !child.empty() ){
	int& temp = child.back();
	if( neg[temp] ){
	  neg[self] = !neg[self];
	}
	value[self].splice( value[self].begin() , move( value[temp] ) );
	child.pop_back();
      }
    } else if( type == factor ){
      assert( child.size() == 1 );
      value[self] = move( value[child.back()] );
    } else if( type == number ){
      assert( child.size() == 0 );
      value[self] = { move( Number( s , i_start , i_final ) ) };
    }
    Debug( type , s , i_start , i_final , value[self] );
    stack.pop_back();
  }
}

inline void Solve()
{
  CIN( int , N );
  CIN( string , S );
  vector<int> syntax( N );
  SetMatchingParenthesis( S , N , syntax );
  list<Data> stack{};
  vector<bool> neg{};
  int val_num = 0;
  stack.push_back( { expression , 0 , N - 1 , val_num , {} } );
  neg.push_back( false );
  val_num++;
  SyntaxAnalysis( S , syntax , stack , neg , val_num );
  abort();
  // vector<list<bigint>> value( val_num );
  // Evaluate( S , syntax , stack , neg , value );
  // RETURN( value[0].front() );
}
REPEAT_MAIN(1);

#else // INCLUDE_MAIN

#ifdef INCLUDE_SUB

template <typename PATH> list<PATH> E( const int& i )
{
  // list<PATH> answer{};
  list<PATH> answer = e<PATH>[i];
  // VVV 入力によらない処理は以下に挿入する。

  // AAA 入力によらない処理は以上に挿入する。
  return answer;
}

template <typename T> inline T F( const T& t ){ return f<T>[t]; }
template <typename T> inline T G( const int& i ){ return g<T>[i]; }

// COMPAREに使用。圧縮時は削除する。
ll Naive( int N , int M , int K )
{
  ll answer = N + M + K;
  return answer;
}

// COMPAREに使用。圧縮時は削除する。
ll Answer( ll N , ll M , ll K )
{
  // START_WATCH;
  ll answer = N + M + K;

  // // TLに準じる乱択や全探索。デフォルトの猶予は100.0[ms]。
  // CEXPR( double , TL , 2000.0 );
  // while( CHECK_WATCH( TL ) ){

  // }
  return answer;
}

// 圧縮時は中身だけ削除する。
inline void Experiment()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 0 , bound ){
  //   FOREQ( M , 0 , bound ){
  //     FOREQ( K , 0 , bound ){
  //   	COUT( N , M , K , ":" , Naive( N , M , K ) );
  //     }
  //   }
  //   // cout << Naive( N ) << ",\n"[N==bound];
  // }
}

// 圧縮時は中身だけ削除する。
inline void SmallTest()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 0 , bound ){
  //   FOREQ( M , 0 , bound ){
  //     FOREQ( K , 0 , bound ){
  //   	COMPARE( N , M , K );
  //     }
  //   }
  //   // COMPARE( N );
  // }
}

#define INCLUDE_MAIN
#include __FILE__

#else // INCLUDE_SUB

#ifdef INCLUDE_LIBRARY

/*

C-x 3 C-x o C-x C-fによるファイル操作用

BFS:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt

CoordinateCompress:
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt

DFSOnTree
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/a.hpp

Divisor:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt

Polynomial
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt

UnionFind
c:/Users/user/Documents/Programming/Utility/VLTree/UnionFindForest/compress.txt

*/

// VVV 常設でないライブラリは以下に挿入する。

// https://yukicoder.me/problems/no/2595
// で指定されたライブラリ
// https://github.com/SSRS-cp/yuki2595-bigint-lib
// を添付。
#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;
}
// AAA 常設でないライブラリは以上に挿入する。

#define INCLUDE_SUB
#include __FILE__

#else // INCLUDE_LIBRARY

// #define REACTIVE
// #define USE_GETLINE
#ifdef DEBUG
  #define _GLIBCXX_DEBUG
  #define REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode , use_getline ); if( exec_mode == sample_debug_mode || exec_mode == submission_debug_mode || exec_mode == library_search_mode ){ return 0; } else if( exec_mode == experiment_mode ){ Experiment(); return 0; } else if( exec_mode == small_test_mode ){ SmallTest(); return 0; }; DEXPR( int , bound_test_case_num , BOUND , min( BOUND , 100 ) ); int test_case_num = 1; if( exec_mode == solve_mode ){ if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); SET_LL( test_case_num ); } FINISH_MAIN
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
  #define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ SET_LL( A ); ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { assert( false ); }
  #define SOLVE_ONLY static_assert( __FUNCTION__[0] == 'S' )
  #define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl
  #define COUT( ... ) VariadicCout( cout << "出力： " , __VA_ARGS__ ) << endl
  #define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl
  #define COUT_A( A , N ) cout << "出力： "; OUTPUT_ARRAY( cout , A , N ) << endl
  #define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl
  #define COUT_ITR( A ) cout << "出力： "; OUTPUT_ITR( cout , A ) << endl
#else
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize ( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
  #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
  #define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
  #define SOLVE_ONLY 
  #define CERR( ... ) 
  #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
  #define CERR_A( A , N ) 
  #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL
  #define CERR_ITR( A ) 
  #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL
#endif
#ifdef REACTIVE
  #define ENDL endl
#else
  #define ENDL "\n"
#endif
#ifdef USE_GETLINE
  #define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); }
  #define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
  #define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#else
  #define SET_LL( A ) cin >> A
  #define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
  #define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; }
  #define CIN_A( LL , A , N ) vector<LL> A( N ); SET_A( A , N );
#endif
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using lld = __float128;
template <typename INT> using T2 = pair<INT,INT>;
template <typename INT> using T3 = tuple<INT,INT,INT>;
template <typename INT> using T4 = tuple<INT,INT,INT,INT>;
using path = pair<int,ll>;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define FINISH_MAIN REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } }
#define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now()
#define CURRENT_TIME static_cast<double>( chrono::duration_cast<chrono::microseconds>( chrono::system_clock::now() - watch ).count() / 1000.0 )
#define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 )
#define TYPE_OF( VAR ) decay_t<decltype( VAR )>
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )
#define FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR + 1 > FINAL ; VAR -- )
#define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end()
#define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES )
#define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS )
#define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS
#define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS
#define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); return
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ return; }

// 入出力用
template <class Traits> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); }
template <class Traits> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const vector<Arg>& arg ) { auto begin = arg.begin() , end = arg.end(); auto itr = begin; while( itr != end ){ ( itr == begin ? os : os << " " ) << *itr; itr++; } return os; }
template <class Traits , typename Arg> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg& arg ) { return os << arg; }
template <class Traits , typename Arg1 , typename Arg2 , typename... ARGS> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); }

// 算術用
template <typename T> constexpr T PositiveBaseResidue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
template <typename T> constexpr T Residue( const T& a , const T& p ){ return PositiveBaseResidue( a , p < 0 ? -p : p ); }
template <typename T> constexpr T PositiveBaseQuotient( const T& a , const T& p ){ return ( a - PositiveBaseResidue( a , p ) ) / p; }
template <typename T> constexpr T Quotient( const T& a , const T& p ){ return p < 0 ? PositiveBaseQuotient( -a , -p ) : PositiveBaseQuotient( a , p ); }

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  static_assert( ! is_same<TYPE_OF( ARGUMENT ),int>::value && ! is_same<TYPE_OF( ARGUMENT ),uint>::value ); \
  TYPE_OF( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT );	\
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;			\
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;	\
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO )		\
  ll ANSWER{ 1 };							\
  {									\
    ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( ARGUMENT ) % ( MODULO ) ) % ( MODULO ); \
    ARGUMENT_FOR_SQUARE_FOR_POWER < 0 ? ARGUMENT_FOR_SQUARE_FOR_POWER += ( MODULO ) : ARGUMENT_FOR_SQUARE_FOR_POWER; \
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CONSTEXPR_LENGTH , MODULO ) \
  ll ANSWER[CONSTEXPR_LENGTH];						\
  ll ANSWER_INV[CONSTEXPR_LENGTH];					\
  ll INVERSE[CONSTEXPR_LENGTH];						\
  {									\
    ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1;				\
    ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL;			\
    FOREQ( i , 1 , MAX_INDEX ){						\
      ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \
    }									\
    ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
    FOREQ( i , 2 , MAX_INDEX ){						\
      ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \
    }									\
  }									\

// 二分探索用
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CONST_TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CONST_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
  static_assert( ! is_same<TYPE_OF( CONST_TARGET ),uint>::value && ! is_same<TYPE_OF( CONST_TARGET ),ull>::value ); \
  ll ANSWER = MINIMUM;							\
  {									\
  ll L_BS = MINIMUM;							\
  ll U_BS = MAXIMUM;							\
  ANSWER = UPDATE_ANSWER;						\
  ll EXPRESSION_BS;							\
  const ll CONST_TARGET_BS = ( CONST_TARGET );				\
  ll DIFFERENCE_BS;							\
  while( L_BS < U_BS ){							\
    DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CONST_TARGET_BS; \
    CERR( "二分探索中：" , "L_BS =" , L_BS , "<=" , ANSWER , "<=" , U_BS , "= U_BS :" , #EXPRESSION , "-" , #CONST_TARGET , "=" , EXPRESSION_BS , "-" , CONST_TARGET_BS , "=" , DIFFERENCE_BS ); \
    if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){				\
      U_BS = UPDATE_U;							\
    } else {								\
      L_BS = UPDATE_L;							\
    }									\
    ANSWER = UPDATE_ANSWER;						\
  }									\
  if( L_BS > U_BS ){							\
    CERR( "二分探索失敗：" , "L_BS =" , L_BS , ">" , U_BS , "= U_BS :" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1  ); \
    CERR( "二分探索マクロにミスがある可能性があります。変更前の版に戻してください。" );	\
    ANSWER = MAXIMUM + 1;						\
  } else {								\
    CERR( "二分探索終了：" , "L_BS =" , L_BS , "<=" , ANSWER , "<=" , U_BS , "= U_BS" ); \
    CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \
    CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" );	\
    EXPRESSION_BS = ( EXPRESSION );					\
    CERR( "二分探索結果：" , #EXPRESSION , "=" , EXPRESSION_BS , ( EXPRESSION_BS > CONST_TARGET_BS ? ">" : EXPRESSION_BS < CONST_TARGET_BS ? "<" : "=" ) , CONST_TARGET_BS ); \
    if( EXPRESSION_BS DESIRED_INEQUALITY CONST_TARGET_BS ){		\
      CERR( "二分探索成功：" , #ANSWER , ":=" , ANSWER );		\
    } else {								\
      CERR( "二分探索失敗：" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \
      CERR( "単調でないか、単調増加性と単調減少性を逆にしてしまったか、探索範囲内に解が存在しません。" ); \
      ANSWER = MAXIMUM + 1;						\
    }									\
  }									\
  }									\

// 単調増加の時にEXPRESSION >= CONST_TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET )	\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CONST_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) \

// 単調増加の時にEXPRESSION <= CONST_TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET )	\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CONST_TARGET , > , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) \

// 単調減少の時にEXPRESSION >= CONST_TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET )	\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CONST_TARGET , < , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) \

// 単調減少の時にEXPRESSION <= CONST_TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CONST_TARGET )	\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CONST_TARGET , <= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) \

// t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLeq( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLt( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGeq( set<T>& S , const T& t ) { return S.lower_bound( t ); }
// tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGt( set<T>& S , const T& t ) { return S.upper_bound( t ); }

// データ構造用
template <typename T> inline T Add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T XorAdd( const T& t0 , const T& t1 ){ return t0 ^ t1; }
template <typename T> inline T Multiply( const T& t0 , const T& t1 ) { return t0 * t1; }
template <typename T> inline const T& Zero() { static const T z = 0; return z; }
template <typename T> inline const T& One() { static const T o = 1; return o; }\
template <typename T> inline T AddInv( const T& t ) { return -t; }
template <typename T> inline T Id( const T& v ) { return v; }
template <typename T> inline T Min( const T& a , const T& b ){ return a < b ? a : b; }
template <typename T> inline T Max( const T& a , const T& b ){ return a < b ? b : a; }

// グリッド問題用
int H , W , H_minus , W_minus , HW;
vector<vector<bool> > non_wall;
inline T2<int> EnumHW( const int& v ) { return { v / W , v % W }; }
inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; }
const string direction[4] = {"U","R","D","L"};
// (i,j)->(k,h)の方向番号を取得
inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return i<k?2:i>k?0:j<h?1:j>h?3:(assert(false),-1);}
// v->wの方向番号を取得
inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);}
// 方向番号の反転U<->D、R<->L
inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back(v);}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back(v);}if(j>0){e[EnumHW_inv(i,j-1)].push_back(v);}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back(v);}}}}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<path> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){const int v=EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back({v,1});}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back({v,1});}if(j>0){e[EnumHW_inv(i,j-1)].push_back({v,1});}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back({v,1});}}}}
inline void SetWallOnGrid( const string& Si , const int& i , vector<vector<bool> >& non_wall , const char& walkable = '.'  , const char& unwalkable = '#' ){non_wall.push_back(vector<bool>(W));auto& non_wall_i=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]==unwalkable),false);}}

// グラフ用
template <typename PATH> vector<list<PATH> > e;
template <typename T> map<T,T> f;
template <typename T> vector<T> g;

// デバッグ用
#ifdef DEBUG
  inline void AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); }
  void AutoCheck( int& exec_mode , const bool& use_getline );
  inline void Solve();
  inline void Experiment();
  inline void SmallTest();
  inline void RandomTest();
  ll GetRand( const ll& Rand_min , const ll& Rand_max );
  int exec_mode;
  CEXPR( int , solve_mode , 0 );
  CEXPR( int , sample_debug_mode , 1 );
  CEXPR( int , submission_debug_mode , 2 );
  CEXPR( int , library_search_mode , 3 );
  CEXPR( int , experiment_mode , 4 );
  CEXPR( int , small_test_mode , 5 );
  CEXPR( int , random_test_mode , 6 );
  #ifdef USE_GETLINE
    CEXPR( bool , use_getline , true );
  #else
    CEXPR( bool , use_getline , false );
  #endif
#else
  ll GetRand( const ll& Rand_min , const ll& Rand_max ) { ll answer = time( NULL ); return answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; }
#endif

// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#define IN inline
#define CL class
#define PU public
#define OP operator
#define CE constexpr
#define CO const
#define NE noexcept
#define RE return 
#define WH while
#define VO void
#define VE vector
#define LI list
#define BE begin
#define EN end
#define SZ size
#define MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&

// VVV 常設ライブラリは以下に挿入する。

// AAA 常設ライブラリは以上に挿入する。

#define INCLUDE_LIBRARY
#include __FILE__

#endif // INCLUDE_LIBRARY

#endif // INCLUDE_SUB

#endif // INCLUDE_MAIN